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Diffstat (limited to '1445')
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diff --git a/1445/CH1/EX1.1/Ex1_1.sce b/1445/CH1/EX1.1/Ex1_1.sce new file mode 100644 index 000000000..35c637d9c --- /dev/null +++ b/1445/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,15 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 1 + +disp("CHAPTER 1"); +disp("EXAMPLE 1"); + +//VARIABLE INITIALIZATION +b=14; //number of branches +n=8; //number of nodes + +//SOLUTION +m=b-n+1; //number of loop equations +disp(sprintf("The total number of independent loop equations are %d",m)); + +//END diff --git a/1445/CH1/EX1.10/Ex1_10.sce b/1445/CH1/EX1.10/Ex1_10.sce new file mode 100644 index 000000000..4bd8f0826 --- /dev/null +++ b/1445/CH1/EX1.10/Ex1_10.sce @@ -0,0 +1,21 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 10 + +disp("CHAPTER 1"); +disp("EXAMPLE 10"); + +//VARIABLE INITIALIZATION +v=10; //voltage source in Volts +I=5; //current source in Amperes +r1=2; //in Ohms +r2=2; //in Ohms +r3=4; //in Ohms + +//SOLUTION +res=I+(v/r1); +v1=res/((1/r1)+(1/r2)+(1/r3)); +I1=v1/r3; +disp(sprintf("By Nodal analysis, the current through resistor R3 is %d A",I1)); + +//END + diff --git a/1445/CH1/EX1.11/Ex1_11.sce b/1445/CH1/EX1.11/Ex1_11.sce new file mode 100644 index 000000000..f78a7b4a2 --- /dev/null +++ b/1445/CH1/EX1.11/Ex1_11.sce @@ -0,0 +1,25 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 11 + +disp("CHAPTER 1"); +disp("EXAMPLE 11"); + +//VARIABLE INITIALIZATION +I3=-5; //direction of I3 is opposite to the current which flows from the current source + +//SOLUTION + +//using mesh analysis, the following equations are obtained +//(4)I1+(-2)I2=10...........eq (1) +//(-2)I1+(6)I2=-20..........eq (2) +//solving the two equations using matrix method +A=[4 -2; -2 6]; +b=[10;-20]; +x=inv(A)*b; +I1=x(1,:); //to access 1st element of 2X1 matrix +I2=x(2,:); //to access 2nd element of 2X1 matrix +I=I2-I3; +disp(sprintf("By mesh analysis, the current through resistor R3 is %d A",I)); + +//END + diff --git a/1445/CH1/EX1.12/Ex1_12.sce b/1445/CH1/EX1.12/Ex1_12.sce new file mode 100644 index 000000000..6ca51aa27 --- /dev/null +++ b/1445/CH1/EX1.12/Ex1_12.sce @@ -0,0 +1,27 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 12 + +disp("CHAPTER 1"); +disp("EXAMPLE 12"); + +//VARIABLE INITIALIZATION +v=10; //voltage source in Volts +I=5; //current source in Amperes +r1=2; //in Ohms +r2=2; //in Ohms +r3=4; //in Ohms + +//SOLUTION + +//deactivating current source +v1=(v/r1)/((1/r1)+(1/r2)+(1/r3)); //using nodal analysis +I1=v1/r3; + +//deactivating voltage source +v2=I/((1/r1)+(1/r2)+(1/r3)); //using nodal analysis +I2=v2/r3; +I_tot=I1+I2; //applying Superposition Theorem (I1 and I2 are in same direction) + +disp(sprintf("By Superposition Theorem, the current through resistor R3 is %d A",I_tot)); + +//END diff --git a/1445/CH1/EX1.13/Ex1_13.sce b/1445/CH1/EX1.13/Ex1_13.sce new file mode 100644 index 000000000..abd93a4fc --- /dev/null +++ b/1445/CH1/EX1.13/Ex1_13.sce @@ -0,0 +1,26 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 13 + +disp("CHAPTER 1"); +disp("EXAMPLE 13"); + +//VARIABLE INITIALIZATION +v=10; //voltage source in Volts +I=5; //current source in Amperes +r1=2; //in Ohms +r2=2; //in Ohms +r3=4; //in Ohms + +//SOLUTION +//solving by nodal analysis +res=I+(v/r1); //'res' is used to make the calculation easy +vth=res/((1/r1)+(1/r2)); //Thevenin voltage +rth=(r1*r2)/(r1+r2); //Thevenin resistance +Ith=vth/(rth+r3); //Thevenin current +disp(sprintf("By Thevenin Theorem, the current through resistor R3 is %d A",Ith)); + +//END + + + + diff --git a/1445/CH1/EX1.14/Ex1_14.sce b/1445/CH1/EX1.14/Ex1_14.sce new file mode 100644 index 000000000..dc2c6f076 --- /dev/null +++ b/1445/CH1/EX1.14/Ex1_14.sce @@ -0,0 +1,30 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 14 + +disp("CHAPTER 1"); +disp("EXAMPLE 14"); + +//VARIABLE INITIALIZATION +v=10; //voltage source in Volts +I3=-5; //current source in Amperes +r1=2; //in Ohms +r2=2; //in Ohms +r3=4; //in Ohms + +//SOLUTION +//by loop analysis +//(1)I1+(-1)I2=0.........eq (1) +//(4)I1+(-2)I2=10........eq (2) +//solving the equations by matrix method +A=[1 -1;4 -2]; +b=[0;10]; +x=inv(A)*b; +I1=x(1,:); //to access 1st element of 2X1 matrix +I2=x(2,:); //to access 2nd element of 2X1 matrix +In=I2-I3; +rn=(r1*r2)/(r1+r2); +I=(rn*In)/(rn+r3); +disp(sprintf("By Norton Theorem, the current through resistor R3 is %d A",I)); + +//END + diff --git a/1445/CH1/EX1.15/Ex1_15.sce b/1445/CH1/EX1.15/Ex1_15.sce new file mode 100644 index 000000000..ec612db54 --- /dev/null +++ b/1445/CH1/EX1.15/Ex1_15.sce @@ -0,0 +1,26 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 15 + +disp("CHAPTER 1"); +disp("EXAMPLE 15"); + +//VARIABLE INITIALIZATION +v=7; //voltage source in Volts +I=7; //current source in Amperes +r3=1; //in Ohms + +//SOLUTION +//(1)I1+(-4)I2+(4)I3=7............eq (1) +//(-1)I1+(6)I2+(-3)I3=0...........eq (2) +//(1)I1+(0)I2+(-1)I3=7............eq (3) +//solving the equations by matrix method +A=[1 -4 4;-1 6 -3;1 0 -1]; +b=[7;0;7]; +x=inv(A)*b; +I1=x(1,:); //to access the 1st element of 3X1 matrix +I2=x(2,:); //to access the 2nd element of 3X1 matrix +I3=x(3,:); //to access the 3rd element of 3X1 matrix +vx=-(I3*r3); +disp(sprintf("By Mesh analysis, the value of Vx is %d V",vx)); + +//END diff --git a/1445/CH1/EX1.16/Ex1_16.sce b/1445/CH1/EX1.16/Ex1_16.sce new file mode 100644 index 000000000..ce11db243 --- /dev/null +++ b/1445/CH1/EX1.16/Ex1_16.sce @@ -0,0 +1,28 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 16 + +disp("CHAPTER 1"); +disp("EXAMPLE 16"); + +//VARIABLE INITIALIZATION +v=7; //voltage source in Volts +I=7; //current source in Amperes +r1=1; //in Ohms +r2=2; //in Ohms +r3=1; //in Ohms +r4=2; //in Ohms +r5=3; //in Ohms + +//SOLUTION +//(4)vb+(-1)vc=0........eq (1) +//(-2)vb+(11)vc=21......eq (2) +//solving the equations by matrix method +A=[4 -1;-2 11]; +b=[0;21]; +x=inv(A)*b; +vb=x(1,:); //to access the 1st element of 2X1 matrix +vc=x(2,:); //to access the 2nd element of 2X1 matrix +vx=-vc; +disp(sprintf("By Nodal analysis, the value of Vx is %d V",vx)); + +//END diff --git a/1445/CH1/EX1.17/Ex1_17.sce b/1445/CH1/EX1.17/Ex1_17.sce new file mode 100644 index 000000000..46d6a28bf --- /dev/null +++ b/1445/CH1/EX1.17/Ex1_17.sce @@ -0,0 +1,36 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 17 + +disp("CHAPTER 1"); +disp("EXAMPLE 17"); + +//VARIABLE INITIALIZATION +v=7; //voltage source in Volts +I=7; //current source in Amperes +r1=1; //in Ohms +r2=2; //in Ohms +r3=1; //in Ohms +r4=2; //in Ohms +r5=3; //in Ohms + +//SOLUTION + +//deactivating the current source +res=(v/4)+(v/2); +vc=res/((1/4)+(1/r1)+(1/r2)); +vx1=-vc; + +//deactivating voltage source +//(4)va+(-1)vb=-21........eq (1) +//(2)va+(-11)vb=0.........eq (2) +//solving the equations by matrix method +A=[4 -1;2 -11]; +b=[-21;0]; +x=inv(A)*b; +va=x(1,:); //to access 1st element of 2X1 matrix +vb=x(2,:); //to access 2nd element of 2X1 matrix +vx2=-vb; +vx=vx1+vx2; +disp(sprintf("By Superposition Theorem, the value of Vx is %d V",vx)); + +//END diff --git a/1445/CH1/EX1.18/Ex1_18.sce b/1445/CH1/EX1.18/Ex1_18.sce new file mode 100644 index 000000000..3dec1c69c --- /dev/null +++ b/1445/CH1/EX1.18/Ex1_18.sce @@ -0,0 +1,28 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 18 + +disp("CHAPTER 1"); +disp("EXAMPLE 18"); + +//VARIABLE INITIALIZATION +v=7; //voltage source in Volts +I=7; //current source in Amperes +r1=1; //in Ohms +r2=2; //in Ohms +r3=1; //in Ohms +r4=2; //in Ohms +r5=3; //in Ohms + +//SOLUTION +//solving by mesh analysis +I2=0; //since mesh 2 is open +I1=I-I2; +I3=I1/6; //from the equation of mesh 3 +vth=-(r2*I3)+v; //Thevenin voltage +r=r1+r5; //series combination of resistors +rth=(r*r4)/(r+r4); //parallel combination of resistors (Thevenin resistance) +I=vth/(rth+r3); //Thevenin current +vx=-I*r3; +disp(sprintf("By Thevenin Theorem, the value of Vx is %d V",vx)); + +//END diff --git a/1445/CH1/EX1.19/Ex1_19.sce b/1445/CH1/EX1.19/Ex1_19.sce new file mode 100644 index 000000000..990af1202 --- /dev/null +++ b/1445/CH1/EX1.19/Ex1_19.sce @@ -0,0 +1,34 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 19 + +disp("CHAPTER 1"); +disp("EXAMPLE 19"); + +//VARIABLE INITIALIZATION +v=7; //voltage source in Volts +I=7; //current source in Amperes +r1=1; //in Ohms +r2=2; //in Ohms +r3=1; //in Ohms +r4=2; //in Ohms +r5=3; //in Ohms + +//SOLUTION +//by using mesh analysis, the following equations are obtained +//(1)I1+(-4)I2+(3)In=7.......eq (1) +//(-1)I1+(6)I1+(-3)In=0......eq (2) +//(0)I1+(1)I2+(-1)In=0.......eq (3) +//solving the equations by matrix method +A=[1 -4 3;-1 6 -3;0 1 -1]; +b=[7;0;0]; +x=inv(A)*b; +I1=x(1,:); //to access the 1st element of 3X1 matrix +I2=x(2,:); //to access the 2nd element of 3X1 matrix +IN=x(3,:); //to access the 3rd element of 3X1 matrix; IN is Norton current +r=r1+r5; //series combination of resistors +rN=(r*r4)/(r+r4); //parallel combination of resistors (Norton resistance) +I=(rN*IN)/(rN+r3); +vx=-I*r3; +disp(sprintf("By Norton Theorem, the value of Vx is %d V",vx)); + +//END diff --git a/1445/CH1/EX1.2/Ex1_2.sce b/1445/CH1/EX1.2/Ex1_2.sce new file mode 100644 index 000000000..d9885ec94 --- /dev/null +++ b/1445/CH1/EX1.2/Ex1_2.sce @@ -0,0 +1,34 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 2 + +disp("CHAPTER 1"); +disp("EXAMPLE 2"); + +//VARIABLE INITIALIZATION +//star values ra, rc and rd +ra=2; //in Ohms +rc=4; //in Ohms +rd=3; //in Ohms +r1=5; //in Ohms +r2=4; //in Ohms +r3=6; //in Ohms + +//SOLUTION +//converting star with points A, C and D into delta ACD +r=(ra*rc)+(rc*rd)+(rd*ra); //'r' is the resistance that appears in the numerator of the equation of star-delta conversion + +//delta values rac, rcd and rad +rac=r/rd; +rcd=r/ra; +rad=r/rc; +req1=(r1*rad)/(r1+rad); //equivalent resistance between A and D +req2=(r2*rcd)/(r2+rcd); //equivalent resistance between C and D +req3=req1+req2; //series combination of resistors +req4=(req3*rac)/(req3+rac); //parallel combination of resistors +req5=req4+r3; +req6=(req5*7)/(req5+7); +disp(sprintf("The eqivalent resistance between points A and B is %.2f Ω",req6)); + +//END + + diff --git a/1445/CH1/EX1.20/Ex1_20.sce b/1445/CH1/EX1.20/Ex1_20.sce new file mode 100644 index 000000000..0255e39d2 --- /dev/null +++ b/1445/CH1/EX1.20/Ex1_20.sce @@ -0,0 +1,32 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 20 + +disp("CHAPTER 1"); +disp("EXAMPLE 20"); + +//VARIABLE INITIALIZATION +I=20; //current source in Amperes +v1=10; //voltage source in Volts +v2=40; //voltage source in Volts +r1=8; //in Ohms +r2=5; //in Ohms +r3=4; //in Ohms +r4=12; //in Ohms + +//SOLUTION +req=r1+r2; +rn=(req*r3)/(req+r3); +//finding In by mesh analysis +//(17)I2+(-4)I3=110.......eq (1) +//(1)I2+(-1)I3=-10........eq (2) +//solving the equations by matrix mehod +A=[17 -4;1 -1]; +b=[110;-10]; +x=inv(A)*b; +I2=x(1,:); //to access the 1st element of 2X1 matrix +I3=x(2,:); //to access the 2nd element of 2X1 matrix +In=I3; +I=(rn*In)/(rn+r4); +disp(sprintf("By Norton Theorem, the value of I is %.3f A",I)); + +//END diff --git a/1445/CH1/EX1.21/Ex1_21.sce b/1445/CH1/EX1.21/Ex1_21.sce new file mode 100644 index 000000000..6529af7b8 --- /dev/null +++ b/1445/CH1/EX1.21/Ex1_21.sce @@ -0,0 +1,35 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 21 + +disp("CHAPTER 1"); +disp("EXAMPLE 21"); + +//VARIABLE INITIALIZATION +I=20; //current source in Amperes +v1=10; //voltage source in Volts +v2=40; //voltage source in Volts +r1=8; //in Ohms +r2=5; //in Ohms +r3=4; //in Ohms +r4=12; //in Ohms + +//SOLUTION + +req=r1+r2; //series combination of resistors +rth=(req*r3)/(req+r3); //parallel connection of resistors (Thevenin resistance) + +//by using nodal analysis, the following equations are obtained +//(13)v1+(-8)v2=750.......eq (1) +//(-4)v1+(9)v2=200........eq (2) +//solving the equations by matrix mehod + +A=[13 -8;-4 9]; +b=[750;200]; +x=inv(A)*b; +v1=x(1,:); //to access the 1st element of 2X1 matrix +v2=x(2,:); //to access the 2nd element of 2X1 matrix +vth=v2; //Thevenin voltage +I=vth/(rth+r4); //Thevenin current +disp(sprintf("By Thevenin Theorem, the value of I is %.3f A",I)); + +//END diff --git a/1445/CH1/EX1.22/Ex1_22.sce b/1445/CH1/EX1.22/Ex1_22.sce new file mode 100644 index 000000000..5f8a39459 --- /dev/null +++ b/1445/CH1/EX1.22/Ex1_22.sce @@ -0,0 +1,30 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 22 + +disp("CHAPTER 1"); +disp("EXAMPLE 22"); + +//VARIABLE INITIALIZATION +I1=20; //current source in Amperes +v1=10; //voltage source in Volts +v2=40; //voltage source in Volts +r1=8; //in Ohms +r2=5; //in Ohms +r3=4; //in Ohms +r4=12; //in Ohms + +//SOLUTION + +//by using mesh analysis the following equations are obtained +//(17)I2+(-4)I3=110.......eq (1) +//(-1)I2+(4)I3=10.........eq (2) +//solving the equations by matrix method +A=[17 -4;-1 4]; +b=[110;10]; +x=inv(A)*b; +I2=x(1,:); //to access the 1st element of 2X1 matrix +I3=x(2,:); //to access the 2nd element of 2X1 matrix +I=I3; +disp(sprintf("By mesh analysis, the value of I is %.3f A",I)); + +//END diff --git a/1445/CH1/EX1.23/Ex1_23.sce b/1445/CH1/EX1.23/Ex1_23.sce new file mode 100644 index 000000000..b94474269 --- /dev/null +++ b/1445/CH1/EX1.23/Ex1_23.sce @@ -0,0 +1,27 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 23 + +disp("CHAPTER 1"); +disp("EXAMPLE 23"); + +//VARIABLE INITIALIZATION +I1=20; //current source in Amperes +v1=10; //voltage source in Volts +v2=40; //voltage source in Volts +r1=8; //in Ohms +r2=5; //in Ohms +r3=4; //in Ohms +r4=12; //in Ohms + +//SOLUTION +//(17)I2+(-4)I3=110.......eq (1) +//(-4)v1+(16)I3=40........eq (2) +//solving the equations by matrix mehod +A=[17 -4;-4 16]; +b=[110;40]; +x=inv(A)*b; +I2=x(1,:); //to access the 1st element of 2X1 matrix +I3=x(2,:); //to access the 2nd element of 2X1 matrix +disp(sprintf("By Nodal analysis, the value of I is %.3f A",I3)); + +//END diff --git a/1445/CH1/EX1.24/Ex1_24.sce b/1445/CH1/EX1.24/Ex1_24.sce new file mode 100644 index 000000000..1bb5528b5 --- /dev/null +++ b/1445/CH1/EX1.24/Ex1_24.sce @@ -0,0 +1,34 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 24 + +disp("CHAPTER 1"); +disp("EXAMPLE 24"); + +//VARIABLE INITIALIZATION +I=20; //current source in Amperes +v1=10; //voltage source in Volt +v2=40; //voltage source in Volts +r1=8; //in Ohms +r2=5; //in Ohms +r3=4; //in Ohms +r4=12; //in Ohms + +//SOLUTION + +//activating 20A current source +r=r2+((r3*r4)/(r3+r4)); +I1=(r*I1)/(r+r1); +I_20=(r3*I1)/(r3+r4); + +//activating 10V battery source +req=r1+r2; +v_10=(-v1/req)/((1/req)+(1/r3)+(1/r4)); +I_10=v_10/r4; + +//activating 40V battery source +v_40=(v2/r3)/((1/req)+(1/r3)+(1/r4)); +I_40=v_40/r4; +I_tot=I_20+I_10+I_40; +disp(sprintf("By Superposition Theorem, the value of I is .3%f A",I_tot)); + +//END diff --git a/1445/CH1/EX1.25/Ex1_25.sce b/1445/CH1/EX1.25/Ex1_25.sce new file mode 100644 index 000000000..e1c250c68 --- /dev/null +++ b/1445/CH1/EX1.25/Ex1_25.sce @@ -0,0 +1,22 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 25 + +disp("CHAPTER 1"); +disp("EXAMPLE 25"); + +//SOLUTION +//(1)I1+(0)I2+(0)I3=5.............eq (1) +//(-20)I1+(50)I2+(-20)I3=0........eq (2) +//(0)I1+(1)I2+(-1)I3=5............eq (3) +//solving the equations by matrix mehod +A=[1 0 0;-20 50 -20;0 1 -1]; +b=[5;0;5]; +x=inv(A)*b; +I1=x(1,:); //to access the 1st element of 3X1 matrix +I2=x(2,:); //to access the 2nd element of 3X1 matrix +I3=x(3,:); //to access the 3rd element of 3X1 matrix +I=I2; +disp(sprintf("By Mesh analysis, the value of I is %d A",I)); + +//END + diff --git a/1445/CH1/EX1.26/Ex1_26.sce b/1445/CH1/EX1.26/Ex1_26.sce new file mode 100644 index 000000000..18b2768c4 --- /dev/null +++ b/1445/CH1/EX1.26/Ex1_26.sce @@ -0,0 +1,19 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 26 + +disp("CHAPTER 1"); +disp("EXAMPLE 26"); + +//VARIABLE INITIALIZATION +I1=5; //current source in Amperes +v2=100; //voltage source in Volts +r1=20; //in Ohms +r2=10; //in Ohms +r3=20; //in Ohms + +//SOLUTION +v1=(I1+(v2/r2))/((1/r1)+(1/r2)); +I=(v1-v2)/r2; +disp(sprintf("By Nodal analysis, the value of I is %d A",I)); + +//END diff --git a/1445/CH1/EX1.27/Ex1_27.sce b/1445/CH1/EX1.27/Ex1_27.sce new file mode 100644 index 000000000..e4aa7816d --- /dev/null +++ b/1445/CH1/EX1.27/Ex1_27.sce @@ -0,0 +1,21 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 27 + +disp("CHAPTER 1"); +disp("EXAMPLE 27"); + +//VARIABLE INITIALIZATION +I1=5; //current source in Amperes +vb=100; //voltage source in Volts +r1=20; //in Ohms +r2=10; //in Ohms +r3=20; //in Ohms + +//SOLUTION +va=I1*r1; //by applying node analysis at point 'a' +vth=va-vb; //Thevenin voltage vth=vab +rth=r1+((r3*0)/(r3+0)); //Thevenin resistance +I=vth/(rth+r2); +disp(sprintf("By Thevenin Theorem, the value of I is %d A",I)); + +//END diff --git a/1445/CH1/EX1.28/Ex1_28.sce b/1445/CH1/EX1.28/Ex1_28.sce new file mode 100644 index 000000000..2391711a6 --- /dev/null +++ b/1445/CH1/EX1.28/Ex1_28.sce @@ -0,0 +1,20 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 28 + +disp("CHAPTER 1"); +disp("EXAMPLE 28"); + +//VARIABLE INITIALIZATION +I1=5; //current source in Amperes +va=100; //voltage source in Volts +r1=20; //in Ohms +r2=10; //in Ohms +r3=20; //in Ohms + +//SOLUTION +IN=I1-(va/r1); //using nodal analysis at point 'a' +rN=r1+((r3*0)/(r3+0)); +I=(rN*IN)/(rN+r2); +disp(sprintf("By Norton Theorem, the value of I is %d A",I)); + +//END diff --git a/1445/CH1/EX1.29/Ex1_29.sce b/1445/CH1/EX1.29/Ex1_29.sce new file mode 100644 index 000000000..319e202f9 --- /dev/null +++ b/1445/CH1/EX1.29/Ex1_29.sce @@ -0,0 +1,25 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 29 + +disp("CHAPTER 1"); +disp("EXAMPLE 29"); + +//VARIABLE INITIALIZATION +I=5; //current source in Amperes +v=100; //voltage source in Volts +r1=20; //in Ohms +r2=10; //in Ohms +r3=20; //in Ohms + +//SOLUTION + +//activating current source +I1=(I*r1)/(r1+r2); //by current divider law + +//activating voltage source +I2=-(v/(r1+r2)); + +I_tot=I1+I2; +disp(sprintf("By Superposition Theorem, the value of I is %d A",I_tot)); + +//END diff --git a/1445/CH1/EX1.3/Ex1_3.sce b/1445/CH1/EX1.3/Ex1_3.sce new file mode 100644 index 000000000..fdaccbce2 --- /dev/null +++ b/1445/CH1/EX1.3/Ex1_3.sce @@ -0,0 +1,38 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 3 + +disp("CHAPTER 1"); +disp("EXAMPLE 3"); + +//VARIABLE INITIALIZATION +r1=4.6; //in Ohms +r2=7.6; //in Ohms + + +//star values +rc=3; +rd=7; +re=5; + +//SOLUTION +//converting star with points C, D and E to delta CDE +r=(rc*rd)+(rd*re)+(re*rc); //'r' is the resistance that appears in the numerator of the equation of star-delta conversion + +//delta values rcd, rde and rec +rcd=r/re; +rde=r/rc; +rec=r/rd; +req1=(8*rec)/(8+rec); //equivalent resistance between C and E +req2=(6*rde)/(6+rde); //equivalent resistance between D and E +req3=(4*rcd)/(4+rcd); //equivalent resistance between C and D +req4=req2+req3; +req5=(req1*req4)/(req1+req4); //parallel combination of resistors +req6=req5+r1; //series combination of resistors +req7=(req6*r2)/(req6+r2); +disp(sprintf("The equivalent resistance between points A and B is %.2f Ω",req7)); + +//END + + + + diff --git a/1445/CH1/EX1.30/Ex1_30.sce b/1445/CH1/EX1.30/Ex1_30.sce new file mode 100644 index 000000000..54c39d141 --- /dev/null +++ b/1445/CH1/EX1.30/Ex1_30.sce @@ -0,0 +1,42 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 30 + +disp("CHAPTER 1"); +disp("EXAMPLE 30"); + +//VARIABLE INITIALIZATION +I1=25; //current source in Amperes +I2=20; //current source in Amperes +v=20; //voltage source in Volts +r1=4; //LHS resistance in Ohms +r2=10; //in Ohms +r3=2; //in Ohms +r4=1; //in Ohms +r5=10; //RHS resistance in Ohms + +//SOLUTION + +//source transformation +v1=I1*r1; //current source I1 is converted to voltage source v1 +v2=I2*r3; //current source I2 is converted to voltage source v2 + +//using mesh analysis +//(8)IA+(-1)IB=30........eq (1) +//(-2)IA+(3)IB=20........eq (2) +//solving the equations by matrix method +A=[8 -1;-2 3]; +b=[30;20]; +x=inv(A)*b; +IA=x(1,:); //to access the 1st element of 2X1 matrix +IB=x(2,:); //to access the 2nd element of 2X1 matrix +disp(sprintf("By Mesh analysis I_A= %d A and I_B= %d A",IA,IB)); + +//using nodal analysis +req=r1+r2; +res=(v1/req)+(v2/r3)+(v/r4); +v3=res/((1/req)+(1/r3)+(1/r4)); +I3=(v1-v3)/req; +I4=(v2-v)/r3; //since here ((v2-v)/r3)=((v3-v)/r4) (this is only done for convinient calculation) +disp(sprintf("By Nodal analysis I_1= %d A and I_2= %d A",I3,I4)); + +//END diff --git a/1445/CH1/EX1.31/Ex1_31.sce b/1445/CH1/EX1.31/Ex1_31.sce new file mode 100644 index 000000000..fd519c1c9 --- /dev/null +++ b/1445/CH1/EX1.31/Ex1_31.sce @@ -0,0 +1,38 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 31 + +disp("CHAPTER 1"); +disp("EXAMPLE 31"); + +//VARIABLE INITIALIZATION +r1=6; //in Ohms +r2=4; //in Ohms +r3=4; //in Ohms +r4=4; //in Ohms +r5=6; //in Ohms +r6=6; //in Ohms +r7=6; //in Ohms +r8=8; //in Ohms +r9=4; //in Ohms +r10=10; //in Ohms +r11=10; //middle resistance in Ohms + +//SOLUTION +//converting delta cde in a star +req1=r5+r6+r7; +req2=(r6*r7)/req1; +req3=(r5*r6)/req1; +req4=(r5*r7)/req1; + +req5=r1+r2+r3; //on LHS of middle resistance +req6=r4+req2; //top LHS +req7=req4+r11; //equivalent middle resistance +req8=req3+r8+r9+r10; //top RHS + +req9=(req7*req8)/(req7+req8); //parallel combination of resistors +req10=req9+req6; //series combination of resistors +req11=(req5*req10)/(req5+req10); + +disp(sprintf("The equivalent resistance between A and B is %d Ω",req11)); + +//END diff --git a/1445/CH1/EX1.32/Ex1_32.sce b/1445/CH1/EX1.32/Ex1_32.sce new file mode 100644 index 000000000..c8b992869 --- /dev/null +++ b/1445/CH1/EX1.32/Ex1_32.sce @@ -0,0 +1,30 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 32 + +disp("CHAPTER 1"); +disp("EXAMPLE 32"); + +//VARIABLE INITIALIZATION +I=10; //current source in Amperes +v=10; //voltage source in Volts +r1=4; //top resistance in Ohms +r1=4; //right resistance in Ohms +r3=4; //bottom resistance in Ohms +r4=6; //left resistance in Ohms +r5=1; //in Ohms + +//SOLUTION +//without converting the current source into voltage source +//(10)I1+(-4)I2+(0)I3=50........eq (1) +//(-4)I1+(9)I2+(-4)I3=0.........eq (2) +//(0)I1+(-4)I2+(8)I3=10.........eq (3) +//solving the equations by matrix method +A=[10 -4 0;-4 9 -4;0 -4 8]; +b=[50;0;10]; +x=inv(A)*b; +I2=x(2,:); //to access the 2nd element of 3X1 matrix +disp(sprintf("By Mesh analysis, the current through 1Ω resistor is %.2f A",I2)); + +//END + + diff --git a/1445/CH1/EX1.33/Ex1_33.sce b/1445/CH1/EX1.33/Ex1_33.sce new file mode 100644 index 000000000..60903ad05 --- /dev/null +++ b/1445/CH1/EX1.33/Ex1_33.sce @@ -0,0 +1,36 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 33 + +disp("CHAPTER 1"); +disp("EXAMPLE 33"); + +//VARIABLE INITIALIZATION +I=10; //current source in Amperes +v=10; //voltage source in Volts +r1=4; //top resistance in Ohms +r1=4; //right resistance in Ohms +r3=4; //bottom resistance in Ohms +r4=6; //left resistance in Ohms +r5=1; //in Ohms + +//SOLUTION + +//by applying nodal analysis at node 1, the following equations are obtained: +//(17)v1+(-12)v2=150.......eq (1) +//(-4)v1+(6)v2=10..........eq (2) +//solving the equations by matrix method + +A=[17 -12;-4 6]; +b=[150;10]; +x=inv(A)*b; +v1=x(1,:); //to access the 1st element of 2X1 matrix +v2=x(2,:); //to access the 1st element of 2X1 matrix +if(v1>v2) then +I=(v1-v2)/r5; +disp(sprintf("By nodal analysis, the current through 1Ω resistor is %.3f A",I)); +else +I=(v2-v1)/r5; +disp(sprintf("By nodal analysis, the current through 1Ω resistor is %.3f A",I)); +end; + +//END diff --git a/1445/CH1/EX1.34/Ex1_34.sce b/1445/CH1/EX1.34/Ex1_34.sce new file mode 100644 index 000000000..2b8ba28a7 --- /dev/null +++ b/1445/CH1/EX1.34/Ex1_34.sce @@ -0,0 +1,51 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 34 + +disp("CHAPTER 1"); +disp("EXAMPLE 34"); + +//VARIABLE INITIALIZATION +I=10; //current source in Amperes +v=10; //voltage source in Volts +r1=4; //top resistance in Ohms +r1=4; //right resistance in Ohms +r3=4; //bottom resistance in Ohms +r4=6; //left resistance in Ohms +r5=1; //in Ohms + +//SOLUTION + +//activating the current source +//(17)v1+(-12)v2=120.......eq (1) +//(-4)v1+(6)v2=0...........eq (2) +//solving the equations by matrix method +A=[17 -12;-4 6]; +b=[120;0]; +x=inv(A)*b; +v1=x(1,:); //to access the 1st element of 2X1 matrix +v2=x(2,:); //to access the 1st element of 2X1 matrix +if(v1>v2) then +I1=(v1-v2)/r5; +else +I1=(v2-v1)/r5; +end; + +//activating the voltage source +//(17)v1+(-12)v2=30.......eq (1) +//(-4)v1+(6)v2=10...........eq (2) +//solving the equations by matrix method +A=[17 -12;-4 6]; +b=[30;10]; +x=inv(A)*b; +v3=x(1,:); //to access the 1st element of 2X1 matrix +v4=x(2,:); //to access the 1st element of 2X1 matrix +if(v3>v4) then +I2=(v3-v4)/r5; +else +I2=(v4-v3)/r5; +end; + +I_tot=I1+I2; +disp(sprintf("By Superposition Theorem, the current through 1Ω resistor is %.3f A",I_tot)); + +//END diff --git a/1445/CH1/EX1.35/Ex1_35.sce b/1445/CH1/EX1.35/Ex1_35.sce new file mode 100644 index 000000000..453b01ba6 --- /dev/null +++ b/1445/CH1/EX1.35/Ex1_35.sce @@ -0,0 +1,27 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 35 + +disp("CHAPTER 1"); +disp("EXAMPLE 35"); + +//VARIABLE INITIALIZATION +I=10; //current source in Amperes +v=10; //voltage source in Volts +r1=4; //top resistance in Ohms +r2=4; //right resistance in Ohms +r3=4; //bottom resistance in Ohms +r4=6; //left resistance in Ohms +r5=1; //in Ohms + +//SOLUTION +res=I+(v/r1); //'res' is used to make calucations easy +va=res/((1/r4)+(1/r1)); //applying nodal analysis at node 1 +vb=(v/r2)/((1/r2)+(1/r3)); //applying nodal analysis at node 2 +vth=va-vb; +req1=(r1*r4)/(r1+r4); +req2=(r2*r3)/(r2+r3); +rth=req1+req2; +Ith=vth/(rth+r5); +disp(sprintf("By Thevenin Theorem, the current through the 1Ω resistor is %.3f A",Ith)); + +//END diff --git a/1445/CH1/EX1.36/Ex1_36.sce b/1445/CH1/EX1.36/Ex1_36.sce new file mode 100644 index 000000000..86044a5a5 --- /dev/null +++ b/1445/CH1/EX1.36/Ex1_36.sce @@ -0,0 +1,30 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 36 + +disp("CHAPTER 1"); +disp("EXAMPLE 36"); + +//VARIABLE INITIALIZATION +I=10; //current source in Amperes +v=10; //voltage source in Volts +r1=4; //top resistance in Ohms +r2=4; //right resistance in Ohms +r3=4; //bottom resistance in Ohms +r4=6; //left resistance in Ohms +r5=1; //in Ohms + +//SOLUTION +//(1)v1+(12/5)In=30........eq (1) +//(2)v1+(-4)In=10..........eq (2) +A=[1 12/5;2 -4]; +b=[30;10]; +x=inv(A)*b; +v1=x(1,:); //to access the 1st element of 2X1 matrix +In=x(2,:); //to access the 2nd element of 2X1 matrix +req1=(r1*r4)/(r1+r4); +req2=(r2*r3)/(r2+r3); +rn=req1+req2; +I1=(rn*In)/(rn+r5); +disp(sprintf("By Norton Theorem, the current through 1Ω resistor is %.3f A",I1)); + +//END diff --git a/1445/CH1/EX1.37/Ex1_37.sce b/1445/CH1/EX1.37/Ex1_37.sce new file mode 100644 index 000000000..b7eb9f63a --- /dev/null +++ b/1445/CH1/EX1.37/Ex1_37.sce @@ -0,0 +1,54 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 37 + +disp("CHAPTER 1"); +disp("EXAMPLE 37"); + +//VARIABLE INITIALIZATION +v1=90; //voltage source in Volts +r1=8; //in Ohms +r2=6; //in Ohms +r3=5; //in Ohms +r4=4; //in Ohms +r5=8; //diagonal resistance in Ohms +r6=8; //in Ohms + +//SOLUTION + +//solution (i): using Thevenin's Theorem +//(3)v1+(-2)v2=90...........eq (1) //applying nodal analysis at node 1 +//(-2)v1+(4)v2=-90..........eq (2) //applying nodal analysis at node 2 +A=[3 -2;-2 4]; +b=[90;-90]; +x=inv(A)*b; +v1=x(1,:); +v2=x(2,:); +vth=v1; +req1=(r1*r5)/(r1+r5); +req2=req1+r4; +req3=(req2*r6)/(req2+r6); +rth=req3+r2; +vab1=(vth*r3)/(rth+r3); +disp(sprintf("By Thevenin Theorem, the value of Vab is %.2f V",vab1)); + +//solution (ii): using Norton's Theorem +//(13)v1+(-7)v2=270.........eq (1) //applying nodal analysis at node 1 +//(7)v1+(-13)v2=0...........eq (2) //applying nodal analysis at node 2 +A=[13 -7;7 -13]; +b=[270;0]; +x=inv(A)*b; +v1=x(1,:); +v2=x(2,:); +req1=(r1*r5)/(r1+r5); +req2=req1+r4; +req3=(req2*r6)/(req2+r6); +rN=req3+r2; +if(v1>v2) then +In=(v1-v2)/r2; +else +IN=(v2-v1)/r2; +end; +vab2=(r3*IN)*(rN/(rth+r3)); +disp(sprintf("By Norton Theorem, the value of Vab is %.2f V",vab2)); + +//END diff --git a/1445/CH1/EX1.38/Ex1_38.sce b/1445/CH1/EX1.38/Ex1_38.sce new file mode 100644 index 000000000..7cde0f2d3 --- /dev/null +++ b/1445/CH1/EX1.38/Ex1_38.sce @@ -0,0 +1,37 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 38 + +disp("CHAPTER 1"); +disp("EXAMPLE 38"); + +//VARIABLE INITIALIZATION +I=2; //current source in Amperes +r1=2; //in Ohms +r2=1; //in Ohms +r3=1; //in Ohms +r4=2; //in Ohms + +//SOLUTION + +//Thevenin Equivalent circuit +I1=1; //since there is equal resistance of 3Ω, hence, current=1A +vth=(I1*r2)+(-I1*r4); +req1=r1+r2; +req2=r3+r4; +rth=(req1*req2)/(req1+req2); +disp("THEVENIN EQUIVALENT CIRCUIT IS-"); +disp(sprintf(" Thevenin voltage= %d V",vth)); +disp(sprintf(" Thevenin resistance= %.2f Ω",rth)); + +//Norton Equivalent circuit +v1=I/((1/r2)+(1/r4)); +v2=-I/((1/r3)+(1/r1)); +req1=r1+r2; +req2=r3+r4; +rn=(req1*req2)/(req1+req2); +Isc=(v1/r4)+v2; +disp("NORTON EQUIVALENT CIRCUIT IS-"); +disp(sprintf(" Norton current= %.3f A",Isc)); +disp(sprintf(" Norton resistance= %.3f Ω",rn)); + +//END diff --git a/1445/CH1/EX1.39/Ex1_39.sce b/1445/CH1/EX1.39/Ex1_39.sce new file mode 100644 index 000000000..237e65eb5 --- /dev/null +++ b/1445/CH1/EX1.39/Ex1_39.sce @@ -0,0 +1,21 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 39 + +disp("CHAPTER 1"); +disp("EXAMPLE 39"); + +//VARIABLE INITIALIZATION +v=2; //in Volts +r=2; //in Ohms + +//SOLUTION +z_star=r/3; +req1=(r/3)+r; +req2=(r/3)+r; +req3=(req1*req2)/(req1+req2); +req4=(r/3)+req3; +req5=(req4*r)/(req4+r); +I=v/req5; +disp(sprintf("The value of I is %d A",I)); + +//END diff --git a/1445/CH1/EX1.4/Ex1_4.sce b/1445/CH1/EX1.4/Ex1_4.sce new file mode 100644 index 000000000..b8847eae1 --- /dev/null +++ b/1445/CH1/EX1.4/Ex1_4.sce @@ -0,0 +1,41 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 4 + +disp("CHAPTER 1"); +disp("EXAMPLE 4"); + +//VARIABLE INITIALIZATION +r1=1; //LHS resistance in Ohms +r2=2; //in Ohms +r3=3; //in Ohms +r4=4; //in Ohms +r5=5; //in Ohms +r6=6; //in Ohms +r7=7; //in Ohms +r8=8; //RHS resistance in Ohms + +//SOLUTION + +//To find resistance between a and b +req1=r1+r2; //series combination of resistors +req2=(req1*r3)/(req1+r3); //parallel combination of resistors +req3=req2+(r4+r5); +req4=(req3*r6)/(req3+r6); +req5=req4+r7; +req6=(req5*r8)/(req5+r8); +disp(sprintf("The eqiuvalent resistance between points a and b is %.2f Ω",req6)); + +//To find resistance between c and d +req7=r7+r8; +req8=(req7*r6)/(req7+r6); +req9=req2+r5+req8; +req10=(req9*r4)/(req9+r4); +disp(sprintf("The eqiuvalent resistance between points c and d is %.2f Ω",req10)); + +//To find resistance between d and e +req11=req2+r4+r5; +req12=(req11*r6)/(req11+r6); +req13=(req12*req7)/(req12+req7); +disp(sprintf("The eqiuvalent resistance between points d and e is %.2f Ω",req13)); + +//END diff --git a/1445/CH1/EX1.40/Ex1_40.sce b/1445/CH1/EX1.40/Ex1_40.sce new file mode 100644 index 000000000..6f60627ea --- /dev/null +++ b/1445/CH1/EX1.40/Ex1_40.sce @@ -0,0 +1,33 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 40 + +disp("CHAPTER 1"); +disp("EXAMPLE 40"); + +//VARIABLE INITIALIZATION +v1=20; //in Volts +v2=10; //in Volts +r1=5; //top resistance in Ohms +r2=10; //bottom resistance in Ohms +r3=5; //in Ohms +r4=5; //in Ohms +r5=10; //in Ohms + +//SOLUTION +//(5)I1+(10)I3+(-10)I4=20............eq (1) +//(0)I1+(10)I3+(10)I4=-50............eq (2) +//(5)I1+(20)I3+(0)I4=-30.............eq (3) (eq(1) + eq(2)) +//Since the determinant of matrix A is 0, hence, the set of these equations cannot be solved by matrix method +//So, solving them directly, + +I3=-15/25; +I1=-3-(3/5); +I4=-5-(-3/5); +I=I1+3+5; +disp("The currents (in Amperes) flowing in different branches are:"); +disp(I1); +disp(I3); +disp(I4); +disp(sprintf("The total current is %.2f A",I)); + +//END diff --git a/1445/CH1/EX1.41/Ex1_41.sce b/1445/CH1/EX1.41/Ex1_41.sce new file mode 100644 index 000000000..53e65b5b2 --- /dev/null +++ b/1445/CH1/EX1.41/Ex1_41.sce @@ -0,0 +1,30 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 41 + +disp("CHAPTER 1"); +disp("EXAMPLE 41"); + +//VARIABLE INITIALIZATION +vs=6; //in Volts +Is=4; //in Amperes +r1=5; //in Ohms +r2=2; //in Ohms +r3=2; //in Ohms +r=2/3; //in Ohms +r4=3; //in Ohms +r5=1; //in Ohms +r6=2; //in Ohms + +//SOLUTION +req1=(r2*r3)/(r2+r3); +req2=req1+r1; //resistance across vs +va=vs/req2; //voltage divider law +rth1=(req1*r1)/(req1+r1); +I1=Is*(r2/req2); //current divider law +vb=I1*r4; +rth2=(r4*r4)/(r4+r4); +I=(vb-va)/(rth1+r+rth2); +disp(sprintf("The value of the current is %d A",I)); + +//END + diff --git a/1445/CH1/EX1.42/Ex1_42.sce b/1445/CH1/EX1.42/Ex1_42.sce new file mode 100644 index 000000000..4d3388dd9 --- /dev/null +++ b/1445/CH1/EX1.42/Ex1_42.sce @@ -0,0 +1,40 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 42 + +disp("CHAPTER 1"); +disp("EXAMPLE 42"); + +//VARIABLE INITIALIZATION +v=10; //in Volts +I=0.5; //in Amperes +r1=4; //top LHS resistance in Ohms +r2=2; //top RHS resistance in Ohms +r3=2; //first resistance in Ohms +r4=2; //second resistance in Ohms + +//SOLUTION + +//using Thevenin's theorem +rth=(r1*r3)/(r1+r3); +vth=v*(r3/(r1+r3)); //Thevenin voltage +R=(40-(56*I))/(24*I); //solving for R directly +disp(sprintf("(i) By Thevenin Theorem, the value of R is %d Ω",R)); + +//v1=(10R+4)/(3R+4)........eq(1) //using nodal analysis at node 1 +//v1=1+R...................eq(2) //using nodal analysis at node 2 +//the following the quadratic equation is formed when both the equations are compared +//(3)R^2+(-3)R+(0)=0 +//solving the quadratic equation +a=3; +b=-3; +c=0; +D=(b^2)-(4*a*c); //discriminant +R1=(-b+sqrt(D))/(2*a); +R2=(-b-sqrt(D))/(2*a); +if(R1==1) then +disp(sprintf("(ii) By Nodal analysis, the value of R is %d Ω",R1)); +else +disp(sprintf("(ii) By Nodal analysis, the value of R is %d Ω",R1)); +end; + +//END diff --git a/1445/CH1/EX1.43/Ex1_43.sce b/1445/CH1/EX1.43/Ex1_43.sce new file mode 100644 index 000000000..ad30b370f --- /dev/null +++ b/1445/CH1/EX1.43/Ex1_43.sce @@ -0,0 +1,25 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 43 + +disp("CHAPTER 1"); +disp("EXAMPLE 43"); + +//VARIABLE INITIALIZATION +Is1=2; //first current source in Amperes +Is2=4; //second current source in Amperes +v=2; //in Volts +r1=200; //in Ohms +r2=100; //in Ohms +r3=4; //in Ohms + +//SOLUTION +req1=34; +I1=Is2*(r3/req1); +req2=24; +Iab=Is1*(req2/req1); +I=Iab+I1; +vab=I*10; +disp(sprintf("By Superposition Theorem the voltage Vab is %.3f V",vab)); + +//END + diff --git a/1445/CH1/EX1.44/Ex1_44.sce b/1445/CH1/EX1.44/Ex1_44.sce new file mode 100644 index 000000000..e060456a9 --- /dev/null +++ b/1445/CH1/EX1.44/Ex1_44.sce @@ -0,0 +1,15 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 44 + +disp("CHAPTER 1"); +disp("EXAMPLE 44"); + +//VARIABLE INITIALIZATION +I=40; //in Amperes +r=5; //in Ohms + +//SOLUTION +v=I*r; //Ohm's Law +disp(sprintf("The voltage required is %d V",v)); + +//END diff --git a/1445/CH1/EX1.45/Ex1_45.sce b/1445/CH1/EX1.45/Ex1_45.sce new file mode 100644 index 000000000..361cfdda5 --- /dev/null +++ b/1445/CH1/EX1.45/Ex1_45.sce @@ -0,0 +1,15 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 45 + +disp("CHAPTER 1"); +disp("EXAMPLE 45"); + +//VARIABLE INITIALIZATION +w=5*1000; //power consumed by coil in Watts +v=200; //applied voltage in Volts + +//SOLUTION +r=(v^2)/w; //since w=(v^2)/r +disp(sprintf("Value of resistance is %d Ω",r)); + +//END diff --git a/1445/CH1/EX1.46/Ex1_46.sce b/1445/CH1/EX1.46/Ex1_46.sce new file mode 100644 index 000000000..4623527b7 --- /dev/null +++ b/1445/CH1/EX1.46/Ex1_46.sce @@ -0,0 +1,26 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 46 + +disp("CHAPTER 1"); +disp("EXAMPLE 46"); + +//VARIABLE INITIALIZATION +v=240; //in Volts + +//SOLUTION +//case1: p=60W +p1=60; //in Watts +r1=(v^2)/p1; +disp(sprintf("Resistance of the metal filament lamp is %d Ω",r1)); + +//case2: p=100W +p2=100; //in Watts +r2=(v^2)/p2; + +if(r1>r2) then +disp(sprintf("Resistance of %d W lamp will be greater",p1)); +else +disp(sprintf("Resistance of %d W lamp will be greater",p2)); +end; + +//END diff --git a/1445/CH1/EX1.47/Ex1_47.sce b/1445/CH1/EX1.47/Ex1_47.sce new file mode 100644 index 000000000..9b53f1882 --- /dev/null +++ b/1445/CH1/EX1.47/Ex1_47.sce @@ -0,0 +1,32 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 47 + +disp("CHAPTER 1"); +disp("EXAMPLE 47"); + +//VARIABLE INITIALIZATION +lc=20; //length of copper wire in m +dc=0.015/100; //diameter of copper wire in m +rhoc=1.7; //specific resistance for copper +lp=15; //length of platinum silver wire in m +dp=0.015/100; //diameter of platinum silver wire in m +rhop=2.43; //specific resistance for platinum silver + +//SOLUTION + +//for copper wire +sc=(%pi/4)*(dc^2); //area +rc=rhoc*(lc/sc); + +//for platinum silver +sp=(%pi/4)*(dp^2); //area +rp=rhop*(lp/sp); + + +if(rc>rp) then +disp("Copper wire has greater resistance"); +else +disp("Platinum silver wire has greater resistance"); +end; + +//END diff --git a/1445/CH1/EX1.48/Ex1_48.sce b/1445/CH1/EX1.48/Ex1_48.sce new file mode 100644 index 000000000..99933d888 --- /dev/null +++ b/1445/CH1/EX1.48/Ex1_48.sce @@ -0,0 +1,32 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 48 + +disp("CHAPTER 1"); +disp("EXAMPLE 48"); + +//VARIABLE INITIALIZATION +v1=2.05; //1st cell in Volts +v2=2.15; //2nd cell in Volts +r1=0.05; //in Ohms +r2=0.04; //in Ohms +r3=1; //in Ohms + +//SOLUTION +//(r3+r1)I1+(r3)I2=v1......eq (1) +//(r3)I1+(r3+r2)I2=v2......eq (2) +req1=r3+r1; +req2=r3+r2; +A=[req1 r3;r3 req2]; +b=[v1;v2]; +x=inv(A)*b; +I1=x(1,:); //to access the 1st element of 2X1 matrix +I2=x(2,:); //to access the 2nd element of 2X1 matrix +I=I1+I2; +pd=I*r3; +disp(sprintf("Current through B1 is %.2f A",I1)); +disp(sprintf("Current through B2 is %.2f A",I2)); +disp(sprintf("Potential difference across AC is %.2f V",pd)); + +//END + + diff --git a/1445/CH1/EX1.49/Ex1_49.sce b/1445/CH1/EX1.49/Ex1_49.sce new file mode 100644 index 000000000..1691f133c --- /dev/null +++ b/1445/CH1/EX1.49/Ex1_49.sce @@ -0,0 +1,38 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 49 + +disp("CHAPTER 1"); +disp("EXAMPLE 49"); + +//VARIABLE INITIALIZATION +v1=110; //voltage source in Volts +v2=80; //voltage source in Volts +v3=50; //voltage source in Volts +r=2; //in Ohms + +//SOLUTION + +//solution (a) +I1=4; //charging +I2=6; //charging +r1=((v1-v2)-((I1+I2)*r))/I1; +r2=((v1-v3)-((I1+I2)*r))/I2; +disp(sprintf("(a) R1= %.2f Ω",r1)); +disp(sprintf(" R2= %.2f Ω",r2)); + +//solution (b) +I1=2; //discharging +I2=20; //charging +r1=((v1-v2)-((I2-I1)*r))/(-I1); +r2=((v1-v3)-((I2-I1)*r))/I2; +disp(sprintf("(b) R1= %.2f Ω",r1)); +disp(sprintf(" R2= %.2f Ω",r2)); + +//solution (c) +I1=0; +I2=(v1-v2)/r; +r2=((v1-v3)-(I2*r))/I2; +disp(sprintf("(c) I1=0 when R2= %d Ω",r2)); + +//END + diff --git a/1445/CH1/EX1.5/Ex1_5.sce b/1445/CH1/EX1.5/Ex1_5.sce new file mode 100644 index 000000000..01fbb7a42 --- /dev/null +++ b/1445/CH1/EX1.5/Ex1_5.sce @@ -0,0 +1,39 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 5 + +disp("CHAPTER 1"); +disp("EXAMPLE 5"); + +//VARIABLE INITIALIZATION +r1=2; //in Ohms +r2=4; //in Ohms +r3=8; //in Ohms +r4=8; //in Ohms +r5=2; //middle resistance in Ohms + +//SOLUTION + +//To find resistance between a and c +req1=r1+r2; +req2=r1+r4; +req3=(req1*r1)/(req1+r1); +rac=(req3*req2)/(req3+req2); +disp(sprintf("The eqiuvalent resistance between points a and c is %.2f Ω",rac)); + +//To find resistance between b and d +//converting delta abc into star with points a, b and c +//delta values +rab=r1; +rbc=r2; +rac=6; +//star values +r=rab+rbc+rac; //'r' is the resistance that appears in the denominator of the equation of delta-star conversion +ra=(rab*rbc)/r; +rb=(rab*rac)/r; +rc=(rbc*rac)/r; +req5=rb+rac; +req6=rc+8; +rbd=ra+((req5*req6)/(req5+req6)); +disp(sprintf("The eqiuvalent resistance between points b and d is %.2f Ω",rbd)); + +//END diff --git a/1445/CH1/EX1.50/Ex1_50.sce b/1445/CH1/EX1.50/Ex1_50.sce new file mode 100644 index 000000000..e1ce34a4e --- /dev/null +++ b/1445/CH1/EX1.50/Ex1_50.sce @@ -0,0 +1,21 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 50 + +disp("CHAPTER 1"); +disp("EXAMPLE 50"); + +//SOLUTION +//(5)I1+(-3)I2=10..........eq (1) +//(-3)I1+(34)I2=40.........eq (2) +A=[5 -3;-3 34]; +b=[10;40]; +x=inv(A)*b; +I1=x(1,:); //to access the 1st element of 2X1 matrix +I2=x(2,:); //to access the 2nd element of 2X1 matrix +I=I2-I1; +disp(sprintf("Current i1 is %.2f A (loop EFAB)",I1)); +disp(sprintf("Current i2 is %.2f A (loop BCDE)",abs(I))); + +//END + + diff --git a/1445/CH1/EX1.51/Ex1_51.sce b/1445/CH1/EX1.51/Ex1_51.sce new file mode 100644 index 000000000..cd7fdbdce --- /dev/null +++ b/1445/CH1/EX1.51/Ex1_51.sce @@ -0,0 +1,23 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 51 + +disp("CHAPTER 1"); +disp("EXAMPLE 51"); + +//SOLUTION +//(9)I1+(-5)I2+(-3)I3=5..........eq (1) +//(-5)I1+(8)I2+(-1)I3=5..........eq (2) +//(-3)I1+(-1)I2+(6)I3=3..........eq (3) +A=[9 -5 -3;-5 8 -1;-3 -1 6]; +b=[5;5;3]; +x=inv(A)*b; +I1=x(1,:); //to access the 1st element of 3X1 matrix +I2=x(2,:); //to access the 2nd element of 3X1 matrix +I3=x(3,:); //to access the 3rd element of 3X1 matrix +disp(sprintf("Current i1 is %.2f A (loop ABGH)",I1)); +disp(sprintf("Current i2 is %.2f A (loop BCDH)",I2)); +disp(sprintf("Current i3 is %.2f A (loop GDEF)",I3)); + +//END + + diff --git a/1445/CH1/EX1.52/Ex1_52.sce b/1445/CH1/EX1.52/Ex1_52.sce new file mode 100644 index 000000000..c669dfdd1 --- /dev/null +++ b/1445/CH1/EX1.52/Ex1_52.sce @@ -0,0 +1,46 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 52 + +disp("CHAPTER 1"); +disp("EXAMPLE 52"); + +//VARIABLE INITIALIZATION +v1=20; //LHS voltage source in Volts +v2=12; //RHS voltage source in Volts +r1=5; //LHS resistance in Ohms +r2=2; //in Ohms +r3=8; //in Ohms +r4=10; //RHS resistance in Ohms + +//SOLUTION + +//by Thevenin's Theorem +rth=r3+((r1*r2)/(r1+r2)); //Thevenin resistance +v=v1*(r2/(r1+r2)); //voltage divider law +vab=-v2+(r3*0)+(rth*0)+v; +It=vab/(rth+r4); //current obtained by applying Thevenin's Theorem +Isc=vab/rth; +disp(sprintf("By Thevenin Theorem, current in the 10Ω resistor is %.2f A",It)); + +//verification by Norton's Theorem +//(7)I1+(2)I2=20.................eq (1) +//(2)I1+(10)I2=12................eq (2) +//solving the equations using matrix method +A=[7 2;2 10]; +b=[20;12]; +x=inv(A)*b; +x1=x(1,:); //to access 1st element of 2X1 matrix +x2=x(2,:); //to access 2nd element of 2X1 matrix and Isc=-x2 +Isc=-x2; //Isc is negative because its direction is opposite to I2 +I=Isc*(rth/(rth+r4)); //current obtained by applying Norton's Theorem +if(It==I) +disp(sprintf("By Norton Theorem, current in the 10Ω resistor is %.2f A",I)); +disp(sprintf("Hence, answer is confirmed by Norton Theorem")); +else +disp(sprintf("The answer is not confirmed by Norton Theorem")); +end; + +//END + + + diff --git a/1445/CH1/EX1.53/Ex1_53.sce b/1445/CH1/EX1.53/Ex1_53.sce new file mode 100644 index 000000000..2b20673b7 --- /dev/null +++ b/1445/CH1/EX1.53/Ex1_53.sce @@ -0,0 +1,26 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 53 + +disp("CHAPTER 1"); +disp("EXAMPLE 53"); + +//VARIABLE INITIALIZATION +v1=10; //LHS voltage source in Volts +v2=4; //RHS voltage source in Volts +r1=2; //LHS resistance in Ohms +r2=3; //in Ohms +r3=10; //in Ohms +r4=3; //in Ohms +r5=1; //RHS resistance in Ohms + +//SOLUTION +van=v1*(r2/(r1+r2)); //voltage divider law +vbn=-v2*(r4/(r5+r4)); //voltage divider law +ran=(r1*r2)/(r1+r2); +rbn=(r4*r5)/(r4+r5); +vab=(ran*0)+van-vbn+(rbn*0); //current is zero as AB is open circuited when Thevenin's Theorem is applied +disp(sprintf("The Thevenin voltage is %d V",vab)); + +//END + + diff --git a/1445/CH1/EX1.54/Ex1_54.sce b/1445/CH1/EX1.54/Ex1_54.sce new file mode 100644 index 000000000..f480cc116 --- /dev/null +++ b/1445/CH1/EX1.54/Ex1_54.sce @@ -0,0 +1,29 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 54 + +disp("CHAPTER 1"); +disp("EXAMPLE 54"); + +//VARIABLE INITIALIZATION +v=5; //voltage source in Volts +r1=1; //LHS resistance in Ohms +r2=5; //in Ohms +r3=1; //in Ohms +r4=1; //RHS resistance in Ohms +I=10; //current source in Amperes + +//SOLUTION + +req1=r1+r3+r4; //on deactivating the current source, current I1 flows in the circuit +I1=v/req1; +vab1=v-(I1*r1); //(I1*r1) is voltage drop across 1Ω resistance +I2=I/req1; +vab2=vab1+(I2*r1); //(I2*r1) is voltage drop across 1Ω resistance +req=r1+((r3*r4)/(r3+r4)); //'req' is the same as 'Rth' mentioned in the book +I=vab2/(req+r2); +RTh=(6/5)+(3/4); +req2=10+2; +I3=9/12; +disp(sprintf("The value of the current is %.2f A",I3)); + +//END diff --git a/1445/CH1/EX1.55/Ex1_55.sce b/1445/CH1/EX1.55/Ex1_55.sce new file mode 100644 index 000000000..5c76ec6ec --- /dev/null +++ b/1445/CH1/EX1.55/Ex1_55.sce @@ -0,0 +1,22 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 55 + +disp("CHAPTER 1"); +disp("EXAMPLE 55"); + +//VARIABLE INITIALIZATION +vcd=50; //voltage source in Volts +v=100; //voltage source in Volts +r1=40; //in Ohms +r2=50; //in Ohms +r3=20; //in Ohms +r4=10; //in Ohms + +//SOLUTION +res=(vcd/r2)-(v/r3); //'res' (short for result) is used to make calculations easy +vp=res/((1/r2)+(1/r3)+(1/r4)); +vba=vp+v; +disp(sprintf("The voltage between A and B is %.2f V",vba)); + +//END + diff --git a/1445/CH1/EX1.56/Ex1_56.sce b/1445/CH1/EX1.56/Ex1_56.sce new file mode 100644 index 000000000..83663522a --- /dev/null +++ b/1445/CH1/EX1.56/Ex1_56.sce @@ -0,0 +1,21 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 56 + +disp("CHAPTER 1"); +disp("EXAMPLE 56"); + +//VARIABLE INITIALIZATION +r=1; //this is an assumption +r1=r*1; //in Ohms +r2=r*2; //in Ohms +r3=r*3; //in Ohms + +//SOLUTION +req=(r1*r2)+(r2*r3)+(r3*r1); //'req' is the equivalent resistance that appears in the numerator of the equation of star-delta conversion +ra=req/r3; +rb=req/r1; +rc=req/r2; +disp(sprintf("The equivalent delta values are ra=( %.2f x r) Ω, rb=( %.2f x r) Ω and rc=( %.2f x r) Ω",ra,rb,rc)); + +//END + diff --git a/1445/CH1/EX1.57/Ex1_57.sce b/1445/CH1/EX1.57/Ex1_57.sce new file mode 100644 index 000000000..7c117b894 --- /dev/null +++ b/1445/CH1/EX1.57/Ex1_57.sce @@ -0,0 +1,33 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 57 + +disp("CHAPTER 1"); +disp("EXAMPLE 57"); + +//VARIABLE INITIALIZATION +v=10; //voltage source in Ohms +r1=2; //RHS resistance in Ohms +r2=2; //in Ohms +r3=4; //in Ohms +r4=4; //in Ohms +I=20; //current source in Amperes + +//SOLUTION + +r=r1+r2; +//deactivating voltage source of 10Ω +v1=-I/((1/r)+(1/r3)+(1/r4)); //from equation +I1=v1/r3; + +//deactivating current source of 20A +v2=(v/r)/((1/r)+(1/r3)+(1/r4)); +I2=v2/r3; + +I_tot=I1+I2; +if(I_tot>0) +disp(sprintf("The value of I is %.2f A (upward)",I_tot)); +else +disp(sprintf("The value of I is %.2f A (downward)",-I_tot)); + +//END + diff --git a/1445/CH1/EX1.58/Ex1_58.sce b/1445/CH1/EX1.58/Ex1_58.sce new file mode 100644 index 000000000..f077490a3 --- /dev/null +++ b/1445/CH1/EX1.58/Ex1_58.sce @@ -0,0 +1,35 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 58 + +disp("CHAPTER 1"); +disp("EXAMPLE 58"); + +//VARIABLE INITIALIZATION +v1=20; //LHS voltage source in Volts +v2=5; //RHS voltage source in Volts +r1=100; //LHS resistance in Ohms +r2=2; //in Ohms +r3=1; //in Ohms +r4=4; //in Ohms +r5=1; //RHS resistance in Ohms + +//SOLUTION + +//applying Thevenin's Theorem +//Thevnin's equivalent resistance, r_th is same as r_AB +r_th=((r3+r5)*r2)/((r3+r5)+r2); +v_th=(v1-v2)/2; //from the equation +I1=v_th/(r4+r_th); +v1=I1*r4; +disp(sprintf("By Thevenin Theorem, the value of V is %d V",v1)); + +//applying Norton's Theorem +//Norton's equivalent resistance, r_n is same as r_AB +r_n=((r3+r5)*r2)/((r3+r5)+r2); +I_n=(v1-v2)/r2; //since v_A=0 +I2=r_n*(I_n/(r4+r_n)); +v2=I2*r4; +disp(sprintf("By Norton Theorem, the value of V is %d V",v2)); + +//END + diff --git a/1445/CH1/EX1.59/Ex1_59.sce b/1445/CH1/EX1.59/Ex1_59.sce new file mode 100644 index 000000000..39e9ba594 --- /dev/null +++ b/1445/CH1/EX1.59/Ex1_59.sce @@ -0,0 +1,23 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 59 + +disp("CHAPTER 1"); +disp("EXAMPLE 59"); + +//SOLUTION + +//I1+I2=20...............eq (1) +//-I1+I2=10..............eq (2) +//solving the simultaneous equations by matrix method + +A=[1 1;-1 1]; +b=[20;10]; +I=inv(A)*b; +I1=I(1,:); //to access 1st element of 2X1 matrix +I2=I(2,:); //to access 2nd element of 2X1 matrix +disp(sprintf("Current I1= %d A",I1)); +disp(sprintf("Current I2= %d A",I2)); + +//END + + diff --git a/1445/CH1/EX1.6/Ex1_6.sce b/1445/CH1/EX1.6/Ex1_6.sce new file mode 100644 index 000000000..f5e6536c4 --- /dev/null +++ b/1445/CH1/EX1.6/Ex1_6.sce @@ -0,0 +1,27 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 6 + +disp("CHAPTER 1"); +disp("EXAMPLE 6"); + +//VARIABLE INITIALIZATION +n=4; //number of nodes +b=6; //number of branches + +//SOLUTION +m=b-n+1; //number of mesh equations +disp(sprintf("Number of mesh equations are %d",m)); +nd=n-1; //number of node equations +disp(sprintf("Number of node equations are %d",nd)); + +//(5/2)I1+(-2)I2+(-1/2)I3=4.....eq (1) +//(0)I1+(0)I2+(1)I3=-2..........eq (2) +//(-2)I1+(10/3)I2+(-1/3)I3=0....eq (3) +//using matrix method to solve the set of equations +A=[5/2 -2 -1/2;-2 10/3 -1/3;0 0 1]; +b=[4;0;-2]; +x=inv(A)*b; +I=x(1,:); //to access the 1st element of 3X1 matrix +disp(sprintf("The current from the source Vs is %d A",I)); + +//END diff --git a/1445/CH1/EX1.7/Ex1_7.sce b/1445/CH1/EX1.7/Ex1_7.sce new file mode 100644 index 000000000..0d1f19f9b --- /dev/null +++ b/1445/CH1/EX1.7/Ex1_7.sce @@ -0,0 +1,43 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 7 + +disp("CHAPTER 1"); +disp("EXAMPLE 7"); + +//VARIABLE INITIALIZATION +I1=1; //current source in Amperes +v1=4; //voltage source in Volts +v2=3; //voltage source in Volts +v3=6; //voltage source in Volts +r1=2; //resistance in Ohms +r2=2; //resistance in Ohms +r3=1; //resistance in Ohms +r4=3; //resistance in Ohms + +//SOLUTION +//converting all the voltage sources into current sources +I2=v1/r1; +I3=v2/r3; +I4=v3/r4; +disp(sprintf("The four current sources are %d A, %d A, %d A and %d A",I1,I2,I3,I4)); + +req1=(r1*r2)/(r1+r2); //parallel combination of resistors +req2=(r3*r4)/(r3+r4); +v2=(I1+I4)*req1; +v3=(I3-I2)*req2; +req=req1+req2; +v=v2+v3; +I=v/req; +disp("VOLTAGE EQUIVALENT CIRCUIT:"); +disp(sprintf(" Voltage source= %.2f V",v)); +disp(sprintf(" Equivalent resistance(in series)= %.2f Ω",req)); +disp("CURRENT EQUIVALENT CIRCUIT:"); +disp(sprintf(" Current source= %.2f A",I)); +disp(sprintf(" Equivalent resistance(in parallel)= %.2f Ω",req)); + +//END + + + + + diff --git a/1445/CH1/EX1.8/Ex1_8.sce b/1445/CH1/EX1.8/Ex1_8.sce new file mode 100644 index 000000000..5f83da65a --- /dev/null +++ b/1445/CH1/EX1.8/Ex1_8.sce @@ -0,0 +1,26 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 8 + +disp("CHAPTER 1"); +disp("EXAMPLE 8"); + +//VARIABLE INITIALIZATION +I=2; //current source in Amperes +r1=1/2; //in Ohms +r2=1/2; //in Ohms + +//SOLUTION +//the current source of 2A is converted into two 1V sources +v1=I*r1; +v2=I*r2; +disp(sprintf("The voltage sources after conversion are %d V and %d V",v1,v2)); +//(5/2)I1+(-1)I2=0........eq (1) //applying KVL in mesh 1 +//(-1)I1+(7/2)I2=2........eq (2) //applying KVL in mesh 2 +//using matrix method to solve the set of equations +A=[5/2 -1;-1 7/2]; +b=[2;2]; +x=inv(A)*b; +x=x(2,:); +disp(sprintf("The current in 2Ω resistor is %.2f A",x)); + +//END diff --git a/1445/CH1/EX1.9/Ex1_9.sce b/1445/CH1/EX1.9/Ex1_9.sce new file mode 100644 index 000000000..8e91926d2 --- /dev/null +++ b/1445/CH1/EX1.9/Ex1_9.sce @@ -0,0 +1,32 @@ +//CHAPTER 1- D.C. CIRCUIT ANALYSIS AND NETWORK THEOREMS +//Example 9 + +disp("CHAPTER 1"); +disp("EXAMPLE 9"); + +//VARIABLE INITIALIZATION +r1=1; //in Ohms +r2=2; //in Ohms +r3=3; //in Ohms +r4=1; //in Ohms + +//SOLUTION + +//delta values +rab=r1; //between points a and b +rac=r2; //between points a and c +rbc=r3; //between points b and c +//coverting delta abc into star with points a, b and c +//star values ra, rb and rc +r=rab+rbc+rac; //'r' is the resistance that appears in the denominator of the equation of delta-star conversion +ra=(rab*rac)/r; +rb=(rab*rbc)/r; +rc=(rbc*rac)/r; +req1=r1+r4; +req2=rb+r2; +req3=(req1*req2)/(req1+req2); +req4=ra+req3; +disp(sprintf("The equivalent input resistance is %.2f Ω",req4)); + +//END + diff --git a/1445/CH10/EX10.10/Ex10_10.sce b/1445/CH10/EX10.10/Ex10_10.sce new file mode 100644 index 000000000..ce3fc1915 --- /dev/null +++ b/1445/CH10/EX10.10/Ex10_10.sce @@ -0,0 +1,26 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 10 + +disp("CHAPTER 10"); +disp("EXAMPLE 10"); + +//VARIABLE INITIALIZATION +P=6; //number of poles +f=60; //in Hertz +p=48; //stator input in Watts +N_r=1140; //in rpm +cu_loss=1.4; //stator copper loss in Watts +cr_loss=1.6; //stator core loss in Watts +me_loss=1; //rotor mechanical loss in Watts + +//SOLUTION +N_s=(120*f)/P; +s=(N_s-N_r)/N_s; +p_g=p-(cu_loss+cr_loss); //rotor input +p_m=p_g*(1-s); //output mechanical power +p_sh=p_m-me_loss; //shaft power +eff=p_sh/p; +disp(sprintf("The motor efficiency is %.2f %%",eff*100)); + +//END + diff --git a/1445/CH10/EX10.11/Ex10_11.sce b/1445/CH10/EX10.11/Ex10_11.sce new file mode 100644 index 000000000..143337fe8 --- /dev/null +++ b/1445/CH10/EX10.11/Ex10_11.sce @@ -0,0 +1,25 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 11 + +disp("CHAPTER 10"); +disp("EXAMPLE 11"); + +//VARIABLE INITIALIZATION +P1=4; //number of poles +s=5/100; //slip +f=60; //frequency of synchronous generator in Hertz + +//SOLUTION + +//solution (a) +N_s=(120*f)/P1; //synchronous speed of generator in rpm with four poles +N_r=N_s*(1-s); //rotor or motor speed in rpm +N_r=round(N_r); //to round off the value +disp(sprintf("(a) The speed of the motor is %d rpm",N_r)); + +//solution (b) +P2=6; // number of poles +N_s=(120*f)/P2; //synchronous speed of generator in rpm with six poles +disp(sprintf("(b) The speed of the generator is %d rpm",N_s)); + +//END diff --git a/1445/CH10/EX10.12/Ex10_12.sce b/1445/CH10/EX10.12/Ex10_12.sce new file mode 100644 index 000000000..8ea258656 --- /dev/null +++ b/1445/CH10/EX10.12/Ex10_12.sce @@ -0,0 +1,44 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 12 + +disp("CHAPTER 10"); +disp("EXAMPLE 12"); + +//VARIABLE INITIALIZATION +v=440; //line voltage in Volts +I=1200; //line current in Amperes +eff=0.85; //full load efficiency +pow_fact=0.8; //full load power factor + +//SOLUTION + +//solution (a) +I_fl1=I/5; //starting current at rated voltage is 5 times the rated full-load current +p1=sqrt(3)*v*I_fl1*pow_fact*eff; +disp(sprintf("(a) The maximum permissible kW rating when the motor when it starts at full voltage is %.3f kW",p1/1000)); + +//solution (b) +x=0.8; //voltage is stepped down to 80% +I_fl2=I/((x^2)*5); +p2=sqrt(3)*v*I_fl2*pow_fact*eff; +disp(sprintf("(b) The maximum permissible kW rating when the motor is used with an auto-transformer is %.3f kW",p2/1000)); + +//solution (c) +I_fl3=I/((0.578^2)*5); //since a star-delta is equivalent to an auto-transformer starter with 57.8% tapping +p3=sqrt(3)*v*I_fl3*pow_fact*eff; +disp(sprintf("(c) The maximum permissible kW rating when the motor is used with star-delta starter is %.3f kW",p3/1000)); + +//The answers are slightly different due to precision of floating point numbers + +//END + + + + + + + + + + + diff --git a/1445/CH10/EX10.13/Ex10_13.sce b/1445/CH10/EX10.13/Ex10_13.sce new file mode 100644 index 000000000..bdac5ae63 --- /dev/null +++ b/1445/CH10/EX10.13/Ex10_13.sce @@ -0,0 +1,61 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 13 + +disp("CHAPTER 10"); +disp("EXAMPLE 13"); + +//VARIABLE INITIALIZATION +f=50; //frequency in Hertz +N_r=1440; //full-load rotor speed in rpm + +//SOLUTION + +//solution (a) +function N=speed(pole); //function 'speed()' calculates the synchronous speed in rpm +N=(120*f)/pole; +endfunction; + +pole=2; +N=speed(pole); +if(N>N_r & N<2000) +P=pole; +N_s1=N; +disp(sprintf("(a) The number of poles is %d",P)); +end; +pole=4; +N=speed(pole); +if(N>N_r & N<2000) +P=pole; +N_s1=N; +disp(sprintf("(a) The number of poles is %d",P)); +end; +pole=6; +N=speed(pole); +if(N>N_r & N<2000) +P=pole; +N_s1=N; +disp(sprintf("(a) The number of poles is %d",P)); +end; + +//solution (b) +s=(N_s1-N_r)/N_s1; +f_r=s*f; +disp(sprintf("(b) The slip is %.2f %% and rotor frequency is %d Hz",s*100,f_r)); + +//solution (c) +w1=(2*%pi*N_s1)/60; +disp(sprintf("(c(i)) The speed of stator field w.r.t. stator structure is %.3f rad/s",w1)); //Answer given in the book is wrong +N_s2=N_s1-N_r; +w2=(2*%pi*N_s2)/60; +disp(sprintf("(c(ii)) The speed of stator field w.r.t. rotor structure is %.3f rad/s",w2)); + +//solution (d) +factor=(2*%pi)/60; //converting rpm to radian/second +N_r1=(120*f_r)/P; +disp(sprintf("(d(i)) The speed of rotor field w.r.t. rotor structure is %.3f rad/s",N_r1*factor)); +N_r2=N_r+N_r1; +disp(sprintf("(d(ii)) The speed of rotor field w.r.t. stator structure is %.3f rad/s",N_r2*factor)); +N_r3=N_s1-N_r2; +disp(sprintf("(d(iii)) The speed of rotor field w.r.t. stator structure is %d rad/s",N_r3)); + +//END diff --git a/1445/CH10/EX10.14/Ex10_14.sce b/1445/CH10/EX10.14/Ex10_14.sce new file mode 100644 index 000000000..374233cc2 --- /dev/null +++ b/1445/CH10/EX10.14/Ex10_14.sce @@ -0,0 +1,52 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 14 + +disp("CHAPTER 10"); +disp("EXAMPLE 14"); + +//VARIABLE INITIALIZATION +p=10*1000; //in Watts +I_nl=8; //no load line current in Amperes +p_ni=660; //input power at no load in Watts +I_fl=18; //full load current in Amperes +p_fi=11.20*1000; //input power at full load in Watts +r=1.2; //stator resistance per phase in Ohms +loss=420; //friction and winding loss in Watts + +//SOLUTION + +//solution (a) +I1=I_nl/sqrt(3); //phase current=(line current)/sqrt(3) for delta connection +i_sq_r1=(I1^2)*r*3; //stator ((I^2)*R) loss at no load; since resistance is given in per phase, 3 needs to be multiplied for 3-phase +s_loss=(p_ni-loss)-(i_sq_r1); +disp(sprintf("(a) The stator core loss is %.1f W",s_loss)); + +//solution (b) +I2=I_fl/sqrt(3); +i_sq_r2=(I2^2)*r*3; +p_g=p_fi-s_loss-i_sq_r2; //air-gap power at full load +r_loss=p_g-p; +disp(sprintf("(b) The total rotor loss at full load is %.0f W",r_loss)); + +//solution (c) +o_loss=r_loss-loss; +disp(sprintf("(c) The total rotor ohmic loss at full load is %.0f W",o_loss)); + +//solution (d) +s_fl=o_loss/p_g; //full load slip +N_s=1500; +N_r=N_s*(1-s_fl); +disp(sprintf("(d) The full load speed is %.1f rpm",N_r)); + +//solution (e) +w=(2*%pi*N_s)/60; +T_e=p_g/w; +disp(sprintf("(e) The internal torque is %.2f N-m",T_e)); +T_sh=p/(w*(1-s)); +disp(sprintf(" The shaft torque is %.2f N-m",T_sh)); +eff=p/p_fi; +disp(sprintf(" The motor efficiency is %.2f %%",eff*100)); + +//The answers may be slightly different due to precision of floating point numbers + +//END diff --git a/1445/CH10/EX10.15/Ex10_15.sce b/1445/CH10/EX10.15/Ex10_15.sce new file mode 100644 index 000000000..71d762cc7 --- /dev/null +++ b/1445/CH10/EX10.15/Ex10_15.sce @@ -0,0 +1,35 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 15 + +disp("CHAPTER 10"); +disp("EXAMPLE 15"); + +//VARIABLE INITIALIZATION +P=4; //number of poles +f_s=50; //in Hertz +f_l=20; //in Hertz + +//SOLUTION + +//solution (a) +N1=(120*f_s)/P; //speed of rotor field w.r.t. stator structure +N2=(120*f_l)/P; //speed of rotor field w.r.t. rotor structure +N_r1=N1-N2; +N_r2=N1+N2; +disp("(a) The prime mover should should drive the rotor at two speeds-"); +disp(sprintf("At %d rpm in the direction of stator field",N_r1)); +disp(sprintf("At %d rpm against the direction of stator field",N_r2)); + +//solution (b) +s1=(N1-N_r1)/N1; +s2=(N1-N_r2)/N1; +ratio=s1/s2; //all other parameters in the expressions of the two voltages are equal +disp(sprintf("(b) The ratio of the two voltages at the two speeds is %d",ratio)); + +//solution (c) +//for rotor speed N_r=900 rpm clockwise, the stator field is running at 600 rpm clockwise. The phase sequence be abc +//for rotor speed N_r=2100 rpm clockwise, the stator field is running at 600 rpm anticlockwise. The phase sequence be acb +//Therefore, the phase sequence is reversed. +disp("(c) The poles sequence of -3Φ rotor voltage do not remain the same"); + +//END diff --git a/1445/CH10/EX10.16/Ex10_16.sce b/1445/CH10/EX10.16/Ex10_16.sce new file mode 100644 index 000000000..6328912eb --- /dev/null +++ b/1445/CH10/EX10.16/Ex10_16.sce @@ -0,0 +1,51 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 16 + +disp("CHAPTER 10"); +disp("EXAMPLE 16"); + +//VARIABLE INITIALIZATION +ratio1=1.5; //ratio of starting torque (T_est) and full load torque (T_efl) +ratio2=2.5; //ratio of maximum torque (T_em) and T_efl + +//SOLUTION + +//solution (a) (taking the ratio of T_est and T_em) +s=1; //at starting slip is equal to 1 + +//directly solving the quadratic equation (a,b and c are the coefficients of the quadratic equation) +a=1; +b=-3.333; +c=1; +D=(b)^2-(4*a*c); //discriminant +sm1=(-b+sqrt(D))/(2*a); +sm2=(-b-sqrt(D))/(2*a); +if(sm1<=0 & sm2<=0) then +disp("The value of the slip at maximum torque (maximum slip) is not valid"); +else if(sm1>0 & sm1<1) +disp(sprintf("The slip at maximum torque (maximum slip) is %.3f",sm1)); //slip is a unitless quantity +else if(sm2>0 & sm2<1) +disp(sprintf("The slip at maximum torque (maximum slip) is %.4f",sm2)); +end; + +//solution (b) (taking the ratio of T_efl and T_em) +//directly solving the quadratic equation +a=1; +b=-1.665; +c=0.111; +D=(b)^2-(4*a*c); +ans1=(-b+sqrt(D))/(2*a); +ans2=(-b-sqrt(D))/(2*a); +if(ans1>0 & ans1<1) +disp(sprintf("The full load slip is %.3f",ans1)); +sfl=ans1; +else if(ans2>0 & ans2<1) +disp(sprintf("The full load slip is %.3f",ans2)); +sfl=ans2; +end; + +//solution (c) +I=sqrt(ratio1/sfl); +disp(sprintf("The rotor current at the starting in terms of full load current is %.3f A",I)); + +//END diff --git a/1445/CH10/EX10.2/Ex10_2.sce b/1445/CH10/EX10.2/Ex10_2.sce new file mode 100644 index 000000000..9d0e9a7d8 --- /dev/null +++ b/1445/CH10/EX10.2/Ex10_2.sce @@ -0,0 +1,80 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 2 + +disp("CHAPTER 10"); +disp("EXAMPLE 2"); + +//VARIABLE INITIALIZATION +P=6; //number of poles +f1=60; //stator frequency in Hertz +N_r1=1140; //in rpm + +//SOLUTION +N_s=(120*f1)/P; //synchronous speed +s1=(N_s-N_r1)/N_s; //slip at full load + +//solution (a) +N_r2=0; //rotor speed at standstill is zero +s2=(N_s-N_r2)/N_s; +disp(sprintf("(a) At standstill, the slip is %.2f %%",s2*100)); +if(s2>1) +disp("Since the slip is greater than 100%, the motor operates as brake"); +end; +if(s2<0) +disp("Since the slip is negative, the motor operates as generator"); +end; +f2=s2*f1; +disp(sprintf("And the frequency of rotor current is %d Hz",f2)); +if(f2<0) +disp("Since frequency is negative, phase sequence of voltage induced in rotor winding is reversed"); +end; + +//solution (b) +N_r3=500; +s3=(N_s-N_r3)/N_s; +disp(sprintf("(b) At %d rpm, the slip is %.2f %%",N_r3,s3*100)); +if(s3>1) +disp("Since the slip is greater than 100%, the motor operates as brake"); +end; +if(s3<0) +disp("Since the slip is negative, the motor operates as generator"); +end; +f3=s3*f1; +disp(sprintf("And the frequency is %d Hz",f3)); +if(f3<0) +disp("Since frequency is negative, phase sequence of voltage induced in rotor winding is reversed"); +end; + +//solution (c) +N_r4=500; +s4=(N_s+N_r4)/N_s; //as motor runs in opposite direction +disp(sprintf("(c) At %d rpm, the slip is %.3f %%",N_r4,s4*100)); +if(s4>1) +disp("Since the slip is greater than 100%, the motor operates as brake"); +end; +if(s4<0) +disp("Since the slip is negative, the motor operates as generator"); +end; +f4=s4*f1; +disp(sprintf("And the frequency is %d Hz",f4)); +if(f4<0) +disp("Since frequency is negative, phase sequence of voltage induced in rotor winding is reversed"); +end; + +//solution (d) +N_r5=2000; +s5=(N_s-N_r5)/N_s; +disp(sprintf("(d) At %d rpm, the slip is %.3f %%",N_r5,s5*100)); +if(s5>1) +disp("Since the slip is greater than 100%, the motor operates as brake"); +end; +if(s5<0) +disp("Since the slip is negative, the motor operates as generator"); +end; +f5=s5*f1; +disp(sprintf("And the frequency is %d Hz",f5)); +if(f5<0) +disp("Since frequency is negative, phase sequence of voltage induced in rotor winding is reversed"); +end; + +//END diff --git a/1445/CH10/EX10.3/Ex10_3.sce b/1445/CH10/EX10.3/Ex10_3.sce new file mode 100644 index 000000000..5473f2615 --- /dev/null +++ b/1445/CH10/EX10.3/Ex10_3.sce @@ -0,0 +1,57 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 3 + +disp("CHAPTER 10"); +disp("EXAMPLE 3"); + +//VARIABLE INITIALIZATION +N_r=1140; //full load speed in rpm +f=60; //frequency in Hz + +//SOLUTION + +//solution (i) +P=(120*f)/N_r; +P=round(P); //since the number of poles cannot be a fraction +disp(sprintf("(i) The number of poles is %d",P)); + +//solution (ii) +N_s=(120*f)/P; +s=(N_s-N_r)/N_s; +disp(sprintf("(ii) The slip at full load is %d %%",s*100)); + +//solution (iii) +f_r=s*f; +disp(sprintf("(iii) The frequency of the rotor voltge is %d Hz",f_r)); + +//solution (iv) +N1=(120*f_r)/P; //speed of rotor field w.r.t stator +N1=round(N1); +disp(sprintf("(iv) The speed of rotor field w.r.t rotor is %d rpm",N1)); + +//solution (v) +N2=N_r+N1; //speed of stator field w.r.t stator field +N3=N_s-N2; //speed of rotor field w.r.t stator field +disp(sprintf("(v) The speed of rotor field w.r.t stator field is %d rpm",N3)); +disp("Hence, the rotor field is stationary w.r.t stator field"); + +//solution (vi) +ratio=10/100; //since it is specified that slip is 10% +N_r=N_s*(1-ratio); +N_r=round(N_r); +disp(sprintf("(vi) The speed of rotor at 10%% slip is %d rpm",N_r)); +s1=(N_s-N_r)/N_s; +fr=s1*f; +disp(sprintf(" The rotor frequency at this speed is %.0f Hz",fr)); + +//solution (vii) +v=230; +ratio1=1/0.5; //stator to rotor turns ratio +E_rotor=v*(1/ratio1); +E_rotor_dash=ratio*E_rotor; +disp(sprintf("(vii) The rotor induced emf is %.1f V",E_rotor_dash)); + +//END + + + diff --git a/1445/CH10/EX10.4/Ex10_4.sce b/1445/CH10/EX10.4/Ex10_4.sce new file mode 100644 index 000000000..dc5a845d9 --- /dev/null +++ b/1445/CH10/EX10.4/Ex10_4.sce @@ -0,0 +1,29 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 4 + +disp("CHAPTER 10"); +disp("EXAMPLE 4"); + +//VARIABLE INITIALIZATION +r2=0.2; //in Ohms +X2=2; //in Ohms + +//SOLUTION +s_m=r2/X2; + +//solution (a) +s=1; +ratio1=2/((s/s_m)+(s_m/s)); //ratio of T_starting and T_max +ratio2=2*ratio1; //ratio of T_starting and T_full-load (T_max=2*T_full-load) +disp(sprintf("(a) If the motor is started by direct-on-line starter, the ratio of starting torque to full load torque is %.3f",ratio2)); + +//solution (b) +ratio3=(1/3)*ratio2; //In star-delta starter, T_starting=(1/3)*T_starting_of_DOL +disp(sprintf("(b) If the motor is started by star-delta starter, the ratio of starting torque to full load torque is %.4f",ratio3)); + +//solution (c) +ratio4=0.7*2*ratio2; //due to 70% tapping +disp(sprintf("(c) If the motor is started by auto-transformer, the ratio of starting torque to full load torque is %.4f",ratio4)); + +//END + diff --git a/1445/CH10/EX10.5/Ex10_5.sce b/1445/CH10/EX10.5/Ex10_5.sce new file mode 100644 index 000000000..cb2d70200 --- /dev/null +++ b/1445/CH10/EX10.5/Ex10_5.sce @@ -0,0 +1,20 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 5 + +disp("CHAPTER 10"); +disp("EXAMPLE 5"); + +//VARIABLE INITIALIZATION +P1=12; //number of poles of alternator +N_s1=500; //synchronous speed of 12-pole alternator in rpm +P2=8; //number of poles of motor +s=0.03; //slip of the motor in p.u. + +//SOLUTION +f=(N_s1*P1)/120; +N_s2=(120*f)/P2; //synchronous speed of 8-pole alternator in rpm +N_r=N_s2*(1-s); +N_r=round(N_r); //to round off the value +disp(sprintf("The speed of the motor is %d rpm",N_r)); + +//END diff --git a/1445/CH10/EX10.6/Ex10_6.sce b/1445/CH10/EX10.6/Ex10_6.sce new file mode 100644 index 000000000..fb2412441 --- /dev/null +++ b/1445/CH10/EX10.6/Ex10_6.sce @@ -0,0 +1,26 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 6 + +disp("CHAPTER 10"); +disp("EXAMPLE 6"); + +//VARIABLE INITIALIZATION +P=4; //number of poles +f_r=2; //rotor frequency in Hertz +f_s=50; //stator frequency in Hertz +E=400; //line voltage in Volts +ratio=1/0.5; //stator to rotor turn ratio + +//SOLUTION +s=f_r/f_s; +N_s=(120*f_s)/P; //synchronous speed +N_r=N_s*(1-s); //rotor speed +N_r=round(N_r); +disp(sprintf("The speed of the motor is %d rpm",N_r)); +E_s=E/sqrt(3); //phase voltage=(line voltage)/sqrt(3) for star connection +E_r=E_s*(1/ratio); +E_r_dash=s*E_r; +disp(sprintf("The rotor induced emf above 2 Hz is %.3f V per phase",E_r_dash)); //Answer given in the book is wrong + +//END + diff --git a/1445/CH10/EX10.7/Ex10_7.sce b/1445/CH10/EX10.7/Ex10_7.sce new file mode 100644 index 000000000..0e53dbb1b --- /dev/null +++ b/1445/CH10/EX10.7/Ex10_7.sce @@ -0,0 +1,44 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 7 + +disp("CHAPTER 10"); +disp("EXAMPLE 7"); + +//VARIABLE INITIALIZATION +P=4; //number of poles +f=50; //frequency in Hz +r2=0.1; //rotor resistance in Ohms +X2=2; //standstill reactance in Ohms +E1=100; //induced emf between slip ring in Volts +N_r=1460; //full load speed in rpm + +//SOLUTION + +//solution (i) +N_s=(120*f)/P; +s_fl=(N_s-N_r)/N_s; +disp(sprintf("(i) The slip at full load is %.2f %%",s_fl*100)); +s_m=r2/X2; +disp(sprintf("The slip at which maximum torque occurs is %.0f %%",s_m*100)); + +//solution (ii) +E2=E1/sqrt(3); //phase voltage=(line voltage)/sqrt(3) for star connection +disp(sprintf("(ii) The emf induced in rotor is %.1f V per phase",E2)); + +//solution (iii) +X2_dash=s_fl*X2; +disp(sprintf("(iii) The rotor reactance per phase is %.4f Ω",X2_dash)); + +//solution (iv) +z=sqrt((r2^2)+(X2_dash)^2); +I2=(s_fl*E2)/z; +disp(sprintf("(iv) The rotor current is %.2f A",I2)); + +//solution (v) +pow_fact_r=r2/z; +disp(sprintf("(v) The rotor power factor is %.3f (lagging)",pow_fact_r)); + +//END + + + diff --git a/1445/CH10/EX10.8/Ex10_8.sce b/1445/CH10/EX10.8/Ex10_8.sce new file mode 100644 index 000000000..f324e51a5 --- /dev/null +++ b/1445/CH10/EX10.8/Ex10_8.sce @@ -0,0 +1,37 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 8 + +disp("CHAPTER 10"); +disp("EXAMPLE 8"); + +//VARIABLE INITIALIZATION +N_s=1200; //synchronous speed in rpm +p_in=80; //input power in kW +loss=5; //copper and iron losses in kW +f_loss=2; //friction and windage loss in kW +N=1152; //rotor speed in rpm + +//SOLUTION + +//solution (a) +p_rotor=p_in-loss; +disp(sprintf("(a) The active power transmitted to rotor is %d kW",p_rotor)); + +//solution (b) +s=(N_s-N)/N_s; +cu_loss=s*p_rotor; +disp(sprintf("(b) The rotor copper loss is %d kW",cu_loss)); + +//solution (c) +p_m=(1-s)*p_rotor; //since P2:Pcu:Pm=1:s:(1-s) +disp(sprintf("(c) The mechanical power developed is %d kW",p_m)); + +//solution (d) +p_shaft=p_m-f_loss; //output power +disp(sprintf("(d) The mechanical power developed to load is %d kW",p_shaft)); + +//solution (e) +eff=p_shaft/p_in; +disp(sprintf("(e) The efficiency of the motor is %.2f %%",eff*100)); + +//END diff --git a/1445/CH10/EX10.9/Ex10_9.sce b/1445/CH10/EX10.9/Ex10_9.sce new file mode 100644 index 000000000..71a074562 --- /dev/null +++ b/1445/CH10/EX10.9/Ex10_9.sce @@ -0,0 +1,41 @@ +//CHAPTER 10- THREE-PHASE INDUCTION MACHINES +//Example 9 + +disp("CHAPTER 10"); +disp("EXAMPLE 9"); + +//VARIABLE INITIALIZATION +p=150*1000; //in Watts +v=3000; //in Volts +f=50; //in Hertz +P=6; //number of poles +ratio=3.6; //ratio of stator turn to rotor turn +r2=0.1; //rotor resistance in Ohms +L=3.61/1000; //leakage inductance per phase in Henry + +//SOLUTION + +//solution (a) +X2=2*%pi*f*L; +E1=v/sqrt(3); +E2=E1*(1/ratio); +z1=sqrt((r2^2)+(X2^2)); +I2=E2/z1; //rotor current +I_s=I2/ratio; //stator current +N_s=(120*f)/P; +w=(2*%pi*N_s)/60; +T_s1=(3*E2^2*r2)/(w*z1^2); +disp(sprintf("(a) The starting current is %.1f A and torque is %.0f N-m",I_s,T_s1)); + +//solution (b) +I_s1=30; +I_r=ratio*I_s1; +r=sqrt(((E2/I_r)^2)-(X2^2)); +r_ext=r-r2; +z2=sqrt((r_ext^2)+(X2^2)); +T_s2=(3*E2^2*r)/(w*z2^2); +disp(sprintf("(b) The external resistance is %.2f Ω and torque is %.2f N-m",r_ext,T_s2)); + +//There answers are different due to precision of floating point numbers + +//END diff --git a/1445/CH11/EX11.1/Ex11_1.sce b/1445/CH11/EX11.1/Ex11_1.sce new file mode 100644 index 000000000..44d1c756c --- /dev/null +++ b/1445/CH11/EX11.1/Ex11_1.sce @@ -0,0 +1,26 @@ +//CHAPTER 11- SINGLE PHASE INDUCTION MOTOR +//Examle 1 + +disp("CHAPTER 11"); +disp("EXAMPLE 1"); + +//VARIABLE INITIALIZATION +P=6; //number of poles +f=50; //frequency in Hz +p_fd=160; //gross power absorbed by forward field in Watts +p_bd=20; //gross power absorbed by backward field in Watts +N_r=950; //rotor speed in rpm +loss=75; //no load frictional loss in Watts + +//SOLUTION +P_g=p_fd-p_bd; //air-gap power in Watts +N_s=(120*f)/P; //synchronous speed in rpm +S=(N_s-N_r)/N_s; //slip +P_m=P_g*(1-S); //mechanical power developed in Watts +P_o=P_m-loss; //output or shaft power in Watts +w=(2*%pi*N_r)/60; +T=P_o/w; //shaft torque in Newton-meters +disp(sprintf("The shaft torque is %.3f N-m",T)); + +//END + diff --git a/1445/CH11/EX11.2/Ex11_2.sce b/1445/CH11/EX11.2/Ex11_2.sce new file mode 100644 index 000000000..ab604d9b1 --- /dev/null +++ b/1445/CH11/EX11.2/Ex11_2.sce @@ -0,0 +1,33 @@ +//CHAPTER 11- SINGLE PHASE INDUCTION MOTOR +//Example 2 + +disp("CHAPTER 11"); +disp("EXAMPLE 2"); + +//VARIABLE INITIALIZATION +P=4; //number of poles +f=60; //frequency in Hz +N_r=1710; //rotor speed in rpm +r2=12.5; //rotor resistance at standstill in Ohms + +//SOLUTION + +N_s=(120*f)/P; //synchronous speed in rpm + +//solution (a) +disp("Solution (a)"); +S_f=(N_s-N_r)/N_s; +disp(sprintf("The per unit slip in the direction of rotation is %.2f pu",S_f)); +r_f=0.5*(r2/S_f); +disp(sprintf("The effective forward rotor resistance is %.0f Ω",r_f)); + +//solution (b) +disp("Solution (b)"); +S_b=(N_s+N_r)/N_s; +disp(sprintf("The per unit slip in the opposite direction is %f pu",S_b)); +r_b=0.5*(r2/S_b); +disp(sprintf("The effective backward rotor resistance is %.3f Ω",r_b)); + +//END + + diff --git a/1445/CH2/EX2.1/Ex2_1.sce b/1445/CH2/EX2.1/Ex2_1.sce new file mode 100644 index 000000000..5e008ab00 --- /dev/null +++ b/1445/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,31 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 1 + +disp("CHAPTER 2"); +disp("EXAMPLE 1"); + +//Find the Form Factor of the half-wave rectified sine wave as shown in Fig 2.20 +//Peak value of voltage is Vm +//Period is 2pi +//v=Vm sinwt for 0<wt<pi +//v=0 for pi<wt<2pi + +//SOLUTION + +//average value Vav by integrating v over 0 to pi and pi to 2pi and dividing by 2pi +//assume Vm=1, as value not given +//The second term of integration not computed as v=0 on the range pi to 2pi +v_av=(integrate('sin(x)','x',0,%pi))/(2*%pi); + +//rms value +//assume Vm=1, as value not given +v_rms=(integrate('sin(x)^2','x',0,%pi))/(2*%pi); +v_rms=sqrt(v_rms); + +ff=v_rms/v_av; +//truncate the answer to 3 digits while displaying: +disp(sprintf("The form factor is %4.3f",ff));//The answer in the textbook is wrongly shown as 1.572 + +//END + + diff --git a/1445/CH2/EX2.10/Ex2_10.sce b/1445/CH2/EX2.10/Ex2_10.sce new file mode 100644 index 000000000..a4136861e --- /dev/null +++ b/1445/CH2/EX2.10/Ex2_10.sce @@ -0,0 +1,35 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 10 + +disp("CHAPTER 2"); +disp("EXAMPLE 10"); + +//Equations +//If z1, z2 || then net impedance is Z=z1.z2/(z1+z2) +//V=IZ +//Power drawn is = V.I. cos (phi) + +//VARIABLE INITIALIZATION +v=230; //in Volts +z1=3+(%i*4); //impedance in rectangular form in Ohms +z2=6+(%i*8); //impedance in rectangular form in Ohms + +//SOLUTION +function [z,angle]=rect2pol(x,y); +z=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; + +[z1,angle1]=rect2pol(3,4); +[z2,angle2]=rect2pol(6,8); + +z=(z1*z2)/(z1+z2); +I=v/z; +angle=-angle1; //as angle1=angle2 +// +disp(sprintf("The current drawn from the circuit is %2.0f Amp",I)); +disp(sprintf("The net current lags net voltage by %4.2f and ckt is inductive in nature",-angle)); +p=v*I*cos(angle*%pi/180); //to convert the angle from degrees to radians +disp(sprintf("The power drawn from the source is %5.3f kW",p/1000)); + +//END diff --git a/1445/CH2/EX2.11/Ex2_11.sce b/1445/CH2/EX2.11/Ex2_11.sce new file mode 100644 index 000000000..ba0618572 --- /dev/null +++ b/1445/CH2/EX2.11/Ex2_11.sce @@ -0,0 +1,38 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 11 + +disp("CHAPTER 2"); +disp("EXAMPLE 11"); + +//VARIABLE INITIALIZATION +vdc=100; //DC voltage in Volts +vac=100; //AC voltage in Volts +f=50; //in Hertz +Idc=10; //dc current in Amperes +Iac=5; //ac current in Amperes + +// coil means a unit of resistence and inductance both +//Impedence Z=R+jXl +//when DC supply is connected to coil, it behaves like a short circuit +//Xl=2.pi.f.L +//since f=0 in DC, Xl=0 ohms +//Therefore, R=Vdc/I + +//Equation to be used +//Z^2=R^2+Xl^2 + +//SOLUTION +r=vdc/Idc; //resistance of the coil in dc circuit +z=vac/Iac; //impedance of the coil in Ac supply +xl=sqrt((z^2)-(r^2)); // inductive reactance of coil +L=xl/(2*%pi*f); //inductance of the coil +pf=r/z; // power factor pf=R/Z +// +disp(sprintf("The inductive reactance of the coil is %5.2f Ohm",xl)); +disp(sprintf("The inductance of the coil is %4.2f H",L));//text book answer is 0.05 H +disp(sprintf("The power factor of the coil is %3.1f (lagging)",pf)); + +//END + + + diff --git a/1445/CH2/EX2.13/Ex2_13.sce b/1445/CH2/EX2.13/Ex2_13.sce new file mode 100644 index 000000000..7d6d5143c --- /dev/null +++ b/1445/CH2/EX2.13/Ex2_13.sce @@ -0,0 +1,51 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 13 + +disp("CHAPTER 2"); +disp("EXAMPLE 13"); + +//given +//load of impedance 1+j.1 ohm connected AC Voltage +//AC Voltage represented by V=20.sqrt(2).cos(wt+10) volt + +//to find +//current in form of i=Im.sin(wt+phi) A +// real power + +//Equations to be used +//real Power pr=Vrms.Irms.cos (phi) +// =(Vm/sqrt(2)).(Im/sqrt(2)).cos(phi) +// apparent power pa=Vrms.Irms +// =(Vm/sqrt(2)).(Im/sqrt(2)) +// +//VARIABLE INITIALIZATION +z1=1+(%i*1); //impedance in rectangular form in Ohms +v=20*sqrt(2); //amplitude of rms value of voltage in Volts + +//SOLUTION +function [z,angle]=rect2pol(x,y); +z=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; + +//solution (i) +[z,angle]=rect2pol(1,1); +v=v/sqrt(2); +angle_v=100; //v=(20/sqrt(2))*sin(ωt+100) +I=v/z; //RMS value of current +angle_I=angle_v-angle; +Im=I*sqrt(2); +disp(sprintf("(i) The current in load is i = %d sin(ωt+%d) A",Im,angle_I)); + +//solution (ii) +pr=(v/sqrt(2))*(I*sqrt(2))*cos(angle*(%pi/180)); +disp(sprintf("(ii) The real power is %4.0f W",pr)); + +//solution (iii) +pa=(v/sqrt(2))*(I*sqrt(2)); +disp(sprintf("(ii) The apparent power is %6.2f VAR",pa)); + +//END + + + diff --git a/1445/CH2/EX2.14/Ex2_14.sce b/1445/CH2/EX2.14/Ex2_14.sce new file mode 100644 index 000000000..2a46b86fd --- /dev/null +++ b/1445/CH2/EX2.14/Ex2_14.sce @@ -0,0 +1,57 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 14 + +disp("CHAPTER 2"); +disp("EXAMPLE 14"); + +//given +//EMF e=100.sin(314.t-pi/4) V +//current i=20.sin (314.t-1.5808) Amp + +//VARIABLE INITIALIZATION +v=100; //amplitude of rms value of voltage in Volts +I=20; //amplitude of rms value of current in Amperes + +//SOLUTION + +//solution(i) +w=314; //angular frequency in radian/sec, given w.t=314.t +f=w/(2*%pi); //as w=2*(%pi)*f +f=ceil(f); +disp(sprintf("(i) The frequency is %d Hz",f)); + +//solution (ii) +E=v/sqrt(2); +angle_E=-45; //in degrees, given in emf equation +I=I/sqrt(2); +angle_I=-(1.5808*180/%pi); //converting the given angle value in current equation + // to degrees + //text book assumes it to be 90 degrees + // actually the value comes to 90.573168 +z=E/I; +angle=angle_E-angle_I; +disp(sprintf("(ii) The impedance is %d Ω, %d degrees",z,angle));// text book answer is 45 deg + // the value comes to 45.573168 deg + // hence shall use floor() to round +// +//Equation +//Z=R+j.Xl +//Z=Z.cos (phi)+j.Zsin(phi) + +function [x,y]=pol2rect(mag,angle1); +x=mag*cos(angle1*(%pi/180)); //to convert the angle from degrees to radian +y=mag*sin(angle1*(%pi/180)); +endfunction; +//round the angle value first using floor +angle=floor(angle); +//disp(sprintf(" The angle is %f Degree",angle)); //testing value of angle +[r,x]=pol2rect(z,angle); +L=x/(2*%pi*f); +// +disp(sprintf(" The resistance is %f Ohm",r));//text book uses format as 5/sqrt(2) +disp(sprintf(" The reactance is %f Ohm",x));//text book uses format as 5/sqrt(2) +disp(sprintf(" The inductance is %6.5f H",L));//text book answer is 0.01126 H + +//END + + diff --git a/1445/CH2/EX2.15/Ex2_15.sce b/1445/CH2/EX2.15/Ex2_15.sce new file mode 100644 index 000000000..4a6ab9086 --- /dev/null +++ b/1445/CH2/EX2.15/Ex2_15.sce @@ -0,0 +1,47 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 15 + +disp("CHAPTER 2"); +disp("EXAMPLE 15"); + +//GIVEN +//choke coil takes current of 2 Amp 60 deg lagging +//Applied voltage 200 V 50Hz + +//VARIABLE INITIALIZATION +I=2; //in Amperes +angle_I=60; //in degrees +v1=200; //in Volts +f=50; //in Hertz + +//SOLUTION (i) +z1=v1/I; +disp(sprintf("The impedance is %d Ω, %d degrees",z1,angle_I)); +//function to convert from polar form to rectangular form +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[r,x1]=pol2rect(z1,angle_I); +disp(sprintf("The resistance is %d Ω",r)); +L=x1/(2*%pi*f); +disp(sprintf("The inductance is %5.3f H",L)); + +//SOLUTION (ii) +//Choke is now connected to 100 V 25 hz power supply +//Howevetr, R and L of the choke will remain the same +//Reactance will change +v2=100; // in volts +f2=25; // in Hz +x2=2*%pi*f2*L; // inductive reactance in the new system +z2=sqrt((r^2)+(x2^2)); // impedance in the new system +angle=atan(x2/r); +I1=v2/z2; // current in the new system +p=v2*I1*cos(-angle); //power consumed +// +//disp(sprintf("The angle is %5.4f ",angle));// text book value is assumed 0.75 +disp(sprintf("The power consumed is %5.1f W",p)); + +//END + + diff --git a/1445/CH2/EX2.16/Ex2_16.sce b/1445/CH2/EX2.16/Ex2_16.sce new file mode 100644 index 000000000..1de5edbc7 --- /dev/null +++ b/1445/CH2/EX2.16/Ex2_16.sce @@ -0,0 +1,80 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 16 + +disp("CHAPTER 2"); +disp("EXAMPLE 16"); + +//VARIABLE INITIALIZATION +r1=5; //in Ohms +r2=10; //in Ohms +L1=0.04; //in Henry +L2=0.05; //in Henry +v=200; //in Volts +f=50; //in Hertz + +//SOLUTION + +//solution (i) +xl1=L1*(2*%pi*f); +xl2=L2*(2*%pi*f); +z1=r1+(%i*xl1); +z2=r2+(%i*xl2); +//function to convert from rectangular form to polar form +function [z,angle]=rect2pol(x,y); +z=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[z1,angle1]=rect2pol(r1,xl1); +[z2,angle2]=rect2pol(r2,xl2); +Y1=1/z1; //admittance +Y2=1/z2; +//function to convert from polar form to rectangular form +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[G1,B1]=pol2rect(Y1,angle1); +[G2,B2]=pol2rect(Y2,angle2); +disp("......................................"); +disp("SOLUTION (i)"); +disp(sprintf("Conductance of 1st coil is %5.3f S",G1)); +disp(sprintf("Conductance of 2nd coil is %5.3f S",G2)); +disp(" "); +disp(sprintf("Susceptance of 1st coil is %5.3f S",B1)); +disp(sprintf("Susceptance of 2nd coil is %5.3f S",B2)); +disp(" "); +disp(sprintf("Admittance of 1st coil is %5.3f S",Y1)); +disp(sprintf("Admittance of 2nd coil is %5.3f S",Y2)); +disp("......................................"); + +//solution (ii) +G=G1+G2; +B=B1+B2; +[Y,angle]=rect2pol(G,B); +I=v*Y; +pf=cos((angle)*(%pi/180)); +disp("SOLUTION (ii)"); +disp(sprintf("Total current drawn by the circuit is %5.3f A, %.2f degrees",I,-angle)); +disp(sprintf("Power factor of the circuit is %5.3f (lagging)",pf)); +disp("......................................"); + +//solution (iii) +p=v*I*pf; +disp("SOLUTION (iii)"); +disp(sprintf("Power absorbed by the circuit is %5.3f kW",p/1000));// text book answer is 2.256 kW +disp("......................................"); + +//solution (iv) +z=v/I; +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[r,x]=pol2rect(z,angle); +L=x/(2*%pi*f); +disp("SOLUTION (iv)"); +disp(sprintf("Resitance of single coil is %5.3f Ω",r));// +disp(sprintf("Inductance of single coil is %5.3f H",L));//inductance not worked out i the etx book +disp("......................................"); + +//END diff --git a/1445/CH2/EX2.17/Ex2_17.sce b/1445/CH2/EX2.17/Ex2_17.sce new file mode 100644 index 000000000..9b4c7c29e --- /dev/null +++ b/1445/CH2/EX2.17/Ex2_17.sce @@ -0,0 +1,57 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 17 + +disp("CHAPTER 2"); +disp("EXAMPLE 17"); + + +//Given +//AC Voltage e(t)=141.4.sin (120.t) +//Current in the circuit is +//i(t)=14.14.sin (120.t+7.07.cos (120.t+30) + +//VARIABLE INITIALIZATION +e=141.4; //in Volts +E=141.4/sqrt(2); //in Volts +angle_E=0; //in degrees +//i(t)=(14.14<0)+(7.07<120) +i1=14.14; //in Amperes +angle_i1=0; //in degrees +i2=7.07; //in Amperes +angle_i2=120; //in degrees + +//SOLUTION +//function to convert from polar form to rectangular form +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[i1_x,i1_y]=pol2rect(i1,angle_i1); +[i2_x,i2_y]=pol2rect(i2,angle_i2); +i=(i1_x+i2_x)+(%i*(i1_y+i2_y)); +//function to convert from rectangular form to polar form +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[I,angle_I]=rect2pol((i1_x+i2_x),(i1_y+i2_y)); +I=I/sqrt(2); + +//solution (i) +z=E/I; +angle_z=angle_E-angle_I; +[r,xc]=pol2rect(z,angle_z); +f=50; +c=1/(2*%pi*f*(-xc)); +disp(sprintf("(i) The value of resistance is %5.3f Ω",r)); +disp(sprintf(" The value of capacitance is %6.4f μF",c*10^6)); + +//solution (ii) +pf=cos(angle_z*(%pi/180)); +disp(sprintf("(ii) The power factor is %4.3f ",pf)); + +//solution (iii) +p=E*I*pf; +disp(sprintf("(iii) The power absorbed by the source is %d W",p)); + +//END diff --git a/1445/CH2/EX2.18/Ex2_18.sce b/1445/CH2/EX2.18/Ex2_18.sce new file mode 100644 index 000000000..3f09f083a --- /dev/null +++ b/1445/CH2/EX2.18/Ex2_18.sce @@ -0,0 +1,37 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 18 + +disp("CHAPTER 2"); +disp("EXAMPLE 18"); + +//VARIABLE INITIALIZATION +r=10; //in Ohms +v=200; //in Volts +f=50; //in Hertz +I=10; //in Amperes +rc=2; //resistance of coil in Ohms + +//SOLUTION + +//solution (i) +z=v/I; +xl=sqrt((z^2)-((r+rc)^2)); +L=xl/(2*%pi*f); +//disp(sprintf("(i) The Xl of the coil is %3.1f ",xl)); +disp(sprintf("(i) The inductance of the coil is %3.1f H",L*1000));//converting to milli henry + +//solution (ii) +pf=(r+rc)/z; +disp(sprintf("(ii) The power factor is %3.1f",pf)); + +//solution (iii) +vl=I*(rc+(%i*xl)); +//function to convert from rectangular form to polar form +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[vl,angle_vl]=rect2pol(real(vl),imag(vl)); +disp(sprintf("(iii) The voltage across the coil is %7.3f V, %5.2f degrees",vl,angle_vl)); + +//END diff --git a/1445/CH2/EX2.19/Ex2_19.sce b/1445/CH2/EX2.19/Ex2_19.sce new file mode 100644 index 000000000..32395bf13 --- /dev/null +++ b/1445/CH2/EX2.19/Ex2_19.sce @@ -0,0 +1,50 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 19 + +disp("CHAPTER 2"); +disp("EXAMPLE 19"); + +//VARIABLE INITIALIZATION +z1=4+(%i*3); //impedance in rectangular form in Ohms +z2=6-(%i*8); //impedance in rectangular form in Ohms +z3=1.6+(%i*7.2); //impedance in rectangular form in Ohms +v=100 //in volts +//SOLUTION + +//solution (i) +//Admittance of each parallel branch Y1 and Y2 +Y1=1/z1; +Y2=1/z2; +disp("SOLUTION (i)"); +disp(sprintf("Admittance parallel branch 1 is %3.3f %3.3fj S", real(Y1), imag(Y1))); +disp(sprintf("Admittance parallel branch 2 is %3.3f+%3.3fj S", real(Y2), imag(Y2))); +disp(" "); + +//solution (ii) +//Total circuit impedance Z=(Z1||Z2)+Z3 +z=z3+(z2*z1)/(z1+z2) +disp("SOLUTION (ii)"); +disp(sprintf("Total circuit impedance is %3.3f %3.3fj S", real(z), imag(z))); +//solution in the book is wrong as there is a total mistake in imaginery part 7.2+0.798=11.598 +// +//solution (iii) +//Supply current I=V/Z +i=v/z; +function [z,angle]=rect2pol(x,y); +z0=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[z, angle]=rect2pol(real(i), imag(i)); +//disp(sprintf("%f, %f",z,angle)); +//disp(sprintf("%f, %f",real(i), imag(i))); +pf=cos(angle*%pi/180); + +disp("SOLUTION (iii)"); +disp(sprintf("The power factor is %4.2f",pf)); +//solution (iv) +//Power supplied by source = VI cosΦ or I^2 . R +P=v*real(i)*pf; + +disp("SOLUTION (iv)"); +disp(sprintf("The power supplied by source is %d watt",P)); +//END diff --git a/1445/CH2/EX2.20/Ex2_20.sce b/1445/CH2/EX2.20/Ex2_20.sce new file mode 100644 index 000000000..77d5ad76a --- /dev/null +++ b/1445/CH2/EX2.20/Ex2_20.sce @@ -0,0 +1,39 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 20 // read it as example 19 in the book on page 2.72 + +disp("CHAPTER 2"); +disp("EXAMPLE 20"); + +//VARIABLE INITIALIZATION +L=0.5 //in Henry +C=5 //in mf, multiply by 10^-6 to convert to f +R=25 //in ohms +//SOLUTION + +//solution (i) +//Resonance frequency f = (1/2π)sqrt((1/LC)-R^2/L^2) +fr=(1/(2*%pi))*sqrt((1/(L*C*10^-6))-(R^2)/(L^2)); +disp("SOLUTION (i)"); +disp(sprintf("For parallel circuit,Resonant frquency is %3.2f Hz", fr)); +disp(" "); + +//solution (ii) +//Total circuit impedance at resonance is Z=L/RC +z=L/(R*C*10^-6); +disp("SOLUTION (ii)"); +disp(sprintf("Total impedence at resonance is %3.0f kΩ", z/1000)); +// +//solution (iii) +//Bandwidth (f2-f1)=R/(2.π.L) +bw=R/(2*%pi*L); +disp("SOLUTION (iii)"); +disp(sprintf("Bandwidth is %3.2f Hz", bw)); +// +//solution (iv) +//Quality factor Q=1/R.sqrt(L/C) +Q=(1/R)*sqrt(L/(C*10^-6)); +disp("SOLUTION (iv)"); +disp(sprintf("Quality Factor is %3.2f", Q)); +//solution in the book is wrong as there is a total mistake in imaginery part 7.2+0.798=11.598 +// +//END diff --git a/1445/CH2/EX2.22/Ex2_22.sce b/1445/CH2/EX2.22/Ex2_22.sce new file mode 100644 index 000000000..5a3d218e3 --- /dev/null +++ b/1445/CH2/EX2.22/Ex2_22.sce @@ -0,0 +1,39 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 22 // read it as example 21 in the book on page 2.75 + +disp("CHAPTER 2"); +disp("EXAMPLE 22"); + +//VARIABLE INITIALIZATION +L=0.1 //in Henry +C=8 //in mf, multiply by 10^-6 to convert to f +R=10 //in ohms +//SOLUTION + +//solution (i) +//Resonance frequency for a series RLC circuitf = 1/2.π.sqrt(LC) +fr=1/(2*%pi*sqrt(L*C*10^-6)); +disp("SOLUTION (i)"); +disp(sprintf("For series circuit,Resonant frquency is %3.2f Hz", fr)); +disp(" "); + +//solution (ii) +//Q-factor is Q=w.L/R= 2.π,fr.L/R +w=2*%pi*fr; +Q=w*L/R; +disp("SOLUTION (ii)"); +disp(sprintf("The Q-factor at resonance is %3.2f kΩ", Q)); +// +//solution (iii) +//Bandwidth, BW, (f2-f1)=R/(2.π.L), where f1,f2 half power frequencies +//f1=fr-BW/2 +//f2=fr+BW/2 +bw=R/(2*%pi*L); +f1=fr-bw/2; +f2=fr+bw/2; +disp("SOLUTION (iii)"); +disp(sprintf("half frequency 1 is %3.2f Hz", f1)); +disp(sprintf("half frequency 2 is %3.2f Hz", f2));// +// +//END + diff --git a/1445/CH2/EX2.23/Ex2_23.sce b/1445/CH2/EX2.23/Ex2_23.sce new file mode 100644 index 000000000..7ff187786 --- /dev/null +++ b/1445/CH2/EX2.23/Ex2_23.sce @@ -0,0 +1,39 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 22 // read it as example 22 in the book on page 2.76 + +disp("CHAPTER 2"); +disp("EXAMPLE 23"); + +//Given +//Equation of an Ac current with respect to origin +//i=100.sin2.pi.50t +//i=100.sin 100.pi.t +// +//VARIABLE INITIALIZATION +A=100 //Amplitude in Amps +f=50 //frquency in Hz +t1=1/600 //sec after wave becomes zero again +a1=86.6 //amplitude at some time t after start +//SOLUTION + +//solution (a) +//Amplitude at 1/600 second after it becomes zero +// +w=f*2*%pi; //angular speed +hp=1/(2*f); //half period, the point where sine beomes zero again after origin +//The hald period , hp, needs to be added to 1/600 sec +t=hp+t1; +a2=A*sin(w*t); +disp("SOLUTION (a)"); +disp(sprintf("Amplitude after 1/600 sec is %3.0f A", a2)); +disp(" "); +//solution (b) +//since A=A0.sinwt, t=asin(A/A0)/w +t2=(asin(a1/A))/w; +disp("SOLUTION (b)"); +disp(sprintf("The time at which amp would be %3.2f is %3.3f sec", a1,t2));//text book answer is 1/300 sec +// + +//END + + diff --git a/1445/CH2/EX2.24/Ex2_24.sce b/1445/CH2/EX2.24/Ex2_24.sce new file mode 100644 index 000000000..ceb0d8ce0 --- /dev/null +++ b/1445/CH2/EX2.24/Ex2_24.sce @@ -0,0 +1,27 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 22 // read it as example 23 in the book on page 2.77 + +disp("CHAPTER 2"); +disp("EXAMPLE 24"); + +//VARIABLE INITIALIZATION +V=200 //Amplitude in Volts +w=314 //angular spped +R=20 //in ohms +//SOLUTION + +//solution +//comparing with standard equation +Im=V/R; // in Amps +rms=Im/2; +Iav=Im/%pi; //average current +ff=rms/Iav; +disp("SOLUTION"); +disp(sprintf("RMS value of current is %3.0f A", rms)); +disp(sprintf("Average value of current is %3.2f A", Iav)); +disp(sprintf("Form Factor of current is %3.2f A", ff)); +disp(" "); +// +//END + + diff --git a/1445/CH2/EX2.25/Ex2_25.sce b/1445/CH2/EX2.25/Ex2_25.sce new file mode 100644 index 000000000..9ac4777b9 --- /dev/null +++ b/1445/CH2/EX2.25/Ex2_25.sce @@ -0,0 +1,31 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 25 // read it as example 24 in the book on page 2.78 + +disp("CHAPTER 2"); +disp("EXAMPLE 25"); + +//VARIABLE INITIALIZATION +V=350 //Amplitude in Volts +f=50 //frquency in Hz +t1=0.005 //sec after wave becomes zero again +t2=0.008 //sec after waves passes tgrough 0 in -ve direction +//SOLUTION +//e=E.sin(wt) + +//solution (a) +// +w=f*2*%pi; //angular speed +v1=V*sin(w*t1); +disp("SOLUTION (a)"); +disp(sprintf("Voltage after %.3f sec is %3d V", t1,v1)); +disp(" "); +//solution (b) +//since wave will pass in -ve direction after half period +hp=1/(2*f); //half period, the point where sine beomes zero again after origin +t=hp+t2; +v2=V*sin(w*t); +disp("SOLUTION (b)"); +disp(sprintf("The voltage would be %5.2f V in %.3f sec", v2,t)); +// +//END + diff --git a/1445/CH2/EX2.26/Ex2_26.sce b/1445/CH2/EX2.26/Ex2_26.sce new file mode 100644 index 000000000..05ce350d7 --- /dev/null +++ b/1445/CH2/EX2.26/Ex2_26.sce @@ -0,0 +1,31 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 26 // read it as example 25 in the book on page 2.79 + +disp("CHAPTER 2"); +disp("EXAMPLE 26"); + +//VARIABLE INITIALIZATION +A=100 //Amplitude in Amps +f=25 //frquency in Hz +a1=20 //value of current in Amps to be achieved in certain time +a2=100 //value of current in Amps tobe achieved in certain time + +//SOLUTION +//i=Im.sin(wt) +//solution (a) +// +w=f*2*%pi; //angular speed +//when current attains 20 amp means instantaneous value of i=20 Amp +t1=(asin(a1/A))/w; +disp("SOLUTION (a)"); +disp(sprintf("The time to reach value %d A is %3.5f sec", a1,t1)); +disp(" "); +//solution (b)//when current attains 100 amp means instantaneous value of i=100 Amp +t2=(asin(a2/A))/w; +disp("SOLUTION (a)"); +disp(sprintf("The time to reach value %d A is %3.2f sec", a2,t2)); +disp(" "); +// +//END + + diff --git a/1445/CH2/EX2.27/Ex2_27.sce b/1445/CH2/EX2.27/Ex2_27.sce new file mode 100644 index 000000000..a88d01676 --- /dev/null +++ b/1445/CH2/EX2.27/Ex2_27.sce @@ -0,0 +1,54 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 27 // read it as example 26 in the book on page 2.79 + +disp("CHAPTER 2"); +disp("EXAMPLE 27"); + +// Given +//Voltage across the circuit +//v=250.sin (314.t-10) +//current is given by +//i=10.sin(314.t+50) +// +//VARIABLE INITIALIZATION +V=250; //Amplitude in Volts +w=314; //angular spped +pv=-10; //phase angle in degrees +I=10; //Amplitude in Amps +pi=50 //phase angle in degrees + +//SOLUTION +//v=Vsin(wt+pv) +//i=Isin(wt+pi) +//solution +//representing V in polar format as V=V0/sqrt(2) <θ, we get +v1=V/sqrt(2); +i1=I/sqrt(2); +//converting polar to rect +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*%pi/180); // angle convert in radians +y=mag*sin(angle*%pi/180); +endfunction; +[x,y]=pol2rect(v1,pv); +V=x+y*%i; +[x,y]=pol2rect(i1,pi); +I=x+y*%i; +Z=V/I; +//convert back into angles in deg +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[mag,angle]=rect2pol(real(Z),imag(Z)); +disp("SOLUTION (a)"); +disp(sprintf("The impedance is %d < %3d Deg", mag,angle));//text book answer is -60 deg +//disp(" "); +//power factor=cos(angle) +pf=cos(-1*angle*%pi/180); //convert to radians and change sign +disp(sprintf("The power factor is %2.1f", pf)); +//Z=R-jXc by comparing real and imag paarts we get +disp(sprintf("The resistance is %3.1fΩ and Reactance is %4.2fΩ", real(Z), imag(Z))); +disp(" "); +// +//END + diff --git a/1445/CH2/EX2.28/Ex2_28.sce b/1445/CH2/EX2.28/Ex2_28.sce new file mode 100644 index 000000000..ce41fd503 --- /dev/null +++ b/1445/CH2/EX2.28/Ex2_28.sce @@ -0,0 +1,66 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 28 // read it as example 27 in the book on page 2.80 + +disp("CHAPTER 2"); +disp("EXAMPLE 28"); +// +//Circuit diagram given with 3 branches +//VARIABLE INITIALIZATION +z1=2+(%i*3); //impedance in rectangular form in Ohms +z2=1-(%i*5); //impedance in rectangular form in Ohms +z3=4+(%i*2); //impedance in rectangular form in Ohms +v=10; //in volts +//SOLUTION + +//solution (a) +//Total impedance +//Total circuit impedance Z=(Z1||Z2)+Z3 +z=z1+(z2*z3)/(z2+z3); +//define function +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[magZ, angleZ]=rect2pol(real(z),imag(z)); +disp("SOLUTION (i)"); +disp(sprintf("Total circuit impedance is %3.2f+%3.1fj S", real(z), imag(z)));// in rectangula rform +disp(sprintf("Total circuit impedance is %3.2f %3.1f S", magZ, angleZ)); //in polar form + +//solution (b) +//Total supply current I=V/Z +i=v/z; +[mag, angle]=rect2pol(real(i), imag(i)); +disp("SOLUTION (b)"); +disp(sprintf("Total current is %3.2f <%3.1f Amp",mag,angle)); +//solution (c) +//Vbc=I.Zbc where Zbc=(z2*z3)/(z2+z3) +Vbc=i*((z2*z3)/(z2+z3)); +[mag1, angle1]=rect2pol(real(Vbc), imag(Vbc)); +disp("SOLUTION (c)"); +disp(sprintf("The voltage across the || circuit is %3.2f-%3.2fj",real(Vbc), imag(Vbc))); +disp(sprintf("The voltage across the || circuit is %3.2f <%3.1f",mag1, angle1)); +disp(sprintf("The voltage Vbc lags circuit by %3.2f Deg",angle-angle1)); +//solution (d) +//i2=Vbc/z2, i3=Vbc/z3 +i2=Vbc/z2; +i3=Vbc/z3; +[mag2, angle2]=rect2pol(real(i2), imag(i2)); +[mag3, angle3]=rect2pol(real(i3), imag(i3)); +disp("SOLUTION (d)"); +disp(sprintf("The current across fist branch of || circuit is %3.2f <%3.1f",mag2, angle2)); +disp(sprintf("The current across second branch of || circuit is %3.2f <%3.1f",mag3, angle3)); +//solution (e) +pf=cos(-1*angle*%pi/180); +disp("SOLUTION (e)"); +disp(sprintf("The power factor is %.3f",pf)); +//solution (iv) +//Apparent power s=VI, True Power, tp I^2R, Reactive Power, rp=I^2X or VISSin(angle) +s=v*mag; //apparent power +tp=(mag^2)*magZ;//true power +rp=v*mag*sin(-1*angle*%pi/180);//reactive power +disp("SOLUTION (f)"); +disp(sprintf("The Apparent power is %.2f VA",s)); +disp(sprintf("The True power is %.2f W",tp));//text book answer is 16.32 may be due to truncation +disp(sprintf("The Reactive power is %.1f vars",rp)); +disp(" "); +//END diff --git a/1445/CH2/EX2.29/Ex2_29.sce b/1445/CH2/EX2.29/Ex2_29.sce new file mode 100644 index 000000000..e09038cf4 --- /dev/null +++ b/1445/CH2/EX2.29/Ex2_29.sce @@ -0,0 +1,28 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 29 // read it as example 28 in the book on page 2.83 + +disp("CHAPTER 2"); +disp("EXAMPLE 29"); +// +//i=120.si(2.pi.f.t) +//VARIABLE INITIALIZATION +I=120; //Amplitude in Amps +f=60; //Hz +t1=1/360; //in sec time to find amplitude +i2=96; //in Amps ,2 to find time taken to reach this +//SOLUTION +//i=Isin(wt) +//solution (a) +w=2*%pi*f; +i=I*sin(w*t1); +disp("SOLUTION (a)"); +disp(sprintf("The amplitude at time %.3f sec is %.1f Amp", t1,i)); +//solution (b) +t2=(asin(i2/I))/w; +disp("SOLUTION (b)"); +disp(sprintf("The time taken to reach %2.0f Amp is %.5f Sec", i2,t2)); +disp(" "); +// +//END + + diff --git a/1445/CH2/EX2.3/Ex2_3.sce b/1445/CH2/EX2.3/Ex2_3.sce new file mode 100644 index 000000000..a6ea8cb77 --- /dev/null +++ b/1445/CH2/EX2.3/Ex2_3.sce @@ -0,0 +1,25 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 3 + +disp("CHAPTER 2"); +disp("EXAMPLE 3"); + +//To find average and rms value rectified sine wave shown in Fig. 2.22 + +//VARIABLE INITIALIZATION +//Time period T=pi +v_m=5; //peak value of voltage in Volts + + +//SOLUTION +//average value Vav by integrating v over 0 to pi and dividing by pi +v_av=(integrate('v_m*sin(x)','x',0,%pi))/(%pi); +//first v squre rms +v_rms=(integrate('(v_m*sin(x))^2','x',0,%pi))/(%pi); +//then V rms: The previous variable reused +v_rms=sqrt(v_rms); +//truncating display to 3 digits +disp(sprintf("Average value of full wave rectifier sine wave is %4.3f V",v_av));// answer is wrongly shown as 3.185 in the book +//truncating display to 2 digits +disp(sprintf("Effective value of full wave rectifier sine wave is %4.2f V",v_rms)); +//END diff --git a/1445/CH2/EX2.30/Ex2_30.sce b/1445/CH2/EX2.30/Ex2_30.sce new file mode 100644 index 000000000..7f36ea719 --- /dev/null +++ b/1445/CH2/EX2.30/Ex2_30.sce @@ -0,0 +1,37 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 30 // read it as example 29 in the book on page 2.83 + +disp("CHAPTER 2"); +disp("EXAMPLE 30"); + +//VARIABLE INITIALIZATION +f=50; //Hz +rms=20; //in Amp +t1=0.0025; //in sec time to find amplitude +t2=0.0125; //in sec, to find amp after passing through +ve maximum +i3=14.14; //in Amps, to find time when will it occur after passing through +ve maxima +//SOLUTION +//i=Isin(wt) +//solution (a) +w=2*%pi*f; +Im=rms*sqrt(2); +disp(sprintf("The equation would be i=%.2f. sin(%f.t)", Im,w)); +t0=(asin(1)/w); //time to reach maxima in +ve direction +i=Im*sin(w*t1); +disp("SOLUTION (a)"); +disp(sprintf("The amplitude at time %f sec is %.2f Amp", t1,i)); +//solution (b) +tx=t0+t2; +i2=Im*sin(w*tx); +disp("SOLUTION (b)"); +disp(sprintf("The amplitude at time %.5f sec is %.2f Amp", t2,i2)); +//solution (c) +ty=(asin(i3/Im))/w; +t3=t0-ty; //since ty is the time starting from 0, the origin needs to be shifted to maxima +disp("SOLUTION (c)"); +disp(sprintf("The amplitude of %.2f Amp would be reached in %.5f Sec", i3,t3)); +disp(" "); +// +//END + + diff --git a/1445/CH2/EX2.31/Ex2_31.sce b/1445/CH2/EX2.31/Ex2_31.sce new file mode 100644 index 000000000..870c20204 --- /dev/null +++ b/1445/CH2/EX2.31/Ex2_31.sce @@ -0,0 +1,21 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 31 // read it as example 30 in the book on page 2.84 + +disp("CHAPTER 2"); +disp("EXAMPLE 31"); + +//VARIABLE INITIALIZATION +//function of the waveform is deduced to be y=10+10.t/T +//SOLUTION +//Yav=(1/T).Integral(ydt) from 0 to T +//say +T=1; // 1 sec +Yav=(1/T)*integrate('(10+10*t/T)', 't', 0, 1); +disp(sprintf("The average value of waveform is %.0f", Yav)); +//RMS value Yrms=(1/T).Integral(y^2.dt) from 0 to T +Yms=(1/T)*integrate('(10+10*t/T)^2', 't', 0, 1); +disp(sprintf("The RMS value of waveform is %.2f", sqrt(Yms))); +disp(" "); +// +//END + diff --git a/1445/CH2/EX2.32/Ex2_32.sce b/1445/CH2/EX2.32/Ex2_32.sce new file mode 100644 index 000000000..dcbdbaf4a --- /dev/null +++ b/1445/CH2/EX2.32/Ex2_32.sce @@ -0,0 +1,25 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 32 // read it as example 31 in the book on page 2.85 + +disp("CHAPTER 2"); +disp("EXAMPLE 32"); + +//VARIABLE INITIALIZATION +//function of the waveform is deduced to be i=Im.sinΘ +//SOLUTION +//Average value of current is Iav=area of rectified wave/interval +//Can be achieved by integration +//Iav=(1/2.π).Integral(ydΘ) from 0 to π, and π to 2.π is zero, interval is 2.π +//need to assume values, let Im=1 +//say +Im=1; // in Amp +Iav=(1/(2*%pi))*integrate('(Im*sin(th))', 'th', 0, %pi); +//disp(sprintf("The average value of waveform is %f", Iav)); +//RMS mean square value (1/π).Integral(y^2.dΘ) from 0 to π +Ims=(1/(2*%pi))*integrate('(Im*sin(th))^2', 'th', 0, %pi); +//disp(sprintf("The RMS value of waveform is %f", sqrt(Ims))); +ff=sqrt(Ims)/Iav; +disp(sprintf("The form factor of waveform is %.2f",ff)); +disp(" "); +// +//END diff --git a/1445/CH2/EX2.33/Ex2_33.sce b/1445/CH2/EX2.33/Ex2_33.sce new file mode 100644 index 000000000..3897c5fcc --- /dev/null +++ b/1445/CH2/EX2.33/Ex2_33.sce @@ -0,0 +1,33 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 33 // read it as example 32 in the book on page 2.86 + +disp("CHAPTER 2"); +disp("EXAMPLE 33"); +//Three coils of resistance 20,30,40 ohms and inductance 0.5,0.3 and 0.2 H are connected in series +//VARIABLE INITIALIZATION +r1=20; //in Ω +r2=30; // +r3=40; // +l1=0.5; //in Henry +l2=0.3; // +l3=0.2; // +V=230; // volts +f=50; //Hz +//coils connected in series +// +//SOLUTION +R=r1+r2+r3; //Total resistance +L=l1+l2+l3; //Total inductance +XL=2*%pi*f*L;//inductive reactance +//impedence Z=sqrt(R*2 +XL^2) +Z=sqrt(R^2 +XL^2); +I=V/Z; +pf=R/Z; +pc=V*I*pf; +disp(sprintf("The total current is %.3f Amp", I)); +disp(sprintf("The Power Factor is %.3f lagging", pf)); +disp(sprintf("The Power consumed in the circuit is %.1f W", pc)); +disp(" "); +// +//END + diff --git a/1445/CH2/EX2.34/Ex2_34.sce b/1445/CH2/EX2.34/Ex2_34.sce new file mode 100644 index 000000000..560d4657d --- /dev/null +++ b/1445/CH2/EX2.34/Ex2_34.sce @@ -0,0 +1,25 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 34 // read it as example 33 in the book on page 2.87 + +disp("CHAPTER 2"); +disp("EXAMPLE 34"); + +//VARIABLE INITIALIZATION +r=100; //in Ω +c=40*10^(-6); // +V=400; // volts +f=50; //Hz +// +//SOLUTION +XC=1/(2*%pi*f*c); //capacitative reactance +//impedence Z=sqrt(R^2 +XL^2) +Z=sqrt(r^2 +XC^2); +I=V/Z; +pf=r/Z; +pc=V*I*pf; +disp(sprintf("The total current is %.2f Amp", I)); +disp(sprintf("The Power Factor is %.3f leading", pf)); +disp(sprintf("The Power consumed in the circuit is %.0f W",pc)); +disp(" "); +// +//END diff --git a/1445/CH2/EX2.35/Ex2_35.sce b/1445/CH2/EX2.35/Ex2_35.sce new file mode 100644 index 000000000..6d46b1c66 --- /dev/null +++ b/1445/CH2/EX2.35/Ex2_35.sce @@ -0,0 +1,45 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 35 // read it as example 34 in the book on page 2.88 + +disp("CHAPTER 2"); +disp("EXAMPLE 35"); + +//VARIABLE INITIALIZATION +R=100; //in Ω +L=0.2; //in Henry +C=20*10^(-6); //farads +V=240; // volts +f=50; //Hz +// +//SOLUTION +//Solution (a) +XL=2*%pi*f*L; +XC=1/(2*%pi*f*C); +//impedence Z=sqrt(R^2 +XL^2) +X=XL-XC; +Z=sqrt(R^2 +X^2); +disp("SOLUTION (a)"); +disp(sprintf("The total impedence is %d Ω", Z)); +I=V/Z; +disp("SOLUTION (b)"); +disp(sprintf("The total current is %.3f Amp", I)); +Vr=I*R; +Vi=I*XL; +Vc=I*XC; +disp("SOLUTION (c)"); +disp(sprintf("The voltage across resistance is %.1f V",Vr)); +disp(sprintf("The voltage across inductance is %.1f V",Vi)); +disp(sprintf("The voltage across capacitance is %.1f V",Vc)); +pf=R/Z; +pc=V*I*pf; +disp("SOLUTION (d)"); +disp(sprintf("The Power Factor is %.2f leading", pf)); +disp("SOLUTION (e)"); +disp(sprintf("The Power consumed in the circuit is %.0f W",pc)); +//XL=XC +f0=1/(2*%pi*sqrt(L*C)); +disp("SOLUTION (f)"); +disp(sprintf("Resonance will occur at %.1f Hz",f0));//The text book answer is 39.8 which is apprently wrong +disp(" "); +// +//END diff --git a/1445/CH2/EX2.36/Ex2_36.sce b/1445/CH2/EX2.36/Ex2_36.sce new file mode 100644 index 000000000..7ea401187 --- /dev/null +++ b/1445/CH2/EX2.36/Ex2_36.sce @@ -0,0 +1,37 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 36 // read it as example 35 in the book on page 2.90 + +disp("CHAPTER 2"); +disp("EXAMPLE 36"); + +//VARIABLE INITIALIZATION +R1=10; //in Ω +XL=15; //in +R2=12; // +C=20; //capacitative reactance in Ω +V=230; // volts +f=50; //Hz +// +//SOLUTION +//Solution (a) +//conductance g, susceptance b +Z12=(R1^2 +XL^2); //squared impedance Z^2 for branch 1 +Z22=(R1^2 +C^2); //squared impedance Z^2 for branch 2 +g1=R1/Z12; //conductance +g2=R2/Z22; +b1=-XL/Z12; //susceptance +b2=C/Z22; +g=g1+g2; //Total conductance +b=b1+b2; //Total susceptance +Y=sqrt(g^2+b^2); //Total admittance +I=V*Y; +disp("SOLUTION (a)"); +disp(sprintf("The total current is %.1f Amp", I));//text book answer is 12.3 A +pf=g/Y; + +disp("SOLUTION (b)"); +disp(sprintf("The power factor is %.3f", pf)); // text book answer is 0.985 +disp(" "); +// +//END + diff --git a/1445/CH2/EX2.37/Ex2_37.sce b/1445/CH2/EX2.37/Ex2_37.sce new file mode 100644 index 000000000..692a599ba --- /dev/null +++ b/1445/CH2/EX2.37/Ex2_37.sce @@ -0,0 +1,41 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 37 // read it as example 36 in the book on page 2.93 + +disp("CHAPTER 2"); +disp("EXAMPLE 37"); + +//VARIABLE INITIALIZATION +R1=20; // +XL=15; // in ohms +R2=0; //assumed +C=50; //in ohms capacitative reactance +V=200; +f=60; //Hz +// +//SOLUTION +//Solution (a) +//conductance g, susceptance b +Z1=sqrt(R1^2 +XL^2); //squared impedance Z^2 for branch 1 +Z2=sqrt(R2^2 +C^2); //squared impedance Z^2 for branch 2 +i1=V/Z1; +i2=V/Z2; +disp("SOLUTION (a)"); +disp(sprintf("The current in Branch 1 is %d Amp", i1)); +disp(sprintf("The current in Branch 2 is %d Amp", i2)); +phi1=atan(XL/R1); +phi2=%pi/2; //atan(C/R2); //R2=0, output is infinity +Icos=i1*cos(phi1)+i2*cos(phi2); // phi in radians +Isin=-i1*sin(phi1)+i2*sin(phi2); // phi in radians +I=sqrt(Icos^2+Isin^2); +// +disp("SOLUTION (b)"); +disp(sprintf("The total current is %.2f Amp", I)); +// +pf=Icos/I; //power factor +disp("SOLUTION (c)"); +disp(sprintf("The power factor is %.3f ", pf)); +disp(" "); +// +//END + + diff --git a/1445/CH2/EX2.38/Ex2_38.sce b/1445/CH2/EX2.38/Ex2_38.sce new file mode 100644 index 000000000..bce55490e --- /dev/null +++ b/1445/CH2/EX2.38/Ex2_38.sce @@ -0,0 +1,26 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 38 // read it as example 37 in the book on page 2.93 + +disp("CHAPTER 2"); +disp("EXAMPLE 38"); +// +//Solve exercise 36 by j method +//VARIABLE INITIALIZATION +z1=10+15*%i; +z2=12-20*%i; +V=230; +//invZ=1/z1+1/z2; +Z=z1*z2/(z1+z2); +magZ=sqrt(real(Z)^2+imag(Z)^2); +I=V/magZ; +pf=real(Z)/magZ; +disp("SOLUTION (a)"); +disp(sprintf("The current is %.1f Amp", I)); +// +disp("SOLUTION (b)"); +disp(sprintf("The Power factor is %.3f lagging", pf)); +disp(" "); +// +//END + + diff --git a/1445/CH2/EX2.39/Ex2_39.sce b/1445/CH2/EX2.39/Ex2_39.sce new file mode 100644 index 000000000..6fe1c5555 --- /dev/null +++ b/1445/CH2/EX2.39/Ex2_39.sce @@ -0,0 +1,64 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 39 // read it as example 38 in the book on page 2.94 + +disp("CHAPTER 2"); +disp("EXAMPLE 39"); + +//VARIABLE INITIALIZATION +z1=2.5+1.5*%i; +z2=4+3*%i; +z3=3-4*%i; +V=200; +f=50; +E=V+0*%i; // representing as a vector +//invZ=1/z1+1/z2; +//Z23=1/Z2+1/Z3 which is equivalent impedance of parallel circuits +//Z13=Z1+Z23 which is symbolic expression of total impedance +// +//SOLUTION +Z23=z2*z3/(z2+z3); +Z=z1+Z23; +disp("SOLUTION (a)"); +disp(sprintf("The symbolic expression of impedance %.1f+j%.1f Amp",real(Z),imag(Z))); +I=E/Z; +magI=sqrt(real(I)^2+imag(I)^2); //total current +phi=atan(-imag(I)/real(I)); //total phase +// +//Voltages across the branches +e12=I*z1; //voltage across series branch +mage12=sqrt(real(e12)^2+imag(e12)^2); +phi12=atan(imag(e12)/real(e12)); +// +e23=E-e12; //voltage across parallel branch +mage23=sqrt(real(e23)^2+imag(e23)^2); +phi23=atan(-imag(e23)/real(e23)); +// +//current in branch 1 upper +i1=e23/z2; +magi1=sqrt(real(i1)^2+imag(i1)^2); +phii1=atan(-imag(i1)/real(i1)); +// +//current in branch 2 lower +i2=e23/z3; +magi2=sqrt(real(i2)^2+imag(i2)^2); +phii2=atan(imag(i2)/real(i2)); +disp("SOLUTION (b)"); +disp(sprintf("The current in Upper branch is %.1f Amp",magi1)); +disp(sprintf("The current in Lower branch is %.1f Amp",magi2)); +disp(sprintf("The Total current is %.2f Amp",magI));//the text book answer is wrongly shown as 328 A +// +pf=cos(phi); // +disp("SOLUTION (c)"); +disp(sprintf("The Power factor is %.3f", pf)); +// +disp("SOLUTION (d)"); +disp(sprintf("The voltage across series branch is %.1f V", mage12)); +disp(sprintf("The voltage across parallel branch is %.0f V", mage23)); +// +tp=V*magI*pf; //total power +disp("SOLUTION (e)"); +disp(sprintf("The total power absorbed in circuit is %d W", tp));// the text book answer is 6480 W +disp(" "); +// +//END + diff --git a/1445/CH2/EX2.4/Ex2_4.sce b/1445/CH2/EX2.4/Ex2_4.sce new file mode 100644 index 000000000..7045a8f28 --- /dev/null +++ b/1445/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,21 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 4 + +disp("CHAPTER 2"); +disp("EXAMPLE 4"); + +//VARIABLE INITIALIZATION +v_m=10; //peak value of voltage in Volts +angle=60*(%pi/180); //delay angle in radians + +//SOLUTION +//average value Vav by integrating v over 0 to pi and dividing by pi +v_av=(integrate('v_m*sin(x)','x',angle,%pi))/(%pi); +//effective value +v_rms=(integrate('(v_m*sin(x))^2','x',angle,%pi))/(%pi); +v_rms=sqrt(v_rms); +disp(sprintf("Average value of full wave rectifier sine wave is %4.2f V",v_av));// truncade to two decimals +// //text book answer is 4.78 +disp(sprintf("Effective value of full wave rectifier sine wave is %4.2f V",v_rms));//text book answer is 6.33 + +//END diff --git a/1445/CH2/EX2.40/Ex2_40.sce b/1445/CH2/EX2.40/Ex2_40.sce new file mode 100644 index 000000000..e70e3d40c --- /dev/null +++ b/1445/CH2/EX2.40/Ex2_40.sce @@ -0,0 +1,27 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 40 // read it as example 39 in the book on page 2.98 + +disp("CHAPTER 2"); +disp("EXAMPLE 40"); +// +//Given +//V=100.sin(314.t+5) V +//current is i=5.sin (314.t-40) +//VARIABLE INITIALIZATION +V=100; // max amplitude of wave +w=314; //angular speed +phiV=5; //phase angle in degrees +I=5; //max current amplitude +phiI=-40; //phase angle in current in deg + +// +//SOLUTION +phi=phiI-phiV; // phase difference +pf=cos(phi*%pi/180); //convert to radians +p=(V/sqrt(2))*(I/sqrt(2))*pf; +// +disp(sprintf("The Power factor is %.3f lagging", pf)); +disp(sprintf("The Power delivered is %.2f W", p)); +disp(" "); +// +//END diff --git a/1445/CH2/EX2.41/Ex2_41.sce b/1445/CH2/EX2.41/Ex2_41.sce new file mode 100644 index 000000000..48ca080c2 --- /dev/null +++ b/1445/CH2/EX2.41/Ex2_41.sce @@ -0,0 +1,34 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 41 // read it as example 40 in the book on page 2.99 + +disp("CHAPTER 2"); +disp("EXAMPLE 41"); + +//VARIABLE INITIALIZATION +lampV=100; //Volts +lampW=60; //watts +V=250; +f=50; +// +//SOLUTION +lampI=lampW/lampV; +lampR=lampW/lampI^2; //W=I^2.R +// +disp("SOLUTION (a)"); +disp(sprintf("The resistance of the lamp is t is %.2f Ohms", lampR)); +// +//in purely resistive / non inductive circuit,V=IR applies, and R=lampR+R +R=V/lampI-lampR; +disp(sprintf("The value value of resistor to be placed in series with the lamp is %.0f Ohms", R)); +// +//in case of inductance +//XL=2*%pi*f*L; +//V=Z.I where Z^2=R^2+XL^2 +//L=sqrt((V^2/I^2-R^2)/2*%pi*f) +L=sqrt((V/lampI)^2-lampR^2)/(2*%pi*f); +disp(sprintf("The inductive resistance to be placed is %.4f H",L)); +disp(" "); +// +//END + + diff --git a/1445/CH2/EX2.42/Ex2_42.sce b/1445/CH2/EX2.42/Ex2_42.sce new file mode 100644 index 000000000..4d3681898 --- /dev/null +++ b/1445/CH2/EX2.42/Ex2_42.sce @@ -0,0 +1,48 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 42 // read it as example 41 in the book on page 2.100 + +disp("CHAPTER 2"); +disp("EXAMPLE 42"); + +//VARIABLE INITIALIZATION +I=10; // max amplitude of wave in Amp +rms1=5; //rms values of current +rms2=7.5; +rms3=10; +phi1=30; //phase angles +phi2=-60; +phi3=45; +f=50; //frequency in Hz +w=2*%pi*f; +// +//SOLUTION +//in case of sinosoidal wave, average value of alternating quantity = RMS values/1.11 +av1=rms1/1.11; //average values of 1,2,3 currents +av2=rms2/1.11; +av3=rms3/1.11; +disp("SOLUTION (i)"); +disp(sprintf("The average value of 1st current is %.2f Amp", av1)); +disp(sprintf("The average value of 2nd current is %.2f Amp", av2)); +disp(sprintf("The average value of 3rd current is %.2f Amp", av3)); +// +//instantaneous values of current +//i(t)=RMS.sqrt(2).sin (w.t+phi) +//w=2.pi.f which for 50 Hz coes to 314 +disp("SOLUTION (ii)"); +disp(sprintf("The instantaneous value of 1st current is %.2f sin(%.0f*t+%.0f) Amp", rms1*sqrt(2), w,phi1)); +disp(sprintf("The instantaneous value of 2nd current is %.2f sin(%.0f*t%.0f) Amp", rms2*sqrt(2), w,phi2)); +disp(sprintf("The instantaneous value of 3rd current is %.2f sin(%.0f*t+%.0f) Amp", rms3*sqrt(2), w,phi3)); +// +//instantaneous values of current at t=100msec=0.1 sec +t=0.1; +i1=(rms1*sqrt(2))*(sin(w*t+phi1*%pi/180)); +i2=(rms2*sqrt(2))*(sin(w*t+phi2*%pi/180)); +i3=(rms3*sqrt(2))*(sin(w*t+phi3*%pi/180)); +disp("SOLUTION (iv)"); +disp(sprintf("The instantaneous value of 1st current is %.3f Amp at %.3f Sec", i1, t)); +disp(sprintf("The instantaneous value of 2nd current is %.3f Amp at %.3f Sec", i2, t)); +disp(sprintf("The instantaneous value of 3rd current is %.3f Amp at %.3f Sec", i3, t)); +disp(" "); +// +//END + diff --git a/1445/CH2/EX2.43/Ex2_43.sce b/1445/CH2/EX2.43/Ex2_43.sce new file mode 100644 index 000000000..b4e1f6b76 --- /dev/null +++ b/1445/CH2/EX2.43/Ex2_43.sce @@ -0,0 +1,21 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 43 // read it as example 42 in the book on page 2.102 + +disp("CHAPTER 2"); +disp("EXAMPLE 43"); + +//VARIABLE INITIALIZATION +I=5; // max amplitude of wave in Amp +f=50; //Hz +//wave for is to be obtained by adding the two waves +//i=5+5.sin(wt)=5+5.sin(theta) +// +//SOLUTION +Iav=(1/(2*%pi))*integrate('5+5*sin(th)', 'th',0,2*%pi); +Ims=(1/(2*%pi))*integrate('(5+5*sin(th))^2', 'th',0,2*%pi); +// +disp(sprintf("The average value of resultant current is %.2f Amp", Iav)); +disp(sprintf("The RMS value of resultant current is %.2f Amp", sqrt(Ims))); +disp(" "); +// +//END diff --git a/1445/CH2/EX2.44/Ex2_44.sce b/1445/CH2/EX2.44/Ex2_44.sce new file mode 100644 index 000000000..b01b90a84 --- /dev/null +++ b/1445/CH2/EX2.44/Ex2_44.sce @@ -0,0 +1,22 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 44 + +disp("CHAPTER 2"); +disp("EXAMPLE 44"); + +//given +//current in the resistor is given by i=4+5.sin wt - 3.cos 3.wt +//VARIABLE INITIALIZATION +r=20; //resistance in Ohms + +//SOLUTION +//Power consumed by the resistor is P=P0+P1+P2 +p0=(4^2)*r; +p1=((5/sqrt(2))^2)*r; +p2=((3/sqrt(2))^2)*r; +p=p0+p1+p2; +I=sqrt(p/r); +disp(sprintf("The power consumed by the resistor is %d W",p)); +disp(sprintf("The effective value of current is %.1f A",I)); + +//END diff --git a/1445/CH2/EX2.45/Ex2_45.sce b/1445/CH2/EX2.45/Ex2_45.sce new file mode 100644 index 000000000..9122b5be2 --- /dev/null +++ b/1445/CH2/EX2.45/Ex2_45.sce @@ -0,0 +1,36 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 45 + +disp("CHAPTER 2"); +disp("EXAMPLE 45"); + +//VARIABLE INITIALIZATION +L=1.405; //inductance in Henry +r=40; //resistance in Ohms +C=20/(10^6); //capacitance in Farad +v=100; //voltage in Volts + +//SOLUTION +//resonant frequency f=1/2.pi.sqrt (L.C) +f0=1/(2*%pi*sqrt(L*C)); +disp(sprintf("The frequency at which the circuit resonates is %d Hz",f0)); + +I0=v/r; +disp(sprintf("The current drawn from the supply is %.1f A",I0)); + +xl0=2*%pi*f0*L; +z0=sqrt((r^2)+(xl0^2)); +vl0=I0*z0; +disp(sprintf("The voltage across the coil is %.1f V",vl0)); + +xc0=1/(2*%pi*f0*C); +disp(sprintf("The capcitative reactance is %.1f Ω",xc0)); + +Q0=(2*%pi*f0*L)/r; +disp(sprintf("The quality factor is %.3f", Q0)); + +bw=r/L; +disp(sprintf("The bandwidth is %.3f Hz",bw)); + +//END + diff --git a/1445/CH2/EX2.46/Ex2_46.sce b/1445/CH2/EX2.46/Ex2_46.sce new file mode 100644 index 000000000..8b73830ef --- /dev/null +++ b/1445/CH2/EX2.46/Ex2_46.sce @@ -0,0 +1,43 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 46 + +disp("CHAPTER 2"); +disp("EXAMPLE 46"); + +//VARIABLE INITIALIZATION +I=120-(%i*(50)); //given, current in Amperes +v=8+(%i*(2)); //given, voltage in Volts + +//SOLUTION + +//function to convert from rectangular form to polar form +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[v,angle_v]=rect2pol(real(v),imag(v)); +[I,angle_I]=rect2pol(real(I),imag(I)); + +//solution (i) +z=v/I; +angle_z=angle_v-angle_I; +disp(sprintf("(i) The impedance is %.4f Ω,<%.2f degrees",z,angle_z)); + +//solution (ii) +phi=angle_z; +pf=cos(phi*(%pi/180)); +disp(sprintf("(ii) The power factor is %.3f (lagging)",pf)); + +//solution (iii) +s=v*I; +angle_s=angle_v-angle_I; +//function to convert from polar form to rectangular form +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[p,q]=pol2rect(s,angle_s); +disp(sprintf("(iii) The power consumed is %.2f W",p)); +disp(sprintf(" The reactive power is %.2f VAR",q)); + +//END diff --git a/1445/CH2/EX2.47/Ex2_47.sce b/1445/CH2/EX2.47/Ex2_47.sce new file mode 100644 index 000000000..1e5f6185b --- /dev/null +++ b/1445/CH2/EX2.47/Ex2_47.sce @@ -0,0 +1,48 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 47 + +disp("CHAPTER 2"); +disp("EXAMPLE 47"); + +//given +//current in the circuit is 5-j.10 A +//VARIABLE INITIALIZATION +r=10; //in Ohms +xl=8.66; //in Ohms +I=5-(%i*10); //in Amperes + +//SOLUTION +z=r+(%i*(xl)); +//function to convert from rectangular form to polar form +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[z,angle_z]=rect2pol(real(z),imag(z)); +[I,angle_I]=rect2pol(real(I),imag(I)); + +//solution(i) +v=I*z; +angle_v=angle_I+angle_z; +disp(sprintf("(i) The applied voltage is %.1f V, %.2f degrees",v,angle_v)); + +//solution (ii) +phi=angle_I-angle_v; +pf=cos(phi*(%pi/180)); +disp(sprintf("(ii) The power factor is %.3f (lagging)",pf)); + +//solution(iii) +//S=phasor voltageXconjugate of phasor current +//Converting v and I from polar to rectangular form +s=v*I; +angle_s=angle_v-angle_I; +//function to convert from polar form to rectangular form +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[p,q]=pol2rect(s,angle_s); +disp(sprintf("(iii) The active power is %.2f W",p)); +disp(sprintf(" The reactive power is %.2f VAR",q)); + +//END diff --git a/1445/CH2/EX2.48/Ex2_48.sce b/1445/CH2/EX2.48/Ex2_48.sce new file mode 100644 index 000000000..9e93c267b --- /dev/null +++ b/1445/CH2/EX2.48/Ex2_48.sce @@ -0,0 +1,37 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 48 + +disp("CHAPTER 2"); +disp("EXAMPLE 48"); + +//VARIABLE INITIALIZATION +pf1=0.8; //power factor of 1st circuit +pf2=0.6; //power factor of 2nd circuit +z=1; //this is an assumption + +//SOLUTION +//convert polar to rectangular form +angle1=acos(pf1)*(180/%pi); //in degrees +angle2=acos(pf2)*(180/%pi); //in degrees +//function to convert from polar form to rectangular form +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[z1_x,z1_y]=pol2rect(z,angle1); +[z2_x,z2_y]=pol2rect(z,angle2); +nr=angle1+angle2; //numerator +z_x=z1_x+z2_x; +z_y=z1_y+z2_y; + +//function to convert from rectangular form to polar form +function [z,angle]=rect2pol(x,y); +I=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[z,angle]=rect2pol(z_x,z_y); +angle_z=nr-angle; +pf=cos(angle_z*(%pi/180)); +disp(sprintf("The power factor of the combination is %.3f",pf)); + +//END diff --git a/1445/CH2/EX2.49/Ex2_49.sce b/1445/CH2/EX2.49/Ex2_49.sce new file mode 100644 index 000000000..a1cd3ec1d --- /dev/null +++ b/1445/CH2/EX2.49/Ex2_49.sce @@ -0,0 +1,61 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 49 + +disp("CHAPTER 2"); +disp("EXAMPLE 49"); + +//Given +//voltage V=200 <30 +//current 20 <60 and 40 <-30 + +//VARIABLE INITIALIZATION +v=200; //in Volts +angle_v=30; //in degrees +I1=20; //in Amperes +angle_I1=60; //in degrees +I2=40; //in Amperes +angle_I2=-30; //in degrees + +//SOLUTION +//function to convert from polar form to rectangular form +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[v_x,v_y]=pol2rect(v,angle_v); +[I1_x,I1_y]=pol2rect(I1,angle_I1); +[I2_x,I2_y]=pol2rect(I2,angle_I2); +s1=v*I1; +angle_s1=-angle_v+angle_I1; +disp(sprintf("The apparent power in 1st branch is %d kVA",s1/1000)); +[s1_x,s1_y]=pol2rect(s1,angle_s1); +disp(sprintf("The true power in 1st branch is %.3f kW",s1_x/1000)); + +disp(" "); + +s2=v*I2; +angle_s2=angle_v-angle_I2; +disp(sprintf("The apparent power in 2nd branch is %d kVA",s2/1000)); +[s2_x,s2_y]=pol2rect(s2,angle_s2); +disp(sprintf("The true power in 2nd branch is %d kW",s2_x/1000)); +I=(I1_x+I2_x)+(%i*(I1_y+I2_y)); //disp(I); + +//function to convert from rectangular form to polar form +function [I,angle]=rect2pol(x,y); +I=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[I,angle]=rect2pol(real(I),imag(I)); +//disp(I); +s=v*I; +angle_s=angle_v-angle; +disp(sprintf("The apparent power in the main circuit is %.3f kVA",s/1000)); +[p,q]=pol2rect(s,angle_s); +disp(sprintf("The true power in the main circuit is %.3f kW",p/1000)); + +//END + + + + + diff --git a/1445/CH2/EX2.5/Ex2_5.sce b/1445/CH2/EX2.5/Ex2_5.sce new file mode 100644 index 000000000..ce799fefc --- /dev/null +++ b/1445/CH2/EX2.5/Ex2_5.sce @@ -0,0 +1,39 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 5 + +disp("CHAPTER 2"); +disp("EXAMPLE 5"); + +//VARIABLE INITIALIZATION +I1=0.75; //current in loop 1 in Amperes +v=240; //voltage supply in Volts +f=50; //frequency in Hertz +p=80; //power consumed by the lamp in Watts + +//SOLUTION +//V.I1.cos(Φ1) = P +res=p/v; //I1cos(Φ1) +pf1=res/I1; //1st power factor = cos(Φ1) +phi1=acos(pf1); +res1=tan(phi1); //result1 = tan(Φ1) +w=2*%pi*f; //w=2.pi.f + +//solution (a) +//Given power factor = unity means cos(Φ2)=1 +//hence Φ2=0, tan (Φ2)=0 +res2=0; //result2 = tan(Φ2) as Φ2=0 +Ic1=res*(res1-res2); +c1=Ic1/(v*w); +disp(sprintf("(a) When power factor is unity, the value of capacitance is %4.2f μF",c1*(10^6))); // in mF + +//solution (b) +pf2=0.95; //given +phi2=acos(pf2); +res2=tan(phi2); +Ic2=res*(res1-res2); +c2=Ic2/(v*w); +disp(sprintf("(b) When power factor is 0.95(lagging), the value of capacitance is %5.3f μF",c2*(10^6))); //textbook answer is 7.458 mF + +//END + + diff --git a/1445/CH2/EX2.50/Ex2_50.sce b/1445/CH2/EX2.50/Ex2_50.sce new file mode 100644 index 000000000..1c1aa59a3 --- /dev/null +++ b/1445/CH2/EX2.50/Ex2_50.sce @@ -0,0 +1,48 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 50 + +disp("CHAPTER 2"); +disp("EXAMPLE 50"); + +//Given +//three impedances +//6+j5 ohm, 8-j6 ohm and 8+j10 ohm +//Circuit in parallel +// +//VARIABLE INITIALIZATION +z1=6+(%i*5); //impedance in Ohms +z2=8-(%i*6); //impedance in Ohms +z3=8+(%i*10); //impedance in Ohms +I=20; //in Amperes + +//SOLUTION +Y1=1/z1; // Admittance +Y2=1/z2; +Y3=1/z3; +Y=Y1+Y2+Y3; // Total admittance +//function to convert from rectangular form to polar form +function [Y,angle]=rect2pol(x,y); +Y=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[Y_tot,angle]=rect2pol(real(Y),imag(Y)); +v=I/Y_tot; +angle_v=-angle; +[z1,angle1]=rect2pol(real(z1),imag(z1)); +[z2,angle2]=rect2pol(real(z2),imag(z2)); +[z3,angle3]=rect2pol(real(z3),imag(z3)); +I1=v/z1; +angle_I1=angle_v-angle1; +I2=v/z2; +angle_I2=angle_v-angle2; +I3=v/z3; +angle_I3=angle_v-angle3; +disp("The current in each branch in polar form is-"); +disp(sprintf(" %.3f A, %.2f degrees",I1,angle_I1)); +disp(sprintf(" %.3f A, %.2f degrees",I2,angle_I2)); +disp(sprintf(" %.3f A, %.2f degrees",I3,angle_I3)); +//Total current +I=I1+I2+I3; +disp(sprintf("The total current is %.3f A",I)); //Answer not clear in the book +// +//END diff --git a/1445/CH2/EX2.51/Ex2_51.sce b/1445/CH2/EX2.51/Ex2_51.sce new file mode 100644 index 000000000..85f7d494b --- /dev/null +++ b/1445/CH2/EX2.51/Ex2_51.sce @@ -0,0 +1,30 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 51 + +disp("CHAPTER 2"); +disp("EXAMPLE 51"); +// +//Given +// admittance of branches are: +//Y1=0.4+j0.6 +//Y2=0.1+j0.4 +//Y3=0.06+j0.23 +// +//VARIABLE INITIALIZATION +Y1=0.4+(%i*0.6); //admittance of 1st branch in Siemens +Y2=0.1+(%i*0.4); //admittance of 2nd branch in Siemens +Y3=0.06+(%i*0.23); //admittance of 3rd branch in Siemens + +//SOLUTION +Y=Y1+Y2+Y3; // total admittance +//function to convert from rectangular form to polar form +function [Y,angle]=rect2pol(x,y); +Y=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[Y,angle]=rect2pol(real(Y),imag(Y)); +disp(sprintf("The total admittance of the circuit is %.3f S, %.2f degrees",Y,angle)); +z=1/Y; +disp(sprintf("The impedance of the circuit is %.3f Ω, %.2f degrees",z,-angle)); +// +//END diff --git a/1445/CH2/EX2.52/Ex2_52.sce b/1445/CH2/EX2.52/Ex2_52.sce new file mode 100644 index 000000000..d0d64ad6f --- /dev/null +++ b/1445/CH2/EX2.52/Ex2_52.sce @@ -0,0 +1,77 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 52 + +disp("CHAPTER 2"); +disp("EXAMPLE 52"); + +//VARIABLE INITIALIZATION +r1=7; //in Ohms +L1=0.015; //in Henry +r2=12; //in Ohms +c2=180*(10^(-6)); //in Farad +r3=5; //in Ohms +L3=0.01; //in Henry +v=230; //in Volts +f=50; //in Hertz + +//SOLUTION + +//solition (a) +xl1=2*%pi*f*L1; +xc2=1/(2*%pi*f*c2); +xl3=2*%pi*f*L3; +Z1=r1+xl1*%i; //complex representations +Z2=r2-xc2*%i; +Z3=r3+xl3*%i; +//function to convert from rectangular form to polar form +function [z,angle]=rect2pol(r,x); +z=sqrt((r^2)+(x^2)); +angle=atan(x/r)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[z1,angle1]=rect2pol(r1,xl1); +[z2,angle2]=rect2pol(r2,xc2); +[z3,angle3]=rect2pol(r3,xl3); +//to obtain rectangular form of (Z1+Z2) +req1=r1+r2; +xeq1=xl1-xc2; +//to obtain polar form of (Z1+Z2) +[zeq1,angle_eq1]=rect2pol(req1,-xeq1); +zp=(z1*z2)/(zeq1); +angle_p=(angle1-angle2)+angle_eq1; +//function to convert from polar form to rectangular form +function [r,x]=pol2rect(z,angle); +r=z*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +x=z*sin(angle*(%pi/180)); +endfunction; +[rp,xp]=pol2rect(zp,angle_p); +[req,xeq]=pol2rect(z3,angle3); +r_tot=req+rp; +x_tot=xeq+xp; +[z_tot,angle_tot]=rect2pol(r_tot,x_tot); +Z=r_tot+x_tot*%i; //complex representation +disp(sprintf("(a) The total impedance is %.3f Ω, %.2f degrees",z_tot,angle_tot)); + +//solution (b) +I=v/Z; //complex division +angle_I=-angle_tot; +[I_x,I_y]=pol2rect(I,angle_I); +disp(sprintf("(b) The total currrent is (%.3f-j%.2f) A",real(I),imag(I))); + +//solution (c) +//Voltage drop across Z3 +Vab=I*Z3; +disp(sprintf(" The Voltage between AB is (%.3f-j%.2f) V",real(Vab),imag(Vab))); +//since we know that V=Vab+Vbc +Vbc=v-Vab; +disp(sprintf(" The Voltage between BC is (%.3f-j%.2f) V",real(Vbc),imag(Vbc))); +I1=Vbc/Z1; //Branch 1 current +I2=Vbc/Z2; //branch 2 current +//I3=I, main branch current +[mag1,angle1]=rect2pol(real(I1),imag(I1)); +[mag2,angle2]=rect2pol(real(I2),imag(I2)); +disp(sprintf("(c) Current in branch 1 is %.3f,< %.2f degrees A",mag1,angle1)); +disp(sprintf(" The currrent in branch 1 is (%.3f-j%.2f) A",real(I1),imag(I1))); +disp(sprintf(" The current in branch 2 is %.3f A,<%.2f degrees A",mag2,angle2)); +disp(sprintf(" The currrent in branch 2 is (%.3f-j%.2f) A",real(I2),imag(I2))); +//END + diff --git a/1445/CH2/EX2.53/Ex2_53.sce b/1445/CH2/EX2.53/Ex2_53.sce new file mode 100644 index 000000000..ccdef8fb0 --- /dev/null +++ b/1445/CH2/EX2.53/Ex2_53.sce @@ -0,0 +1,47 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 53 Read Example 52 of the Text Book + +disp("CHAPTER 2"); +disp("EXAMPLE 53"); + +//Given +//Voltage 230 <30 V +//Current in branches 20 <60 A & 40<-30 A +// +//VARIABLE INITIALIZATION +v=230; //in Volts +angle_v=30; //in degrees +I1=20; //in Amperes +angle_I1=60; //in degrees +I2=40; //in Amperes +angle_I2=-30; //in degrees + +//SOLUTION +//function to convert from polar form to rectangular form +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[x1,y1]=pol2rect(I1,angle_I1); +[x2,y2]=pol2rect(I2,angle_I2); +X=x1+x2; +Y=y1+y2; + +//function to convert from rectangular form to polar form +function [I,angle]=rect2pol(x,y); +I=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[I,angle]=rect2pol(X,Y); + +//solution (i) +z=v/I; +angle_z=angle_v-angle; +disp(sprintf("(i) The total impedance of the circuit is %.2f Ω, %.2f degrees",z,angle_z)); + +//solution (ii) +//disp(sprintf("The value of I is %f and angle is %f",I, angle_z)); +pf=cos(angle_z*(%pi/180)); //power factor +p=v*I*pf; // Power taken +disp(sprintf("(ii) The power taken is %.0f W",p)); +//END diff --git a/1445/CH2/EX2.54/Ex2_54.sce b/1445/CH2/EX2.54/Ex2_54.sce new file mode 100644 index 000000000..4b6e43d75 --- /dev/null +++ b/1445/CH2/EX2.54/Ex2_54.sce @@ -0,0 +1,33 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 54 Read example 53 of the Book + +disp("CHAPTER 2"); +disp("EXAMPLE 54"); + +//VARIABLE INITIALIZATION +C=2.5/(10^6); //capcaitance in Farads +R=15; //in Ohms +L=260/1000; //in Henry + +//SOLUTION +//resonant Frequency is given by +//fr= 1/ 2.pi.(sqrt (1/LC - R^2/L^2)) +//Q-factor is given by: +//Qf=2.pi.fr.L/R +//dynamic impedance is given by +//Zr=L/C.R +// +//solution (i) +f_r=(1/(2*%pi))*sqrt((1/(L*C)-(R^2/L^2))); +f_r=round(f_r); //to round off the value +disp(sprintf("(i) The resonant frequency is %d Hz",f_r)); + +//solution (ii) +q_factor=(2*%pi*f_r*L)/R; +disp(sprintf("(ii) The Q-factor of the circuit is %.2f",q_factor)); + +//solution (iii) +Z_r=L/(C*R); +disp(sprintf("(iii) The dynamic impedance of the circuit is %.0f Ω",Z_r)); + +//END diff --git a/1445/CH2/EX2.6/Ex2_6.sce b/1445/CH2/EX2.6/Ex2_6.sce new file mode 100644 index 000000000..378b29151 --- /dev/null +++ b/1445/CH2/EX2.6/Ex2_6.sce @@ -0,0 +1,29 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 6 + +disp("CHAPTER 2"); +disp("EXAMPLE 6"); + +//VARIABLE INITIALIZATION +f=50; //in Hertz +I1=20; //in Amperes +pf1=0.75; //power factor +v=230; //in Volts +pf2=0.9; //power factor(lagging) + +//SOLUTION +//V.I1.cos(Φ1) = P +phi1=acos(pf1); +res1=tan(phi1); //result1 = tan(Φ1) +phi2=acos(pf2); +res2=tan(phi2); //result2 = tan(Φ2) +Ic=I1*pf1*(res1-res2); +w=2*%pi*f; //w=2.pi.f +c=Ic/(v*w); +disp(sprintf("The value of capacitance is %5.2f μF",c*(10^6)));//text book answer is 82.53 mF +Qc=v*Ic; // reactive power in kVAr +disp(sprintf("The reactive power is %6.4f kVAR",Qc/(10^3)));//text book answer is 1.3716 +I2=I1*(pf1/pf2); //I1.cos(Φ1) = I2.cos(Φ2) +disp(sprintf("The new supply current is %5.2f A",I2)); + +//END diff --git a/1445/CH2/EX2.7/Ex2_7.sce b/1445/CH2/EX2.7/Ex2_7.sce new file mode 100644 index 000000000..97183894a --- /dev/null +++ b/1445/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,24 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 7 + +disp("CHAPTER 2"); +disp("EXAMPLE 7"); + +//VARIABLE INITIALIZATION +s1=300; //apparent power absorbed by the plant in kVA +pf1=0.65; //power factor(lagging) +pf2=0.85; //power factor(lagging) + +//SOLUTION + +//solution (a) +p=s1*pf1; //active power P=S.cos(Φ) +q1=sqrt((s1^2)-(p^2)); //Q=sqrt(S^2-P^2) in kVAr +disp(sprintf("(a) To bring the power factor to unity, the capacitor bank should have a capacity of %3.0f kVAR",q1)); + +//solution (b) +s2=p/pf2; //since P=S.cos(Φ) +q2=sqrt((s2^2)-(p^2)); //Q=sqrt(S^2-P^2) in kVAr +disp(sprintf("(b) To bring the power factor to 85%% lagging, the capacitor bank should have a capacity of %3.0f kVAR",q2)); + +//END diff --git a/1445/CH2/EX2.8/Ex2_8.sce b/1445/CH2/EX2.8/Ex2_8.sce new file mode 100644 index 000000000..adfd7b625 --- /dev/null +++ b/1445/CH2/EX2.8/Ex2_8.sce @@ -0,0 +1,31 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 8 + +disp("CHAPTER 2"); +disp("EXAMPLE 8"); + +//Given +//V=300.cos(314.t+20) volts +//i=15.cos(314.t-10) Amp +// +//VARIABLE INITIALIZATION +//V=300.cos(314.t+20) volts +//V=300.sin(314.t+110) volts as cos(theta)=sin(theta+90) +//i=15.cos(314.t-10) Amp +//i=15.sin(314.t+80) Amp as cos(theta)=sin(theta+90) +//Now +V=300/sqrt(2); //in Volts +angle_V=110; //in degrees +I=15/sqrt(2); //in Amperes +angle_I=80; //in degrees + +//SOLUTION +Z=V/I; //circuit impedance +angle_Z=angle_V-angle_I; //angle between current and voltage +disp(sprintf("The circuit impedance is %d Ω",Z)); +disp(sprintf("The phase angle is %d degrees",angle_Z)); +//Pav=Vm*Im.cos (phi) in RL circuit +Pav=V*I*cos(angle_Z*(%pi/180)); //to convert angle_z from degrees to radians +disp(sprintf("The average power drawn is %7.2f W",Pav));// textboo answer is 1949.85 w + +//END diff --git a/1445/CH2/EX2.9/Ex2_9.sce b/1445/CH2/EX2.9/Ex2_9.sce new file mode 100644 index 000000000..0fd9a5c6d --- /dev/null +++ b/1445/CH2/EX2.9/Ex2_9.sce @@ -0,0 +1,26 @@ +//CHAPTER 2- STEADY-STATE ANALYSIS OF SINGLE-PHASE A.C. CIRCUIT +//Example 9 + +disp("CHAPTER 2"); +disp("EXAMPLE 9"); + + +//VARIABLE INITIALIZATION +V=120; //voltage of lamp in Volts +P=100; //in Watts +Vsupp=220; //supply voltage in Volts +f=50; //in Hertz +//Equations to be used +//Z=R+jXl +//Vsupply=V+jVl=sqrt(V^2+Vl^2) +//Hence Vl=sqrt(Vsupply^2-V^2) +//P=VI +//Xl=2.pi.f.L + +//SOLUTION +Vl=sqrt((Vsupp^2)-(V^2)); +Xl=(V*Vl)/P; +L=Xl/(2*%pi*f); //inductance +disp(sprintf("The pure inductance should have a value of %6.4f H",L)); //text book answer is 0.7046 H + +//END diff --git a/1445/CH3/EX3.1/Ex3_1.sce b/1445/CH3/EX3.1/Ex3_1.sce new file mode 100644 index 000000000..f9883c955 --- /dev/null +++ b/1445/CH3/EX3.1/Ex3_1.sce @@ -0,0 +1,46 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 1 + +disp("CHAPTER 3"); +disp("EXAMPLE 1"); + +//VARIABLE INITIALIZATION +v_l=400; //line voltage in Volts +r=15; //resistance in Ohms +xc=10; //capacitive reactance in Ohms + +//SOLUTION + +//solution (i) +v_ph=v_l/sqrt(3); //phase voltage=(line voltage)/sqrt(3) for star connection +disp(sprintf("(i) The phase voltage is %.2f V",v_ph)); + +//solution (ii) +z_ph=sqrt((r^2)+(xc^2)); +I_l=v_ph/z_ph; //phase current = line current for star connection +disp(sprintf("(ii) The line current is %.2f A",I_l)); + +//solution (iii) +disp(sprintf("(iii) The phase current is %.2f A",I_l)); + +//solution (iv) +pow_fact=r/z_ph; +disp(sprintf("(iv) The power factor of the circuit is %.2f (leading)",pow_fact)); + +//solution (v) +p=sqrt(3)*v_l*I_l*pow_fact; +disp(sprintf("(v) The total power absorbed is %.0f W",p)); + +//solution (vi) +va=sqrt(3)*v_l*I_l; +disp(sprintf("(vi) The apparent power is %.0f VA",va)); +var=sqrt((va^2)-(p^2)); +disp(sprintf("The reactive power is %.0f VAR",var)); + +//Answers (v) and (vi) are different due to precision of floating point numbers + +//END + + + + diff --git a/1445/CH3/EX3.11/Ex3_11.sce b/1445/CH3/EX3.11/Ex3_11.sce new file mode 100644 index 000000000..03c2bf54d --- /dev/null +++ b/1445/CH3/EX3.11/Ex3_11.sce @@ -0,0 +1,68 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 11 + +disp("CHAPTER 3"); +disp("EXAMPLE 11"); + +//SOLUTION +function power_sum=p1(phi); +power_sum=20*cos(phi); //power_sum=p1+p2=20*cos(phi) and in KiloWatts +endfunction; +function power_diff=p2(phi); +power_diff=(20*sin(phi))/sqrt(3); //power_diff=p1-p2=(20*sin(phi))/sqrt(3) and in KiloWatts +endfunction; + +//solution (a): when phi=0 +power_sum=20*cos(0); //eq(i) +power_diff=(20*sin(0))/sqrt(3); //eq(ii) +//solving eq(i) and eq(ii) to get values of p1 and p2 +A=[1 1;1 -1]; +b=[power_sum;power_diff]; +x=inv(A)*b; +x1=x(1,:); //to access the 1st row of 2X1 matrix +x2=x(2,:); //to access the 2nd row of 2X1 matrix +disp("Solution (a)"); +disp(sprintf("P1 + P2 = %d kW",power_sum)); +disp(sprintf("P1 - P2 = %d kW",power_diff)); +disp(sprintf("The two wattmeter readings are %d kW and %d kW",x1,x2)); + +//solution (b): when phi=30 or %pi/6 (lagging) +power_sum=20*cos(%pi/6); +power_diff=(20*sin(%pi/6))/sqrt(3); +A=[1 1;1 -1]; +b=[power_sum;power_diff]; +x=inv(A)*b; +x1=x(1,:); +x2=x(2,:); +disp("Solution (b)"); +disp(sprintf("P1 + P2 = %.2f kW",power_sum)); +disp(sprintf("P1 - P2 = %.2f kW",power_diff)); +disp(sprintf("The two wattmeter readings are %.2f kW and %.2f kW",x1,x2)); + +//solution (c): when phi=60 or %pi/3 +power_sum=20*cos(%pi/3); +power_diff=(20*sin(-(%pi/3)))/sqrt(3); //leading +A=[1 1;1 -1]; +b=[power_sum;power_diff]; +x=inv(A)*b; +x1=x(1,:); +x2=x(2,:); +disp("Solution (c)"); +disp(sprintf("P1 + P2 = %.2f kW",power_sum)); +disp(sprintf("P1 - P2 = %.2f kW",power_diff)); +disp(sprintf("The two wattmeter readings are %.2f kW and %.2f kW",x1,x2)); + +//solution (d): when phi=90 or %pi/2 +power_sum=20*cos(%pi/2); +power_diff=(20*sin(%pi/2))/sqrt(3); //leading +A=[1 1;1 -1]; +b=[power_sum;power_diff]; +x=inv(A)*b; +x1=x(1,:); +x2=x(2,:); +disp("Solution (d)"); +disp(sprintf("P1 + P2 = %.2f kW",power_sum)); +disp(sprintf("P1 - P2 = %.2f kW",power_diff)); +disp(sprintf("The two wattmeter readings are %.2f kW and %.2f kW",x1,x2)); + +//END diff --git a/1445/CH3/EX3.12/Ex3_12.sce b/1445/CH3/EX3.12/Ex3_12.sce new file mode 100644 index 000000000..07ceb2454 --- /dev/null +++ b/1445/CH3/EX3.12/Ex3_12.sce @@ -0,0 +1,34 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 12 + +disp("CHAPTER 3"); +disp("EXAMPLE 12"); + +//VARIABLE INITIALIZATION +v_l=400; //in Volts +f=50; //in Hertz +w1=2000; //in Watts +w2=800; //in Watts + +//SOLUTION +//solution (a) +p1=w1+w2; +p2=w1-w2; +phi=atan((sqrt(3)*p2)/p1); //this equation comes from two-wattmeter method +pow_fact=cos(phi); +disp(sprintf("(a) The power factor of the circuit is %.3f (leading)",pow_fact)); + +//solution (b) +I_l=p1/(sqrt(3)*v_l*pow_fact); +disp(sprintf("(b) The line current is %.2f A",I_l)); + +//solution (c) +v_ph=v_l/sqrt(3); +z_ph=v_ph/I_l; //phase current = line current for delta connection +r_ph=z_ph*pow_fact; +disp(sprintf("(c) The resistance of each phase is %.2f Ω",r_ph)); +xc=sqrt((z_ph^2)-(r_ph^2)); +c=1/(2*%pi*f*xc); +disp(sprintf("The capacitance of each phase is %.3E F",c)); + +//END diff --git a/1445/CH3/EX3.2/Ex3_2.sce b/1445/CH3/EX3.2/Ex3_2.sce new file mode 100644 index 000000000..c5a2d35e0 --- /dev/null +++ b/1445/CH3/EX3.2/Ex3_2.sce @@ -0,0 +1,24 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 2 + +disp("CHAPTER 3"); +disp("EXAMPLE 2"); + +//VARIABLE INITIALIZATION +v_l=400; //line voltage in Volts +I_l=30; //line current in Amperes +p=12*1000; //power absorbed in Watts + +//SOLUTION +v_ph=v_l/sqrt(3); //phase voltage = (line voltage)/sqrt(3) +z_ph=v_ph/I_l; //phase current = line current for star connection +pow_fact=p/(sqrt(3)*v_l*I_l); //three-phase power = sqrt(3)*v_l*I_l*pow_fact +r_ph=z_ph*pow_fact; //from impedance tringle +disp(sprintf("The resisatnce of each impedance is %.2f Ω",r_ph)); +x_ph=sqrt((z_ph^2)-(r_ph^2)); +disp(sprintf("The ractance of each impedance is %.2f Ω",x_ph)); + +//END + + + diff --git a/1445/CH3/EX3.3/Ex3_3.sce b/1445/CH3/EX3.3/Ex3_3.sce new file mode 100644 index 000000000..e99995138 --- /dev/null +++ b/1445/CH3/EX3.3/Ex3_3.sce @@ -0,0 +1,35 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 3 + +disp("CHAPTER 3"); +disp("EXAMPLE 3"); + +//VARIABLE INITIALIZATION +r_ph=30; //resistance of coils in Ohms +l=0.07; //inductance of coils in Henry +v_l=400; //line voltage in Volts +f=50; //frequency in Hertz + +//SOLUTION + +//solution (a) +x_ph=2*(%pi)*f*l; //inductive reactance +z_ph=sqrt((r_ph^2)+(x_ph^2)); +I_ph=v_l/z_ph; //phase voltage = line voltage for delta connection +disp(sprintf("(a) The phase current is %.2f A",I_ph)); + +//solution (b) +I_l=sqrt(3)*I_ph; //phase current = (line current)/sqrt(3) for delta connection +disp(sprintf("(b) The line current is %.2f A",I_l)); + +//solution (c) +pow_fact=r_ph/z_ph; +disp(sprintf("(c) The power factor is %.3f (lagging)",pow_fact)); + +//solution (d) +p=sqrt(3)*v_l*I_l*pow_fact; +disp(sprintf("(d) The power absorbed is %.0f W",p)); + +//Answer is different due to precision of floating point numbers + +//END diff --git a/1445/CH3/EX3.4/Ex3_4.sce b/1445/CH3/EX3.4/Ex3_4.sce new file mode 100644 index 000000000..085e72919 --- /dev/null +++ b/1445/CH3/EX3.4/Ex3_4.sce @@ -0,0 +1,71 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 4 + +disp("CHAPTER 3"); +disp("EXAMPLE 4"); + +//VARIABLE INITIALIZATION +v_l=866; //line voltage in Volts +z_delta=177-(%i*246); //impedance of delta connected load in Ohms +z_wire=1+(%i*2); //impedance of each wire of the line in Ohms + +//SOLUTION +v_ph=v_l/sqrt(3); //phase current = (line current)/sqrt(3) for star connection +z_star=z_delta/3; +z=z_wire + z_star; +I=v_ph/z; //I_na in rectangular form +//I_na, I_nb and I_nc are same in magnitude and are the line currents for delta connection or vice-versa +//function is not used to covert quantities in rectangular form to polar form +//I_na +I_na=sqrt((real(I))^2+(imag(I))^2); //I_na from rectangular to polar form +a=atan(imag(I)/real(I)); //angle in radians +a=a*(180/%pi); //radians to degrees +//I_nb +I_na=sqrt((real(I))^2+(imag(I))^2); +b=a-120; //lags by 120 degrees +//I_nc +I_na=sqrt((real(I))^2+(imag(I))^2); +c=a-240; // lags by another 120 degrees ie.,240 degrees +disp(sprintf("The line currents are %.3f A (%.2f degrees), %.3f A (%.2f degrees) and %.3f A (%.2f degrees)",I_na,a,I_na,b,I_na,c)); + + +//line current lags phase current by 30 degrees, hence (-30) +//I_AB +I_AB=I_na/sqrt(3); +a1=a-(-30); +//I_BC +I_BC=I_na/sqrt(3); +b1=b-(-30); +//I_AC +I_AC=I_na/sqrt(3); +c1=c-(-30); +disp(sprintf("The phase currents are %.3f A (%.2f degrees), %.3f A (%.2f degrees) and %.3f A (%.2f degrees)",I_AB,a1,I_BC,b1,I_AC,c1)); + +//converting z_delta from polar form to rectangular form +z=sqrt((real(z_delta))^2+(imag(z_delta))^2); +angle=atan(imag(z_delta)/real(z_delta)); +angle=angle*(180/%pi); + +//line voltages for load or phase voltages for the delta load- +//v_AB +v_AB=I_AB*z; +a2=a1+angle; +//v_B +v_BC=I_BC*z; +b2=b1+angle; +//v_AC +v_AC=I_AC*z; +c2=c1+angle; +disp(sprintf("The phase voltages for the delta load are %.3f A (%.2f degrees), %.3f A (%.2f degrees) and %.3f A (%.2f degrees)",v_AB,a2,v_BC,b2,v_AC,c2)); + +p_AB=(I_AB^2)*real(z_delta); +p_load=3*p_AB; +disp(sprintf("The power absorbed by the load is %.2f W",p_load)); +p_l=3*(I_na^2)*real(z_wire); +disp(sprintf("The power dissipated by the line is %.2f W",p_l)); +p=p_load+p_l; +disp(sprintf("The total power supplied by 3-ϕ source is %.2f W",p)); + +//Answers may be slightly different due to precision of floating point numbers + +//END diff --git a/1445/CH3/EX3.5/Ex3_5.sce b/1445/CH3/EX3.5/Ex3_5.sce new file mode 100644 index 000000000..2804e3e92 --- /dev/null +++ b/1445/CH3/EX3.5/Ex3_5.sce @@ -0,0 +1,25 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 5 + +disp("CHAPTER 3"); +disp("EXAMPLE 5"); + +//VARIABLE INITIALIZATION +w1=5000; //reading of 1st wattmeter in Watts +w2=-1000; //reading of 2nd wattmeter in Watts + +//SOLUTION + +//solution (a) +p1=w1+w2; +disp(sprintf("(a) The total power is %d W",p1)); + +//solution (b) +p2=w1-w2; +phi=atan((sqrt(3)*p2)/p1); //this equation comes from two-wattmeter method +pow_fact=cos(phi); +disp(sprintf("(b) The power factor of the load is %.3f", pow_fact)); + +//END + + diff --git a/1445/CH3/EX3.6/Ex3_6.sce b/1445/CH3/EX3.6/Ex3_6.sce new file mode 100644 index 000000000..52cdce49a --- /dev/null +++ b/1445/CH3/EX3.6/Ex3_6.sce @@ -0,0 +1,34 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 6 + +disp("CHAPTER 3"); +disp("EXAMPLE 6"); + +//VARIABLE INITIALIZATION +v_l=3300; //line voltage in Volts +p_out=1500*735.5; //output power in Watts (1 metric horsepower= 735.498W) +eff=0.85; +pow_fact=0.81; + +//SOLUTION + +//solution (a) +p_in=p_out/eff; +disp(sprintf("(a) The motor input is %.2f kW",p_in/1000)); + +//solution (b) +I=p_in/(sqrt(3)*v_l*pow_fact);//phase current = line current for star connection +disp(sprintf("(b) The line and phase current of the alternator is %.2f A",I)); + +//solution (c) +I_l=I; +I_ph=I_l/sqrt(3); //phase current = (line current)/sqrt(3) for delta connection +disp(sprintf("(c) The line current of the motor is %.2f A",I_l)); +disp(sprintf("The phase current of the motor is %.2f A",I_ph)); + +//Answers may be different due to precision of floating point numbers + +//END + + + diff --git a/1445/CH3/EX3.7/Ex3_7.sce b/1445/CH3/EX3.7/Ex3_7.sce new file mode 100644 index 000000000..3371d0fe9 --- /dev/null +++ b/1445/CH3/EX3.7/Ex3_7.sce @@ -0,0 +1,33 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 7 + +disp("CHAPTER 3"); +disp("EXAMPLE 7"); + +//VARIABLE INITIALIZATION +v_ph=200; //phase voltage in Volts +r1=5; //in Ohms +r2=8; //in Ohms +r3=10; //in Ohms + +//SOLUTION +I1=v_ph/r1; +I2=v_ph/r2; +I3=v_ph/r3; +disp(sprintf("The current in the three phases are %d A, %d A and %d A",I1,I2,I3)); + +I_x=0+I2*(sqrt(3)/2)-I3*(sqrt(3)/2); //x-component of the three currents =>I_x = I1*cos(90) + I2*cos(30) + I3*cos(30) +I_y=I1-(I2*0.5)-(I3*0.5); //y-component of the three currents =>I_y = I1*sin(90) + I2*sin(30) + I3*sin(30) +I=sqrt((I_x^2)+(I_y^2)); +disp(sprintf("The neutral current is %.2f A",I)); + +p1=v_ph*I1; //power consumed in 1st phase +p2=v_ph*I2; //power consumed in 2nd phase +p3=v_ph*I3; //power consumed in 3rd phase +disp(sprintf("The power consumed in the three phases are %d W, %d W and %d W",p1,p2,p3)); + +p=p1+p2+p3; +disp(sprintf("The total power is %d W",p)); + +//END + diff --git a/1445/CH3/EX3.8/Ex3_8.sce b/1445/CH3/EX3.8/Ex3_8.sce new file mode 100644 index 000000000..bfc910b2f --- /dev/null +++ b/1445/CH3/EX3.8/Ex3_8.sce @@ -0,0 +1,34 @@ +//CHAPTER 3- THREE-PHASE A.C. CIRCUITS +//Example 8 + +disp("CHAPTER 3"); +disp("EXAMPLE 8"); + +//VARIABLE INITIALIZATION +v_ph=230; //in Volts and in polar form +z=8+(%i*6); //in Ohms and in rectanglar form + +//SOLUTION +//converting z from rectangular form to polar form +z_mag=sqrt(real(z)^2+imag(z)^2); +phi=atan(imag(z)/real(z)); //atan() gives output in radians + +I_ph=v_ph/z_mag; +I_l=sqrt(3)*I_ph; +disp(sprintf("The line current is %.2f A",I_l)); + +pow_fact=cos(phi); +disp(sprintf("The power factor is %.2f",pow_fact)); + +p=sqrt(3)*v_ph*I_l*pow_fact; //phase volt=line volt in delta connection(v_l=v_ph) +disp(sprintf("The power is %.2f W",p)); + +var=sqrt(3)*v_ph*I_l*sin(phi); +var=var/1000; //from VAR to kVAR +disp(sprintf("The reactive power is %.2f kVAR",var)); + +va=sqrt(3)*v_ph*I_l; +va=va/1000; //from VA to kVA +disp(sprintf("The total volt amperes is %.2f kVA",va)); + +//END diff --git a/1445/CH3/EX3.9/Ex4_9.sce b/1445/CH3/EX3.9/Ex4_9.sce new file mode 100644 index 000000000..037cea75c --- /dev/null +++ b/1445/CH3/EX3.9/Ex4_9.sce @@ -0,0 +1,28 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 9 + +disp("CHAPTER 4"); +disp("EXAMPLE 9"); + +//VARIABLE INITIALIZATION +I=50; //in Amperes +v=230; //in Volts +rev=61; //revolutions +t=37/3600; //from seconds to hours +m_c=500; //meter constant in rev/kwh +pow_fact=1; //since load is purely resistive + +//SOLUTION +E1=(v*I*t*pow_fact)/1000; //energy consumed in 37 seconds in kWh +E2=rev/m_c; //energy consumption registered by meter +err=(E2-E1)/E1; +err=err*100; //percentage error +disp(sprintf("The percentage error is %.2f %%",err)); +if(err<0) then +disp("The negative sign indicates that the meter will run slow"); +end + +//END + + + diff --git a/1445/CH4/EX4.1/Ex4_1.sce b/1445/CH4/EX4.1/Ex4_1.sce new file mode 100644 index 000000000..e46040447 --- /dev/null +++ b/1445/CH4/EX4.1/Ex4_1.sce @@ -0,0 +1,20 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 1 + +disp("CHAPTER 4"); +disp("EXAMPLE 1"); + +//VARIABLE INITIALIZATION +N=10; //number of turns +I=5; //in amperes +B=500; //flux density in Wb/m^2 +ar=15/10000; //area in m^2 + +//SOLUTION +T_d=N*B*I*ar; +disp(sprintf("The deflecting torque exerted on the coil is %.3f N-m",T_d)); + +//END + + + diff --git a/1445/CH4/EX4.10/Ex4_10.sce b/1445/CH4/EX4.10/Ex4_10.sce new file mode 100644 index 000000000..b60ae7828 --- /dev/null +++ b/1445/CH4/EX4.10/Ex4_10.sce @@ -0,0 +1,19 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 10 + +disp("CHAPTER 4"); +disp("EXAMPLE 10"); + +//VARIABLE INITIALIZATION +r1=2; //in Ohms (r1=2 is an assumption) +r2=2; //in Ohms (since r1=r2) +v=100; //in Volts + +//SOLUTION +v1=(v*r1)/(r1+r2); //voltage divider law +v2=(v*r2)/(r1+r2); //voltage divider law +disp(sprintf("Reading of the 1st voltmeter is %d V",v1)); +disp(sprintf("Reading of the 2nd voltmeter is %d V",v2)); + +//END + diff --git a/1445/CH4/EX4.11/Ex4_11.sce b/1445/CH4/EX4.11/Ex4_11.sce new file mode 100644 index 000000000..c52886b03 --- /dev/null +++ b/1445/CH4/EX4.11/Ex4_11.sce @@ -0,0 +1,21 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 11 + +disp("CHAPTER 4"); +disp("EXAMPLE 11"); + +//VARIABLE INITIALIZATION +r1=30000; //in Ohms +r2=20000; //in Ohms +v=600; //in Volts + +//SOLUTION +v1=(r1*v)/(r1+r2); //voltage divider law +v2=(r2*v)/(r1+r2); //voltage divider law +disp(sprintf("Reading of the 1st voltmeter is %d V",v1)); +disp(sprintf("Reading of the 2nd voltmeter is %d V",v2)); + +//END + + + diff --git a/1445/CH4/EX4.12/Ex4_12.sce b/1445/CH4/EX4.12/Ex4_12.sce new file mode 100644 index 000000000..4b5b1249e --- /dev/null +++ b/1445/CH4/EX4.12/Ex4_12.sce @@ -0,0 +1,22 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 12 + +disp("CHAPTER 4"); +disp("EXAMPLE 12"); + +//VARIABLE INITIALIZATION +I1=1; //full scale current in 1st ammeter in mA +I2=10; //full scale current in 2nd ammeter in mA +r1=100; //internal resistance of 1st ammeter in Ohms +r2=25; //internal resistance of 2nd ammeter in Ohms + +//SOLUTION +R1=r2/(r1+r2); //resistance for 1st ammeter +R2=r1/(r1+r2); //resistance for 2nd ammeter +I=I1/R1; //by current divider law I1=(I*r2)/(r1+r2) =>I1=I*R1 =>I=I1/R1 +A2=I*R2; //A2=reading of second ammeter +disp(sprintf("The total current that the two ammeters can carry is %d mA",I)); + +//END + + diff --git a/1445/CH4/EX4.2/Ex4_2.sce b/1445/CH4/EX4.2/Ex4_2.sce new file mode 100644 index 000000000..701df6ff4 --- /dev/null +++ b/1445/CH4/EX4.2/Ex4_2.sce @@ -0,0 +1,22 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 2 + +disp("CHAPTER 4"); +disp("EXAMPLE 2"); + +//VARIABLE INITIALIZATION +G=10; //galvanometer resistance in Ohms +S=1; //shunt resistance in Ohms +r=12; //total resistance in Ohms +emf=2; //emf of cell in Volts + +//SOLUTION +I=emf/r; //current in the circuit +I_g=(S*I)/(S+G); +disp(sprintf("The current through the galvanometer is %.3f A",I_g)); + +//END + + + + diff --git a/1445/CH4/EX4.3/Ex4_3.sce b/1445/CH4/EX4.3/Ex4_3.sce new file mode 100644 index 000000000..b66ea829a --- /dev/null +++ b/1445/CH4/EX4.3/Ex4_3.sce @@ -0,0 +1,27 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 3 + +disp("CHAPTER 4"); +disp("EXAMPLE 3"); + +//VARIABLE INITIALIZATION +I=1; //in Amperes (I=1 is an assumption) +I_g=I/100; //in Amperes +G=2970; //in Ohms + +//SOLUTION +S=(G*I_g)/(I-I_g); //since I_g=(S*I)/(S+G); + +disp(sprintf("The wire should have a resistance of %.0f Ω",S)); + +//END + + + + + + + + + + diff --git a/1445/CH4/EX4.4/Ex4_4.sce b/1445/CH4/EX4.4/Ex4_4.sce new file mode 100644 index 000000000..67b16af41 --- /dev/null +++ b/1445/CH4/EX4.4/Ex4_4.sce @@ -0,0 +1,28 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 4 + +disp("CHAPTER 4"); +disp("EXAMPLE 4"); + +//VARIABLE INITIALIZATION +r_A=10; //in Ohms +I_A=15/1000; //from mA to A +I=100; //in A +V=500; //in Volts + +//SOLUTION + +//solution (a) +R_sh=r_A/((I/I_A)-1); //(I/I_A) is the multiplying factor of the shunt + +disp(sprintf("The required shunt resistance is %.2f Ω",R_sh)); + +//solutuion (b) +r=V/I_A; //total resistance required +R_se=r-r_A; +disp(sprintf("The required resistance to be added in series is %.3f Ω",R_se)); + +//END + + + diff --git a/1445/CH4/EX4.5/Ex4_5.sce b/1445/CH4/EX4.5/Ex4_5.sce new file mode 100644 index 000000000..92c7bc1cf --- /dev/null +++ b/1445/CH4/EX4.5/Ex4_5.sce @@ -0,0 +1,26 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 5 + +disp("CHAPTER 4"); +disp("EXAMPLE 5"); + +//VARIABLE INITIALIZATION +m_c=100; //meter constant in rev/kWh +I=20; //load current in Amperes +v=230; //supply voltage in Volts +pow_fact=0.8; +rev_act=360; //actual number of revolutions + +//SOLUTION +E=(v*I*pow_fact)/1000; //'E' is energy consumed in one hour in kWh +rev=m_c*E; //number of revolutions for true energy +disp(sprintf("The number of revolutions made by the meter is %.0f",rev)); +err=(rev_act-rev)/rev; //error +err=err*100; //percentage error +disp(sprintf("The percentage error is %.2f %%",err)); +if(err<0) then +disp("The negative sign indicates that the meter will run slow"); +end + +//END + diff --git a/1445/CH4/EX4.6/Ex4_6.sce b/1445/CH4/EX4.6/Ex4_6.sce new file mode 100644 index 000000000..73dca4c0c --- /dev/null +++ b/1445/CH4/EX4.6/Ex4_6.sce @@ -0,0 +1,17 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 6 + +disp("CHAPTER 4"); +disp("EXAMPLE 6"); + +//VARIABLE INITIALIZATION +I_m=20/1000; //full scale deflection in Amperes +v_m=50/1000; //applied potential difference in Volts +v=500; //in Volts + +//SOLUTION +r_m=v_m/I_m; //resistance of moving-coil instrument +r_s=(v/I_m)-r_m; +disp(sprintf("The series resistance to measure 500 V on full scale is %.2f Ω",r_s)); + +//END diff --git a/1445/CH4/EX4.7/Ex4_7.sce b/1445/CH4/EX4.7/Ex4_7.sce new file mode 100644 index 000000000..9dc6529ee --- /dev/null +++ b/1445/CH4/EX4.7/Ex4_7.sce @@ -0,0 +1,27 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 7 + +disp("CHAPTER 4"); +disp("EXAMPLE 7"); + +//VARIABLE INITIALIZATION +m_c=100; //meter constant in rev/kwh +I=20; //in Amperes +v=210; //in Volts +pow_fact=0.8; //leading +rev_act=350; //actual revolution + +//SOLUTION +E=(v*I*pow_fact)/1000; //from Wh to kWh +rev_true=m_c*E; +disp(sprintf("The number of revolutions made by the meter is %.0f",rev_true)); +err=(rev_act-rev_true)/rev_true; +err=err*100; //percentage error +disp(sprintf("The percentage error is %.2f %%",err)); +if(err<0) then +disp("The negative sign indicates that the meter will run slow"); +end + +//END + + diff --git a/1445/CH4/EX4.8/Ex4_8.sce b/1445/CH4/EX4.8/Ex4_8.sce new file mode 100644 index 000000000..d298ccbd6 --- /dev/null +++ b/1445/CH4/EX4.8/Ex4_8.sce @@ -0,0 +1,22 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 8 + +disp("CHAPTER 4"); +disp("EXAMPLE 8"); + +//VARIABLE INITIALIZATION +I_m=15/1000; //from mA to A +r_m=5; //in Ohms +I=2; //in Amperes +v=30; //in Volts + +//SOLUTION +R_sh=(I_m*r_m)/I; //I_m=I*(R_sh/(R_sh+r_m)) if R_sh<<5Ω, then I_m=I*(R_sh/r_m) neglecting R_sh in the denominator +disp(sprintf("In order to read upto 2A, a shunt of %.2f Ω has to be connected in parallel",R_sh)); + +R_se=(v-(I_m*r_m))/I_m; +disp(sprintf("In order to read upto 30V, a resistance of %.2f Ω has to be connected in series",R_se)); + +//END + + diff --git a/1445/CH4/EX4.9/Ex4_9.sce b/1445/CH4/EX4.9/Ex4_9.sce new file mode 100644 index 000000000..037cea75c --- /dev/null +++ b/1445/CH4/EX4.9/Ex4_9.sce @@ -0,0 +1,28 @@ +//CHAPTER 4- MEASURING INSTRUMENTS +//Example 9 + +disp("CHAPTER 4"); +disp("EXAMPLE 9"); + +//VARIABLE INITIALIZATION +I=50; //in Amperes +v=230; //in Volts +rev=61; //revolutions +t=37/3600; //from seconds to hours +m_c=500; //meter constant in rev/kwh +pow_fact=1; //since load is purely resistive + +//SOLUTION +E1=(v*I*t*pow_fact)/1000; //energy consumed in 37 seconds in kWh +E2=rev/m_c; //energy consumption registered by meter +err=(E2-E1)/E1; +err=err*100; //percentage error +disp(sprintf("The percentage error is %.2f %%",err)); +if(err<0) then +disp("The negative sign indicates that the meter will run slow"); +end + +//END + + + diff --git a/1445/CH6/EX6.1/Ex6_1.sce b/1445/CH6/EX6.1/Ex6_1.sce new file mode 100644 index 000000000..f43815de9 --- /dev/null +++ b/1445/CH6/EX6.1/Ex6_1.sce @@ -0,0 +1,58 @@ +//CHAPTER 6- MAGNETIC CIRCUITS +//Example 1 + +disp("CHAPTER 6"); +disp("EXAMPLE 1"); + +//VARIABLE INITIALIZATION +lA=17/100; //length of A in meters (lA is calculated in the solution in the book; here it is initialised directly for the sake of convinience) +l=3/100; //in meters +lg=2/1000; //width of air-gap in meters +N=1000; //number of turns +AB=10/100; //in meters +BC=20/100; //in meters +CD=10/100; //in meters +I=1; //exciting current in Amperes +murA=1000; //relative permeability of part A +murB=1200; //relative permeability of part B +mu0=4*%pi*10^(-7);//absolute permeability in Henry/meters + +//SOLUTION + +//solution (i) +ar=l*l; //area of cross-section +rA=lA/(mu0*murA*ar); +disp(sprintf("(i) Reluctance of part A is %.3E AT/Wb",rA)); +lB=(AB-(l/2))+(BC-l)+(CD-(l/2)); +rB=lB/(mu0*murB*ar); +disp(sprintf("Reluctance of part B is %.3E AT/Wb",rB)); + +//solution (ii) +lg=2*lg; +murg=1; +rg=lg/(mu0*murg*ar); +disp(sprintf("(ii) Reluctance of the two air gaps is %.3E AT/Wb",rg)); + +//solution (iii) +rT=rA+rB+rg; +disp(sprintf("(iii) Total reluctance is %.2E AT/Wb",rT)); + +//solution (iv) +mmf=N*I; +disp(sprintf("(iv) MMF is %d AT",mmf)); + +//solution (v) +totFlux=mmf/rT; +disp(sprintf("(v) Total flux is %.3E Wb",totFlux)); + + +//solution (vi) +b=totFlux/ar; +disp(sprintf("(vi) Flux density is %.3f Wb/m^2",b)); + +//Answers of (v) and (vi) do not match due to calculation mistake in the book + +//END + + + diff --git a/1445/CH6/EX6.2/Ex6_2.sce b/1445/CH6/EX6.2/Ex6_2.sce new file mode 100644 index 000000000..983c61b58 --- /dev/null +++ b/1445/CH6/EX6.2/Ex6_2.sce @@ -0,0 +1,50 @@ +//CHAPTER 6- MAGNETIC CIRCUITS +//Example 2 + +disp("CHAPTER 6"); +disp("EXAMPLE 2"); + +//VARIABLE INITIALIZATION +dr=25/100; //diameter of steel ring in m +ds=3/100; //diameter of circular section in m +lg=1.5/1000; //length of air-gap in m +N=700; //number of turns +mu0=4*%pi*10^(-7); //absolute permeability in Henry/m +I=2; //in Amperes + +//SOLUTION + +//solution (i) +mmf=N*I; +disp(sprintf("(i) MMF is %d AT", mmf)); + +//solution (ii) +netMMF=(mmf-(0.35*mmf)); //mmf taken by iron path is 35% of total mmf +b=(mu0*netMMF)/lg; //phi=b*area, r=lg/(mu0*area) & mmf=phi*r => mmf=(b*lg)/mu0 => b=(mmf*mu0)/lg +disp(sprintf("(ii) The flux density of the air gap is %.3E Wb/m^2", b)); + +//solution (iii) +ar=%pi*((ds/2)^2); //area of cross-section of circular section +phi=ar*b; +disp(sprintf("(iii) The magnetic flux is %.3E Wb",phi)); + +//solution (iv) +rt=mmf/phi; +disp(sprintf("(iv) The total reluctance is %.4E AT/wb",rt)); + +//solution (v) +rg=lg/(mu0*ar); //reluctance of air gap +rs=rt-rg; //reluctance of steel +lr=%pi*dr; //circumference of ring +mur=lr/(mu0*rs*ar); +disp(sprintf("(v) The relative permeability of the steel ring is %3.3E",mur)); + +//solution (vi) +disp(sprintf("(vi) Reluctance of steel is %.2E AT/Wb",rs)); + +//END + + + + + diff --git a/1445/CH6/EX6.3/Ex6_3.sce b/1445/CH6/EX6.3/Ex6_3.sce new file mode 100644 index 000000000..906b2d0a8 --- /dev/null +++ b/1445/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,49 @@ +//CHAPTER 6- MAGNETIC CIRCUITS +//Example 3 + +disp("CHAPTER 6"); +disp("EXAMPLE 3"); + +//VARIABLE INITIALIZATION +lg1=0.025/100; //length of 1st air-gap in m +a1=(1*1)/10000; //in m^2 +lg2=0.02/100; //length of 2nd air-gap in m +a2=(1*1)/10000; //in m^2 +lg3=0.02/100; //length of 3rd air-gap in m +a3=(2*1)/10000; //in m^2 +phi=0.75/1000; //flux in Wb +lc1=0.5; //length through outer limb in m +lc2=0.5; //length through outer limb in m +lc3=0.2; //length through central limb in m +mu0=4*%pi*10^(-7); //absolute permeability in Henry/m + +//SOLUTUION + +//solution (a): when mur=infinity i.e., no mmf drops in any member of the core +rg1=lg1/(mu0*a1); //reluctance of 1st air-gap +rg2=lg2/(mu0*a2); //reluctance of 2nd air-gap +rg3=lg3/(mu0*a3); //reluctance of 3rd air-gap +rgeq=(rg1*rg2)/(rg1+rg2); //parallel combination of resistors +mmf1=phi*(rgeq+rg3); +mmf1=round(mmf1); //to round off the value +disp(sprintf("(a) MMF of the exciting coil when permeability is infinity is %d AT",mmf1)); + +//solution (b): when mur=5000 i.e., reluctance of magnetic core must be considered +mur=5000; +rc1=lc1/(mu0*mur*a1); //reluctance of first path in the core +rc2=lc2/(mu0*mur*a2); //reluctance of second path in the core +rc3=lc3/(mu0*mur*a3); //reluctance of third path in the core +r1=rg1+rc1; +r2=rg2+rc2; +r3=rg3+rc3; +req=(r1*r2)/(r1+r2); +totr=req+r3; //total resistance +mmf2=phi*totr; +mmf2=round(mmf2); +disp(sprintf("(b) MMF of the exciting coil when permeability is 5000 is %d AT",mmf2)); + +//END + + + + diff --git a/1445/CH6/EX6.4/Ex6_4.sce b/1445/CH6/EX6.4/Ex6_4.sce new file mode 100644 index 000000000..6ff7d2c9f --- /dev/null +++ b/1445/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,41 @@ +//CHAPTER 6- MAGNETIC CIRCUITS +//Example 4 + +disp("CHAPTER 6"); +disp("EXAMPLE 4"); + +//VARIABLE INITIALIZATION +di=10; //diameter of iron ring in cm +dr=1.5; //diameter of iron rod in cm +mui=900; //relative permeability of rod +mu0=4*%pi*10^(-7); //absolute permeability in Henry/m +lg=5/10; //length of air-gap in cm +N=400; //number of turns +I=3.4; //current through the winding in Amperes + +//SOLUTION +li=(di*%pi)-lg; //length of iron path +area=((dr^2)*%pi)/4; //area of iron cross-section + +//solution (a) +mmf=(4*%pi*N*I)/10; //in gilberts, since 1 AT=(4*pi)/10 +mmf=round(mmf); //to round off the value +disp(sprintf("(a) MMF is %d Gilberts",mmf)); + +//solution (b) +//tot reluctance = iron reluctance + air gap reluctance(mur=1 for air) +totR=(li/(area*mu0*mui))+(lg/(area*mu0*1)); +disp(sprintf("(b) The total reluctance is %.3E Gilberts/Maxwell",totR)); + +//solution (c) +phi=mmf/totR; +disp(sprintf("(c) The flux in the circuit is %.3f Maxwell",phi)); + +//solution (d) +b=phi/area; +disp(sprintf("(d) The flux density in the circuit is %.3f Gauss",b)); + +//Answers of (b), (c) & (d) are different because absolute permeability is not included in (b) + +//END + diff --git a/1445/CH6/EX6.5/Ex6_5.sce b/1445/CH6/EX6.5/Ex6_5.sce new file mode 100644 index 000000000..7bde18a7f --- /dev/null +++ b/1445/CH6/EX6.5/Ex6_5.sce @@ -0,0 +1,43 @@ +//CHAPTER 6- MAGNETIC CIRCUITS +//Example 5 + +disp("CHAPTER 6"); +disp("EXAMPLE 5"); + +//VARIABLE INITIALIZATION +li=100/100; //length of iron part in m +ls=200/100; //length of steel part in m +lg=1/100; //length of air gap in m +ai=20/10000; //cross-sectional area of iron in m^2 +as=10/10000; //cross-sectional area of steel in m^2 +ag=20/10000; //cross-sectional area of air-gap in m^2 +muRi=300; //relative permeability of iron +muRs=900; //relative permeability of steel +muRg=1; //relative permeability of air +N=170; //number of turns +phi=9000*10^(-8); //flux in Wb (1 line = 10^(-8) Wb) +lkg=1.2; //leakage coefficient +mu0=4*%pi*10^(-7); //absolute permeability in Henry/m + +//SOLUTION +rg=lg/(mu0*muRg*ag); +mg=rg*phi; +mg=round(mg); //to round off the value +disp(sprintf("MMF of the air gap is %d AT",mg)); + +ri=li/(mu0*muRi*ai); //reluctance of iron paths +mi=lkg*ri*phi; //MMF for iron path +mi=round(mi); +disp(sprintf("MMF of iron is %d AT",mi)); + +rs=ls/(mu0*muRs*as); //reluctance of steel paths +ms=lkg*rs*phi; //MMF for steel path +ms=round(ms); +disp(sprintf("MMF of cast steel is %d AT",ms)); + +totMMF=mg+mi+ms; +I=totMMF/N; +disp(sprintf("Current through the coil is %.3f A",I)); + +//END + diff --git a/1445/CH7/EX7.1/Ex7_1.sce b/1445/CH7/EX7.1/Ex7_1.sce new file mode 100644 index 000000000..c88808117 --- /dev/null +++ b/1445/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,35 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 1 + +disp("CHAPTER 7"); +disp("EXAMPLE 1"); + +//VARIABLE INITIALIZATION +I_0=10; //no load current in Amperes +pf=0.25; //power factor +v1=400; //in Volts +f=50; //in Hertz + +//SOLUTION + +//solution (a) +//magnetizing component +//Iphi=I0.sin theta +theta=acos(pf); //taking value of theta from the given power factor +I_phi=I_0*sin(theta); +disp(sprintf("(a) The magnetizing component of no load current is %.2f A",I_phi)); + +//solution (b) +//iron loss +//Pc=V1.Ic +//Ic=I0.cos theta & also Ic=I0.pf as pf=cos theta +p_c=v1*I_0*pf; +disp(sprintf("(b) The iron loss is %d W",p_c)); + +//solution (c) +N1=500; // number of turns in primary given +phi_m=v1/(sqrt(2)*%pi*f*N1); +disp(sprintf("(c) The maximum value of flux in the core is %.2f mWb",phi_m*1000)); + +//END + diff --git a/1445/CH7/EX7.10/Ex7_10.sce b/1445/CH7/EX7.10/Ex7_10.sce new file mode 100644 index 000000000..d9018d0ec --- /dev/null +++ b/1445/CH7/EX7.10/Ex7_10.sce @@ -0,0 +1,30 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 10 + +disp("CHAPTER 7"); +disp("EXAMPLE 10"); + +//6600/220 V single phase transformer +//VARIABLE INITIALIZATION +v1=6600; //primary voltage in Volts +v2=220; //secondary voltage in Volts +coreA=0.05; //core section m^2 +fluxD=1.2; //flux density in wm/m^2 +f=50; //Hz + +//SOLUTION +//E1=sqrt(2).pi.f.N1.φm +//flux density = Phimax/core area +phiM=coreA*fluxD; +N1=v1/(4.44*f*phiM); //4.44=sqrt(2).pi +N1=round(N1); +// +//N2=N1.E2/E1 +N2=N1*(v2/v1); +N2=round(N2); +disp(sprintf("The no. of turns on HT side is %d",N1)); +disp(sprintf("The no. of turns on LT side is %d",N2)); +disp(" "); +// +//END + diff --git a/1445/CH7/EX7.11/Ex7_11.sce b/1445/CH7/EX7.11/Ex7_11.sce new file mode 100644 index 000000000..df17e61c0 --- /dev/null +++ b/1445/CH7/EX7.11/Ex7_11.sce @@ -0,0 +1,28 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 11 + +disp("CHAPTER 7"); +disp("EXAMPLE 11"); + +//2200/220 V 44 kVA transformer with 50 turns in the secondary +//VARIABLE INITIALIZATION +va=44000; // +v1=2200; //primary voltage in Volts +v2=220; //secondary voltage in Volts +N2=50; //turns in secondary coil + +//SOLUTION +// N1/N2=V1/V2 +N1=N2*(v1/v2); +disp("SOLUTION (a)"); +disp(sprintf("The no. of turns on HT side is %f",N1)); +// +//since losses are negligible, input=output, V1.I1=V2.I2 +I1=va/v1; +I2=va/v2; +disp("SOLUTION (b)"); +disp(sprintf("The primary full load current is %.0f Amp",I1)); +disp(sprintf("The secondary full load current is %.0f Amp",I2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.12/Ex7_12.sce b/1445/CH7/EX7.12/Ex7_12.sce new file mode 100644 index 000000000..980b54bd2 --- /dev/null +++ b/1445/CH7/EX7.12/Ex7_12.sce @@ -0,0 +1,40 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 12 + +disp("CHAPTER 7"); +disp("EXAMPLE 12"); + +//no load cuurent of transformer ia 10A at pf of 0.25 lagging when connected to 400V, 50 Hz supply +//VARIABLE INITIALIZATION +v1=400; //primary voltage in Volts +f=50; //Hz +Io=10; //in Amp no load current +pf =0.25; //lagging +N1=500; //given + +//SOLUTION +//magnetizing component of no load current +// N1/N2=V1/V2 +//Iphi=Io.sin phi0 +//pf=cos phi0 +phi0=acos(pf); +Iphi=Io*sin(phi0); +disp("SOLUTION (a)"); +disp(sprintf("The magnetic component of no load current is %f Amp",Iphi)); +// +//iron loss +//Pi=ironloss=power input on no load +//Pi=Wo=V1.Io.cos phi0 +ironLoss=v1*Io*pf; +disp("SOLUTION (b)"); +disp(sprintf("The iron loss on no load is %.0f W",ironLoss)); +// +//maximum flux in the core +//E1=sqrt(2).pi.f.N1.φm +//E1=V1 +phiM=v1/(4.44*f*N1); +disp("SOLUTION (c)"); +disp(sprintf("The value of flux in the core is %5.4f mWb",phiM*1000)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.13/Ex7_13.sce b/1445/CH7/EX7.13/Ex7_13.sce new file mode 100644 index 000000000..047444eca --- /dev/null +++ b/1445/CH7/EX7.13/Ex7_13.sce @@ -0,0 +1,34 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 13 + +disp("CHAPTER 7"); +disp("EXAMPLE 13"); +//230/115 V single phase transformer +//VARIABLE INITIALIZATION +v1=230; //primary voltage in Volts +v2=115; +f=50; //Hz +Io=2; //in Amp no load current +pf0 =0.28; //lagging +I2=20; // +pf2=0.8; //lagging + +//SOLUTION +// +//given power factors in primary and secondary +// I1.N1=I2.N2 +phi0=acos(pf0); +phi2=acos(pf2); +//let Ix and Iy be the components of I0 and I'1 along X and Y axes +//then +//Ix=Io.sin phi0 + I'2.sin phi2 +// +//Ix=Io.cos phi0 + I'2.cos phi2 +I_dash_2=I2*v2/v1; +Ix=Io*sin(phi0)+I_dash_2*sin(phi2); +Iy=Io*cos(phi0)+I_dash_2*cos(phi2); +I1=sqrt(Ix^2+Iy^2); +disp(sprintf("The current taken by primary is %.1f Amp",I1)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.14/Ex7_14.sce b/1445/CH7/EX7.14/Ex7_14.sce new file mode 100644 index 000000000..4f635a60b --- /dev/null +++ b/1445/CH7/EX7.14/Ex7_14.sce @@ -0,0 +1,51 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 14 + +disp("CHAPTER 7"); +disp("EXAMPLE 14"); + +//1100/110 V 22 kVA single phase transformer +//VARIABLE INITIALIZATION +va=22000; //apparent power +v1=1100; //primary voltage in Volts +v2=110; //secondary voltage in Volts +R1=2; //in Ohms +R2=0.02; //in Ohms +X1=5; //in Ohms +X2=0.045; //in Ohms + +//SOLUTION +//N1/N2=v1/v2; + +R_dash_2=R2*((v1/v2)^2); +X_dash_2=X2*((v1/v2)^2); +disp("SOLUTION (a)"); +disp(sprintf("The equivalent resistance of secondary referred to primary is %.1fΩ",R_dash_2)); +disp(sprintf("The equivalent reactance of secondary referred to primary is %.1f Ω",X_dash_2)); +// +R_e1=R_dash_2+R1; +X_e1=X_dash_2+X1; +disp("SOLUTION (b)"); +disp(sprintf("The total resistance referred to primary is %.1f Ω",R_e1)); +disp(sprintf("The total reactance referred to primary is %.1f Ω",X_e1)); +// +R_dash_1=R1*((v2/v1)^2); +X_dash_1=X1*((v2/v1)^2); +disp("SOLUTION (c)"); +disp(sprintf("The equivalent resistance of secondary referred to secondary is %.2f Ω",R_dash_1)); +disp(sprintf("The equivalent reactance of secondary referred to secondary is %.2f Ω",X_dash_1)); +// +R_e2=R_dash_1+R2; +X_e2=X_dash_1+X2; +disp("SOLUTION (d)"); +disp(sprintf("The total resistance referred to secondary is %.3f Ω",R_e2)); +disp(sprintf("The total reactance referred to secondary is %.3f Ω",X_e2)); +// +I1=va/v1; +I2=va/v2; +copperLoss=R1*I1^2+R2*I2^2; +disp("SOLUTION (e)"); +disp(sprintf("The total copper loss is %4.0f W",copperLoss)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.15/Ex7_15.sce b/1445/CH7/EX7.15/Ex7_15.sce new file mode 100644 index 000000000..62b09f20e --- /dev/null +++ b/1445/CH7/EX7.15/Ex7_15.sce @@ -0,0 +1,38 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 15 + +disp("CHAPTER 7"); +disp("EXAMPLE 15"); +//20kVA single phase transformer +//VARIABLE INITIALIZATION +va=20000; //apparent power +v1=2000; //primary voltage in Volts +v2=200; //secondary voltage in Volts +R1=2.5; //in Ohms +R2=0.04; //in Ohms +X1=8; //in Ohms +X2=0.07; //in Ohms +pf2=0.8; + +//SOLUTION +//N1b/N2=v1/v2; +I2=va/v2; +phi2=acos(pf2); +// +R_dash_1=R1*((v2/v1)^2); +X_dash_1=X1*((v2/v1)^2); +// +R_e2=R_dash_1+R2; +X_e2=X_dash_1+X2; +//disp(sprintf("The total resistance referred to secondary is %f Ω",R_e2)); +//disp(sprintf("The total reactance referred to secondary is %f Ω",X_e2)); +// +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R +V2=v2-(I2*R_e2*pf2+I2*X_e2*sin(phi2)); +%reg=(v2-V2)*100/v2; +disp(sprintf("The secondary terminal voltage is %.2f V",V2)); +disp(sprintf("The percent regulation at full load is %.2f",%reg)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.16/Ex7_16.sce b/1445/CH7/EX7.16/Ex7_16.sce new file mode 100644 index 000000000..99cf22818 --- /dev/null +++ b/1445/CH7/EX7.16/Ex7_16.sce @@ -0,0 +1,47 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 16 + +disp("CHAPTER 7"); +disp("EXAMPLE 16"); + +//Values from the previous example. +//VARIABLE INITIALIZATION +va=20000; //apparent power +v1=2000; //primary voltage in Volts +v2=200; //secondary voltage in Volts +R1=2.5; //in Ohms +R2=0.04; //in Ohms +X1=8; //in Ohms +X2=0.07; //in Ohms +pf2=0.8; + +//SOLUTION +//N1/N2=v1/v2; +I2=va/v2; +phi2=acos(pf2); + +// +R_dash_1=R1*((v2/v1)^2); +X_dash_1=X1*((v2/v1)^2); +// +R_e2=R_dash_1+R2; +X_e2=X_dash_1+X2; +//disp(sprintf("The total resistance referred to secondary is %f Ω",R_e2)); +//disp(sprintf("The total reactance referred to secondary is %f Ω",X_e2)); +// +//power factor angle at which regulation is zero is given by tan.phi2=-Re2/Xe2 +phi2=atan(-R_e2/X_e2); +disp(sprintf("The PF at which the regulation is zero is %.3f",cos(phi2))); +// +//power factor angle at which regulation is maximum is given by tan.phi2=Xe2/Re2 +phi2=atan(X_e2/R_e2); +disp(sprintf("The PF at which the regulation is maximum is %.3f",cos(phi2))); +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R + +V2=v2-(I2*R_e2*cos(phi2)+I2*X_e2*sin(phi2)); +%reg=(v2-V2)*100/v2; +disp(sprintf("The maximum value of percent regulation is %.2f ",%reg)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.17/Ex7_17.sce b/1445/CH7/EX7.17/Ex7_17.sce new file mode 100644 index 000000000..7ae2f47e6 --- /dev/null +++ b/1445/CH7/EX7.17/Ex7_17.sce @@ -0,0 +1,43 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 17 + +disp("CHAPTER 7"); +disp("EXAMPLE 17"); + +//200kVA single phase transformer +//VARIABLE INITIALIZATION +va=200000; // +ironLoss=1000; // Watts +cuLoss=2000; //Watts +pf=0.8; +// +//SOLUTION +// +Pout=va*pf; //Full load output +loss=ironLoss+cuLoss; +Pin=Pout+loss; //INPUT=OUTPUT+LOSS +eff=Pout*100/Pin; +disp("SOLUTION (a)"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +// +//at half load +Pout=va*pf/2; +loss=ironLoss+cuLoss*(1/2)^2; // ironloss is independent of output +Pin=Pout+loss; +eff=Pout*100/Pin; +disp("SOLUTION (b)"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +// +//fraction x of copperloss=ironloss for maximum efficiency +//x^2.cuLoss=ironLoss +x=sqrt(ironLoss/cuLoss); +Pout=x*va*pf; +loss=ironLoss+cuLoss*x^2; +Pin=Pout+loss; +eff=Pout*100/Pin; +disp("SOLUTION (c)"); +disp(sprintf("The percent efficiency at %f load is %.2f ",x,eff)); + +disp(" "); +// +//END diff --git a/1445/CH7/EX7.18/Ex7_18.sce b/1445/CH7/EX7.18/Ex7_18.sce new file mode 100644 index 000000000..5d9e22bf4 --- /dev/null +++ b/1445/CH7/EX7.18/Ex7_18.sce @@ -0,0 +1,47 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 18 + +disp("CHAPTER 7"); +disp("EXAMPLE 18"); + +//400kVA distribution transformer variously loaded during day +//VARIABLE INITIALIZATION +va=400000; // +ironLoss=1500; // Watts +cuLoss=4000; //Watts +//during the day frommidnight to midnight is as below: +h1=6; //first 6 hours from midnight to 6 hrs +load1=0; +pf1=0; +h2=6; //next 6 hours from 6 am to noon +load2=100000; //kVA converted to VA +pf2=0.8; +h3=5; //next from noon to 5 pm +load3=400000; +pf3=0.8; +h4=3; //next from 5 pm to 8 pm +load4=300000; +pf4=0.7; +h5=4; //next from 8 pm to midnight +load5=200000; +pf5=0.85; +// +//SOLUTION +// +//energy loss at any load=(VA output/VA rated)^2 .Full load cuLoss +loss1=h1*load1; +loss2=h2*(load2/va)^2*cuLoss; +loss3=h3*(load3/va)^2*cuLoss; +loss4=h4*(load4/va)^2*cuLoss; +loss5=h5*(load5/va)^2*cuLoss; +//loss in 24 hours +loss24=loss1+loss2+loss3+loss4+loss5; +//disp(sprintf("The all day loss is %f ",loss24)); +Pout=h1*load1*pf1+h2*load2*pf2+h3*load3*pf3+h4*load4*pf4+h5*load5*pf5; +//disp(sprintf("The all day energy output is %f ",Pout)); +Pin=Pout+ironLoss*24+loss24; +eff=Pout*100/Pin; +disp(sprintf("The all day percent efficiency is %.2f ",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.19/Ex7_19.sce b/1445/CH7/EX7.19/Ex7_19.sce new file mode 100644 index 000000000..5673a8c80 --- /dev/null +++ b/1445/CH7/EX7.19/Ex7_19.sce @@ -0,0 +1,70 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 19 + +disp("CHAPTER 7"); +disp("EXAMPLE 19"); + +//Open circuit and short circuit test on 10 kVA transformer 500/250 V 50 Hz single phase transformer +//VARIABLE INITIALIZATION +va=10000; //apparent power +v1=500; //primary voltage in Volts +v2=250; //secondary voltage in Volts +f=50; +//open circuit parameters +Voc=500; +Io=2; +Wi=100; // watts HT side +Woc=Wi; //just another nomenclature +//short circuit test +Vsc=25; +Isc=20; +Wc=90; // watts HT side +// +pf=0.8; +//SOLUTION +//open circuit +phi0=acos(Woc/(v1*Io)); +Ic=Io*cos(phi0); +Iphi=Io*sin(phi0); +Rc=v1/Ic; +X=v1/Iphi; +disp("SOLUTION (a)"); +disp(sprintf("The value of Ic is %.2f Amp",Ic)); +disp(sprintf("The value of IΦ is %.2f Amp",Iphi)); +disp(sprintf("The value of Rc is %.0f Ohm",Rc)); +disp(sprintf("The value of X is %.0fΩ",X)); +// +//short circuit +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Vsc*pf1/Isc; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp(sprintf("The value of Power factor is %.3f",pf1)); +disp(sprintf("The value of Re1 is %.3f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %.3f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %.3fΩ",X_e1)); +// +//Regulation and efficiency +//% Regulation +I1=va/v1; +phi=acos(pf); +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R +%reg=(Isc*R_e1*pf+Isc*X_e1*sin(phi))*100/v1; +disp("SOLUTION (c(i))"); +disp(sprintf("The percent regulation at full load is %.2f",%reg)); +// +//Efficiency +//full load output at pf=0.8 +Pout=va*pf; +ironLoss=Wi; +cuLoss=Wc; +loss=ironLoss+cuLoss; +Pin=Pout+loss; +eff=Pout*100/Pin; +disp("SOLUTION (c(ii))"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.2/Ex7_2.sce b/1445/CH7/EX7.2/Ex7_2.sce new file mode 100644 index 000000000..df6d083dd --- /dev/null +++ b/1445/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,42 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 2 + +disp("CHAPTER 7"); +disp("EXAMPLE 2"); +// +//400/200V transformer +//VARIABLE INITIALIZATION +v1=400; //primary voltage in Volts +v2=200; //secondary voltage in Volts +I0=1; //in Amperes +pf1=0.4; //power factor in degrees on no load +I2=50; //secondary current in Amperes +pf2=0.8; //secondary supplies lagging power factor in degrees + +//SOLUTION +//primary current is given by +//I1=I0+I2 +//function to convert from polar to rectangular form +function [x,y]=pol2rect(mag,angle1); +x=mag*cos(angle1); +y=mag*sin(angle1); +endfunction; +// +phi_0=acos(pf1); // cosine inverse of the power factor which is given +phi=acos(pf2); // cosine inverse of the power factor which is given +I2_dash=(v2*I2)/v1; //v1.i1=v2.i2 +//I0=1 < phi_0 in polar format +[x0,y0]=pol2rect(I0,-phi_0); +[x2_dash,y2_dash]=pol2rect(I2_dash,-phi); +I1_x=x0+x2_dash; //x-component of I1 +I1_y=y0+y2_dash; //y-component of I1 +disp(sprintf("The primary current in reactangular form is (%.3f-j%.2f) A",I1_x,-I1_y)); +// +//function to convert from rectangular form to polar form +function [I,angle]=rect2pol(x,y); +I=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[I,angle]=rect2pol(I1_x,I1_y); // converting current from rectangular to polar form +disp(sprintf("The primary current in polar form is (%.3f <%.2f) A",I,angle)); +//END diff --git a/1445/CH7/EX7.20/Ex7_20.sce b/1445/CH7/EX7.20/Ex7_20.sce new file mode 100644 index 000000000..0c5f59379 --- /dev/null +++ b/1445/CH7/EX7.20/Ex7_20.sce @@ -0,0 +1,44 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 20 + +disp("CHAPTER 7"); +disp("EXAMPLE 20"); + +//4 kVA 200/400 V 50 hz single phase transformer +//VARIABLE INITIALIZATION +va=4000; //apparent power +v1=200; //primary voltage in Volts +v2=400; //secondary voltage in Volts +f=50; +R_e1=0.15; +Pi=60; //core losses iron core +pf1=0.9; //power factor of primary +pf2=0.8; //power factor of secondary + +//SOLUTION +//Copper loss on full load +R_e2=(v2/v1)^2*R_e1; +I1=va/v1; +I2=va/v2; +Pcu=I2^2*R_e2; //cu losses +disp("SOLUTION (i)"); +disp(sprintf("The value of Copper Losses at full load is %.0f W",Pcu)); +// +//efficiency +Pout=va*pf1; +Pin=Pout+Pi+Pcu; +eff=Pout*100/Pin; +disp("SOLUTION (ii)"); +disp(sprintf("The percent efficiency at full load %f PF is %.2f",pf1,eff)); +// +// +//efficiency at half load +Pout=va*pf2/2; +Pin=Pout+Pi+Pcu*(1/2)^2; +eff=Pout*100/Pin; +disp("SOLUTION (ii)"); +disp(sprintf("The percent efficiency at half load %f PF is %.2f",pf2,eff)); + +disp(" "); +// +//END diff --git a/1445/CH7/EX7.21/Ex7_21.sce b/1445/CH7/EX7.21/Ex7_21.sce new file mode 100644 index 000000000..7135f11c4 --- /dev/null +++ b/1445/CH7/EX7.21/Ex7_21.sce @@ -0,0 +1,36 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 21 + +disp("CHAPTER 7"); +disp("EXAMPLE 21"); + +//250/125 V 5kVA single phase transformer +//VARIABLE INITIALIZATION +va=5000; //apparent power +v1=250; //primary voltage in Volts +v2=125; //secondary voltage in Volts +R1=0.2; //resistance of primary +X1=0.75; //leakage reactance of primary +R2=0.05; //resistance of secondary +X2=0.2; //leakage reactance of secondary +pf=0.8; //power factor (leading) + +//SOLUTION +R_e2=(v2/v1)^2*R1+R2; +X_e2=(v2/v1)^2*X1+X2; +I1=va/v1; +I2=va/v2; +// +//at full load leading +phi=acos(pf); +%reg=(I2*R_e2*pf-I2*X_e2*sin(phi))*100/v2; +disp("SOLUTION (i)"); +disp(sprintf("The percent regulation at full load is %.2f",%reg)); +// +//%R=(E2-V2).100/E2 +V2=v2-%reg*v2/100; +disp("SOLUTION (ii)"); +disp(sprintf("The secondary terminal voltage at full load is %.2f V",V2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.22/Ex7_22.sce b/1445/CH7/EX7.22/Ex7_22.sce new file mode 100644 index 000000000..8262bd109 --- /dev/null +++ b/1445/CH7/EX7.22/Ex7_22.sce @@ -0,0 +1,29 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 22 + +disp("CHAPTER 7"); +disp("EXAMPLE 22"); + +//6600/400 V single phase transformer +//VARIABLE INITIALIZATION +v1=6600; //primary voltage in Volts +v2=400; //secondary voltage in Volts +R1=2.5; //primary resistance +R2=0.01; //secondary resistance + +//SOLUTION +//while finding equivalent resistance referrd to primary +//transfer R2 resistance to R'2 +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +// +//to find total equivalent resistance referred to secondary +//first calculate R'1 +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +// +disp(sprintf("The total equivalent resistance referred to primary is %.6f Ω",R_e1)); +disp(sprintf("The total equivalent resistance referred to secondary is %.6f Ω",R_e2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.23/Ex7_23.sce b/1445/CH7/EX7.23/Ex7_23.sce new file mode 100644 index 000000000..c794f2e98 --- /dev/null +++ b/1445/CH7/EX7.23/Ex7_23.sce @@ -0,0 +1,79 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 23 + +disp("CHAPTER 7"); +disp("EXAMPLE 23"); + +//33kVA 2200/220 V 50Hz single phase transformer +//VARIABLE INITIALIZATION +va=33000; +v1=2200; //primary voltage in Volts +v2=220; //secondary voltage in Volts +f=50; // frequency in Hz +R1=2.4; //primary winding (High Voltage side) resistance +X1=6; //primary winding (High Voltage side)leakage reactance +R2=0.03; //secondary winding (Low Voltage side) resistance +X2=0.07; //secondary winding (Low Voltage side)leakage reactance + +//SOLUTION +// +//Primary resistance and leakage reactance referred to secondary +//R'1 & X'1 +//Secondary resistance and leakage reactance referred to primary +//R'2 & X'2 +//Equivalent resistance & leakage reactance referred to primary +//Re1 & Xe1 +//Equivalent resistance & leakage reactance referred to secondary +//Re2 & Xe2 +// +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +X_dash_2=X2*(v1/v2)^2; +X_e1=X1+X_dash_2; +// +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +X_dash_1=X1*(v2/v1)^2; +X_e2=X2+X_dash_1; + +disp("SOLUTION (a)"); +disp(sprintf("The primary resistance referred to secondary %.2f Ω",R_dash_1)); +disp(sprintf("The primary leakage reactance referred to secondary %.2f Ω",X_dash_1)); +// +disp("SOLUTION (b)"); +disp(sprintf("The secondary resistance referred to secondary %.2f Ω",R_dash_2)); +disp(sprintf("The secondary leakage reactance referred to secondary %.2f Ω",X_dash_2)); +// +disp("SOLUTION (C(i))"); +disp(sprintf("The equivalent resistance referred to primary %.2f Ω",R_e1)); +disp(sprintf("The equivalent leakage reactance referred to primary %.2f Ω",X_e1)); +// +disp("SOLUTION (C(ii))"); +disp(sprintf("The equivalent resistance referred to secondaryy %.2f Ω",R_e2)); +disp(sprintf("The equivalent leakage reactance referred to secondary %.2f Ω",X_e2)); +// +//Ohmic load +I1=va/v1; // primary full load current +I2=va/v2; // secondary full load current +oLoss=I2^2*R_e2; //ohmic loss +disp("SOLUTION (d)"); +disp(sprintf("The ohmic loss at full load %.0f W",oLoss)); +// +//Voltage to be applied on the HV side +//to obtain short circuit currnet of 160 A in L.V side winding +Z_e1=sqrt(R_e1^2+X_e1^2); // equivalent leakage impedance +//voltage to be applied on HV side is equivalent leakage reactance x primary current +//relationship between current and voltage in transformer +//I1/I2=V2/V1 +//Given V2=220 V, V1=2200 V, I2=160 Amp +//Therefore, I1=I2.(V2/V1) +I1=160*(v2/v1); +V=I1*Z_e1; //160*(v2/v1)*Z_e1; +//Power Input +P=(I1)^2*R_e1 //P=I^2.R +disp("SOLUTION (e)"); +disp(sprintf("The voltage to be applied on HV side is %.2f V",V)); +disp(sprintf("The power input is %.1f W",P)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.24/Ex7_24.sce b/1445/CH7/EX7.24/Ex7_24.sce new file mode 100644 index 000000000..6a74149b1 --- /dev/null +++ b/1445/CH7/EX7.24/Ex7_24.sce @@ -0,0 +1,61 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 24 + +disp("CHAPTER 7"); +disp("EXAMPLE 24"); + +//10kVA 2500/250 V single phase transformer +//VARIABLE INITIALIZATION +va=10000; +v1=2500; //primary voltage in Volts +v2=250; //secondary voltage in Volts +R1=4.8; //primary HV side winding resistance +X1=11.2; //primary HV side winding leakage reactance +R2=0.048; //secondary LV side winding resistance +X2=0.112; //secondary LV side winding leakage reactaance + +//SOLUTION +// +//Primary resistance and leakage reactance referred to secondary +//R'1 & X'1 +//Secondary resistance and leakage reactance referred to primary +//R'2 & X'2 +//Equivalent resistance & leakage reactance referred to primary +//Re1 & Xe1 +//Equivalent resistance & leakage reactance referred to secondary +//Re2 & Xe2 +// +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +X_dash_2=X2*(v1/v2)^2; +X_e1=X1+X_dash_2; +// +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +X_dash_1=X1*(v2/v1)^2; +X_e2=X2+X_dash_1; +//leakage impedence +//The transformer leakage impedance=z0=Re2+j.Xe2 +//Therefore: +z0=R_e2+X_e2*%i; +//Further Given +//the LV winding side is connected to load impedance of 5+j.3.5 Ohm +//The power factor 0.8 lagging on LV side +//applied load is +Zl=5+3.5*%i; +//total impedence in series +//The leakage impedance and load impedance are in series, therefore, total impedance is sum of the two +// +Z=z0+Zl; +magZ=sqrt(real(Z)^2+imag(Z)^2); +magZl=sqrt(real(Zl)^2+imag(Zl)^2); +//V2=I2.Zl +I2=v2/magZ; +V2=I2*magZl +disp("SOLUTION (a)"); +disp(sprintf("The secondary terminal voltage is %.0f V",V2)); +// +//part (b) and (c) of the problem cannot be solved mathematically alone. +disp(" "); +// +//END diff --git a/1445/CH7/EX7.25/Ex7_25.sce b/1445/CH7/EX7.25/Ex7_25.sce new file mode 100644 index 000000000..acb81a060 --- /dev/null +++ b/1445/CH7/EX7.25/Ex7_25.sce @@ -0,0 +1,66 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 25 + +disp("CHAPTER 7"); +disp("EXAMPLE 25"); + +//15kVA 2200/110 V transformer +//VARIABLE INITIALIZATION +va=25000; //power rating +v1=2200; //primary voltage in Volts +v2=110; //secondary voltage in Volts +f=50; +R1=1.75; +X1=2.6; +R2=0.0045; +X2=0.0075; + +//SOLUTION +// +//Primary resistance and leakage reactance referred to secondary +//R'1 & X'1 +//Secondary resistance and leakage reactance referred to primary +//R'2 & X'2 +//Equivalent resistance & leakage reactance referred to primary +//Re1 & Xe1 +//Equivalent resistance & leakage reactance referred to secondary +//Re2 & Xe2 +// +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +X_dash_2=X2*(v1/v2)^2; +X_e1=X1+X_dash_2; +// +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +X_dash_1=X1*(v2/v1)^2; +X_e2=X2+X_dash_1; +// +Z_e1=R_e1+X_e1*%i; +Z_e2=R_e2+X_e2*%i; +magZ_e1=sqrt(real(Z_e1)^2+imag(Z_e1)^2); +magZ_e2=sqrt(real(Z_e2)^2+imag(Z_e2)^2); +// +// +disp("SOLUTION (a)"); +disp(sprintf("The equivalent resistance referred to primary %.2f Ω",R_e1)); +disp("SOLUTION (b)"); +disp(sprintf("The equivalent resistance referred to secondaryy %.5f Ω",R_e2)); +disp("SOLUTION (c)"); +disp(sprintf("The equivalent leakage reactance referred to primary %.1f Ω",X_e1)); +disp("SOLUTION (d)"); +disp(sprintf("The equivalent leakage reactance referred to secondary %.3f Ω",X_e2)); +disp("SOLUTION (e)"); +disp(sprintf("The equivalent impedance referred to primary %.5f Ω",magZ_e1)); +disp("SOLUTION (f)"); +disp(sprintf("The equivalent impedance referred to secondary %.5f Ω",magZ_e2)); +// +//primary and secondary full load current and voltage relationship with power rating +I1=va/v1; //primary current +I2=va/v2; //secondary current +cuLoss=I2^2*R_e2; //copper loss or also as I1^2.R1 + I2^2.R2 +disp("SOLUTION (d)"); +disp(sprintf("The copper loss at full load %f W",cuLoss)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.26/Ex7_26.sce b/1445/CH7/EX7.26/Ex7_26.sce new file mode 100644 index 000000000..7fed48bc9 --- /dev/null +++ b/1445/CH7/EX7.26/Ex7_26.sce @@ -0,0 +1,68 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 26 + +disp("CHAPTER 7"); +disp("EXAMPLE 26"); + +//open circuit & short circuit test +//10 kVA 500/250 V 50 Hz single phase +//VARIABLE INITIALIZATION +va=10000; //apparent power +v1=500; //primary voltage in Volts +v2=250; //secondary voltage in Volts +f=50; // frequency +//open circuit parameters +Voc=500; +Io=2; +Wi=100; // watts HT side +Woc=Wi; //just to keep symbology +//short circuit test +Vsc=25; +Isc=20; +Wc=90; // watts HT side +// +pf=0.8; +//SOLUTION +//open circuit +phi0=acos(Woc/(v1*Io)); +Ic=Io*cos(phi0); +Iphi=Io*sin(phi0); +Rc=v1/Ic; +X=v1/Iphi; +disp("SOLUTION (a)"); +disp(sprintf("The value of Ic is %.2f Amp",Ic)); +disp(sprintf("The value of IΦ is %.2f Amp",Iphi)); +disp(sprintf("The value of Rc is %.2f Ohm",Rc)); +disp(sprintf("The value of X is %.2fΩ",X)); +// +//short circuit +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Vsc*pf1/Isc; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp(sprintf("The value of Power factor is %f",pf1)); +disp(sprintf("The value of Re1 is %f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %fΩ",X_e1)); +// +I1=va/v1; +phi=acos(pf); +//R=er.cos phi2+vx.sin phi2 +//E2=V2+I2.R +%reg=(Isc*R_e1*pf+Isc*X_e1*sin(phi))*100/v1; +disp("SOLUTION (c(i))"); +disp(sprintf("The percent regulation at full load is %.2f",%reg)); +// +//full load output at pf=0.8 +Pout=va*pf; // Output Power +ironLoss=Wi; +cuLoss=Wc; +loss=ironLoss+cuLoss; +Pin=Pout+loss; //Input Power +eff=Pout*100/Pin; //efficiency +disp("SOLUTION (c(ii))"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.27/Ex7_27.sce b/1445/CH7/EX7.27/Ex7_27.sce new file mode 100644 index 000000000..b72abacee --- /dev/null +++ b/1445/CH7/EX7.27/Ex7_27.sce @@ -0,0 +1,73 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 27 + +disp("CHAPTER 7"); +disp("EXAMPLE 27"); + +//200kVA 1100/400 V delta star distribution transformer +//three phase +//VARIABLE INITIALIZATION +va=200000; //apparent power +v1=11000; //primary voltage in Volts +v2=400; //secondary voltage in Volts +f=50; // frequency +//open circuit test parameters +V3=400; +I3=9; +W3=1500; //load in watts HT side +//short circuit test parameters +Vsc=350; +Isc=20; +Wc=2100; //load in watts HT side +// +pf=0.8; +//SOLUTION +Voc=V3/sqrt(3); //per phase applied voltage in open circiut +Io=9; //per phase exciting current.= I3 +Wi=W3/3; // per phase core loss in watts HT side +Pc=Wi; //core losses +//power factor Pc=V1.Io.cos phi0 //v1=Voc +//open circuit test performed on LV side +phi0=acos(Wi/(Voc*Io)); +Ic=Io*cos(phi0); //core loss current +Iphi=Io*sin(phi0); //magnetising current +Rc=Voc/Ic; //Core loss resistance +X=Voc/Iphi; // +disp("SOLUTION (a)"); +disp(sprintf("The value of Ic is %.0f Amp",Ic)); +disp(sprintf("The value of IΦ is %.2f Amp",Iphi)); +disp(sprintf("The value of Rc is %.2f Ohm",Rc)); +disp(sprintf("The value of X is %.2fΩ",X)); +// +//core loss resistance referred to hv side +Rch=Rc*(v1/Voc)^2; +XphiH=X*(v1/Voc)^2; +disp(sprintf("The value of Rch is %.2f kΩ",Rch/1000)); +disp(sprintf("The value of XΦh is %.2f KΩ",XphiH/1000)); +//short circuit +//This test performed on HV side +//first find rated current +Isc=va/(3*v1); +Psc=Wc/3; //ohmic loss per phase +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Psc/Isc^2; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp(sprintf("The value of ohmic loss per phase is %.0f W",Psc)); +disp(sprintf("The value of Re1 is %.2f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %.2f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %.2fΩ",X_e1)); +// +//efficiency at half load +pf=1; //unity power factor +Pout=(va/3)*(1/2)*pf; +//core losses=Pc +//cuLosses ohmic loss =Psc +Pin=Pout+Pc+(1/2)^2*Psc; +eff=Pout*100/Pin; +disp(sprintf("The efficiency at half load is %.2f",eff)); + +disp(" "); +// +//END diff --git a/1445/CH7/EX7.28/Ex7_28.sce b/1445/CH7/EX7.28/Ex7_28.sce new file mode 100644 index 000000000..022c5502e --- /dev/null +++ b/1445/CH7/EX7.28/Ex7_28.sce @@ -0,0 +1,97 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 28 + +disp("CHAPTER 7"); +disp("EXAMPLE 28"); + +//10 kVA 2500/250 V single phase transformer +//open circuit and short circuit tests +//VARIABLE INITIALIZATION +va=10000; //apparent power +v1=2500; //primary voltage in Volts +v2=250; //secondary voltage in Volts +f=50; +//open circuit parameters +Voc=250; +Io=0.8; +Wi=50; // watts HT side +//short circuit test +Vsc=60; +Isc=3; +Wc=45; // watts HT side +// +//loads +pf=0.8; +//SOLUTION +//Open circuit test conducted on lv because 250 V during this test is equal to rated voltage on lv side. +I1=va/v1; //full rated current on hv side +Psc0=Wc*(I1/Isc)^2; //ohmic loss/ cu loss at full load rated current +Pc=Wi; // core losses +// 1/4 load +Psc=(1/4)^2*Psc0; +Pout=va*pf*(1/4); +Pin=Pout+Pc+Psc; +eff=Pout*100/Pin; +disp("SOLUTION (a)"); +disp(sprintf("The efficiency at 1/4 load is %.2f",eff)); +// +// 1/2 load +Psc=(1/2)^2*Psc0; +Pout=va*pf*(1/2); +Pin=Pout+Pc+Psc; +eff=Pout*100/Pin; +disp(sprintf("The efficiency at 1/2 load is %.2f",eff)); +// +// full load +Psc=(1/1)^2*Psc0; +Pout=va*pf*(1/1); +Pin=Pout+Pc+Psc; +eff=Pout*100/Pin; +disp(sprintf("The efficiency at full load is %.2f",eff)); +// +// 1 1/4 = 5/4 load +Psc=(5/4)^2*Psc0; +Pout=va*pf*(5/4); +Pin=Pout+Pc+Psc; +eff=Pout*100/Pin; +disp(sprintf("The efficiency at 1 1/4 or 5/4 load is %.2f",eff)); +// +//maximum efficiency at x, but then ohmic loss=core loss +x=sqrt(Pc/Psc0); +Pout=va*x*pf; +Pin=Pout+Pc+Pc; //Ohmic losses = core losses at max efficiency +eff=Pout*100/Pin; +disp("SOLUTION (b)"); +disp(sprintf("The maximum efficiency is %.2f",eff)); +// +//short circuit test performed on lv side +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Vsc*pf1/Isc; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp("SOLUTION (c)"); +disp(sprintf("The value of Re1 is %.2f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %.2f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %.2fΩ",X_e1)); +// +//ee, ex; +er=I1*R_e1/v1; +ex=I1*X_e1/v1; +disp(sprintf("The value of Er is %.3f pu",er)); +disp(sprintf("The value of Ex is %.3f",ex)); +// +phi=acos(pf); +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R +%reg=(I1*R_e1*pf+I1*X_e1*sin(phi))*100/v1; //same as using er and ex +disp(sprintf("The percent regulation at full load lagging is %.2f",%reg)); +%reg1=(I1*R_e1*pf-I1*X_e1*sin(phi))*100/v1; //same as using er and ex +disp(sprintf("The percent regulation at full load leading is %.2f",%reg1)); +V21=(1-%reg/100)*v2; +V22=(1-%reg1/100)*v2; +disp(sprintf("The secondary terminal voltage at full load lagging is %.2f",V21)); +disp(sprintf("The secondary terminal voltage at full load leading is %.2f",V22)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.29/Ex7_29.sce b/1445/CH7/EX7.29/Ex7_29.sce new file mode 100644 index 000000000..5e8b2f759 --- /dev/null +++ b/1445/CH7/EX7.29/Ex7_29.sce @@ -0,0 +1,59 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 29 + +disp("CHAPTER 7"); +disp("EXAMPLE 29"); + +//20kVA 4000/1000 V single phase transformer +//VARIABLE INITIALIZATION +va=200000; //apparent power +v1=4000; //primary voltage in Volts +v2=1000; //secondary voltage in Volts +f=50; // frequency in Hz +//loads +pf=1; //power factor is unity +eff=0.97; // at full load and at 60% of full load +nlpf=0.5; //no load pf +lpf=0.8 //lagging pf +reg=0.05; //%regulation at 0.8 pf +// +//SOLUTION +loss=(1-eff)*va/eff; //=Pc+Pcu losses +//simultaneous equation to be solved +//eq 1: Pc+Pcu=loss; +//fractipon of copper/ ohmic losses +f=(0.6)^2; // 60% of full load +//the 2nd equation is Pc+f*Pcu=loss +//now the matrix +M=[1,1;1,f]; +A=[loss,loss*0.6]; +Mi=inv(M); +Ans=A*inv(M); +Pc=Ans(1,1); +Pcu=Ans(1,2); +//disp(sprintf("The Pc is %f",Pc)); +//disp(sprintf("The Pcu is %f",Pcu)); +//LV side +R_e2=Pcu/va; +//from %reg find X_e2 +phi=acos(lpf); +X_e2=(reg-R_e2*cos(phi))/sin(phi); +//in oms units +R_e2=R_e2*v2^2/va; // in ohms +X_e2=X_e2*v2^2/va; // in ohms +disp(sprintf("The Re2 is %.3f Ω",R_e2)); +disp(sprintf("The Xe2 is %.3f Ω",X_e2)); +// +Rc=v2^2/Pc; +Ie2=Pc/(v2*0.25); +Ic=Pc/v2; +Iphi=sqrt(Ie2^2-Ic^2); +Xphi=v2/Iphi; +disp(sprintf("The Rc is %.2f Ω",Rc)); +disp(sprintf("The Ie2 is %.3f A",Ie2)); +disp(sprintf("The Ic is %.3f A",Ic)); +disp(sprintf("The Iphi is %.4f A",Iphi)); +disp(sprintf("The Xphi is %.2f Ω",Xphi)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.3/Ex7_3.sce b/1445/CH7/EX7.3/Ex7_3.sce new file mode 100644 index 000000000..870db87c8 --- /dev/null +++ b/1445/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,72 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 3 + +disp("CHAPTER 7"); +disp("EXAMPLE 3"); +// +//2300/230 V 50 Hz transformer +//VARIABLE INITIALIZATION +v1=2300; //primary voltage in Volts +v2=230; //secondary voltage in Volts +f=50; +R1=0.286; +X1=0.73; +R_dash_2=0.319; +X_dash_2=0.73; +Rc=250; +Xphi=1250; +Zl=0.387+0.29*%i; +// +//SOLUTION +Z_e1=(R1+R_dash_2)+(X1+X_dash_2)*%i; +Z_dash_l=(v1/v2)^2*Zl; +// +I_dash_1=v1/(Z_dash_l+Z_e1); +//[mag,angle]=rect2pol(real(I_dash_1),imag(I_dash_1)); +//disp(sprintf("The current is %f <%f A",mag,angle)); +//impedance of shunt branch +Zm=Rc*(Xphi*%i)/(Rc+Xphi*%i); +//[mag,angle]=rect2pol(real(Zm),imag(Zm)); +//disp(sprintf("The Zm is %f <%f A",mag,angle)); +I0=v1/Zm; +//[mag,angle]=rect2pol(real(I0),imag(I0)); +//disp(sprintf("The I0 is %f <%f A",mag,angle)); +// +//primary current +I1=I0+I_dash_1; +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[mag,angle]=rect2pol(real(I1),imag(I1)); +theta1=angle; +disp("SOLUTION (i)"); +disp(sprintf("The primay current in rectangulr form is %.3f -j%.2f A",real(I1),-imag(I1))); +disp(sprintf("The primay current in polar form is %.3f <%.2f A",mag,angle)); +// +//input power +Pin=v1*I1; ; //=I1.cos(theta1) +//disp(sprintf("The input power is %.3f kW",Pin/1000)); +//output power +V_dash_2=I_dash_1*Z_dash_l; +[mag,angle]=rect2pol(real(V_dash_2),imag(V_dash_2)); +theta2=angle; +//disp(sprintf("The V_dash_2 is %.2f <%.2f A",mag,angle)); +// +Pout= V_dash_2*I_dash_1; //I_dash_1.cos(theta1) +//disp(sprintf("The output power is %.3f kW",real(Pout)/1000)); +//Efficiency +disp("SOLUTION (ii)"); +disp(sprintf("The Efficiency is %.2f kW",Pout*100/Pin));// text Book answer is 78.75% +//Losses +Pc=v1*I0; //core loss +loss=Pin-Pout; +Pcu=loss-Pc; //copper loss +disp(sprintf("The core loss is %.2f kW",Pc/1000));//text book answer is 0.8 kW +disp(sprintf("The copper loss is %.2f kW",Pcu/1000));//text book answer is 1..38 kW +//efficiency +//eff=Pout*100/Pin; +//disp(sprintf("The percent efficiency is %f W",eff)); +disp(" "); +// The answers from V_dash_2 calculation onward do not match with the book on page 7.21 and 7.22 +//END diff --git a/1445/CH7/EX7.30/Ex7_30.sce b/1445/CH7/EX7.30/Ex7_30.sce new file mode 100644 index 000000000..7d78d4b84 --- /dev/null +++ b/1445/CH7/EX7.30/Ex7_30.sce @@ -0,0 +1,23 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 30 + +disp("CHAPTER 7"); +disp("EXAMPLE 30"); + +//6600/440 V single phase transformer +//VARIABLE INITIALIZATION +v1=6600; //primary voltage in Volts +v2=440; //secondary voltage in Volts +e_r=0.02; //equivalent resistance +e_x=0.05; //equivalent reactance +pf=0.8; //power factor +// +//SOLUTION +//worked out differently a bit from the text book in terms of the steps +phi=acos(pf); //phase angle +reg=e_r*cos(phi)+e_x*sin(phi); //voltage regulation +V2=v2*(1-reg); //secondary terminal voltage +disp(sprintf("The secondary terminal voltage is %.2f V",V2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.31/Ex7_31.sce b/1445/CH7/EX7.31/Ex7_31.sce new file mode 100644 index 000000000..0150a59be --- /dev/null +++ b/1445/CH7/EX7.31/Ex7_31.sce @@ -0,0 +1,29 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 31 + +disp("CHAPTER 7"); +disp("EXAMPLE 31"); + +//single phase transformer having 400 primary and 1000 secondary turns +//VARIABLE INITIALIZATION +N1=400; +N2=1000; +coreA=60; //net core area in cm^2 +v1=500; //primary voltage in Volts +f=50; //frequency + +// +//SOLUTION +//v1=E1=4.44.Φm.N1.f Volts +phiM=v1/(4.44*N1*f); +//flux density Bm=Φm/area +Bm=phiM/coreA; //lines per cm +//voltage per turn +vpt=v1/N1; +v2=N2*vpt; +// +disp(sprintf("The maximum flux density is %.3fx10^-5 Wb per cm^2",Bm*10^5));//text book anser is 9383 lines per cm^2 +disp(sprintf("The secondary voltage is %.0f V",v2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.32/Ex7_32.sce b/1445/CH7/EX7.32/Ex7_32.sce new file mode 100644 index 000000000..05a91a7ea --- /dev/null +++ b/1445/CH7/EX7.32/Ex7_32.sce @@ -0,0 +1,62 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 32 + +disp("CHAPTER 7"); +disp("EXAMPLE 32"); + +//50 kVA 4400/220 V single phase transformer +//VARIABLE INITIALIZATION +va=50000; +v1=4400; //primary voltage in Volts +v2=220; //secondary voltage in Volts +f=50; +R1=3.45; +X1=5.2; +R2=0.0009; +X2=0.015; + +//SOLUTION +// +//Primary resistance and leakage reactance referred to secondary +//R'1 & X'1 +//Secondary resistance and leakage reactance referred to primary +//R'2 & X'2 +//Equivalent resistance & leakage reactance referred to primary +//Re1 & Xe1 +//Equivalent resistance & leakage reactance referred to secondary +//Re2 & Xe2 +// +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +X_dash_2=X2*(v1/v2)^2; +X_e1=X1+X_dash_2; +// +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +X_dash_1=X1*(v2/v1)^2; +X_e2=X2+X_dash_1; +// +Z_e1=R_e1+X_e1*%i; +Z_e2=R_e2+X_e2*%i; +magZ_e1=sqrt(real(Z_e1)^2+imag(Z_e1)^2); +magZ_e2=sqrt(real(Z_e2)^2+imag(Z_e2)^2); +// +disp("SOLUTION (i)"); +disp(sprintf("The equivalent resistance referred to primary %.4f Ω",R_e1));//text book answer is 7.05 ohm +disp("SOLUTION (ii)"); +disp(sprintf("The equivalent resistance referred to secondaryy %.4f Ω",R_e2)); +disp("SOLUTION (iii)"); +disp(sprintf("The equivalent leakage reactance referred to primary %.4f Ω",X_e1)); +disp(sprintf("The equivalent leakage reactance referred to secondary %.4f Ω",X_e2)); +disp("SOLUTION (iv)"); +disp(sprintf("The equivalent impedance referred to primary %.4f Ω",magZ_e1)); // text book answer is 13.23 ohm +disp(sprintf("The equivalent impedance referred to secondary %.4f Ω",magZ_e2));//text book answer is 0.0331 ohm +// +I1=va/v1; +I2=va/v2; +Pcu=I2^2*R_e2; +disp("SOLUTION (d)"); +disp(sprintf("The copper loss at full load %.0f W",Pcu)); +disp(" "); +//The answers in the book on page 7.77 are wrong for all but Xe1 and Xe2 values. +//END diff --git a/1445/CH7/EX7.33/Ex7_33.sce b/1445/CH7/EX7.33/Ex7_33.sce new file mode 100644 index 000000000..35ea4a24d --- /dev/null +++ b/1445/CH7/EX7.33/Ex7_33.sce @@ -0,0 +1,66 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 33 + +disp("CHAPTER 7"); +disp("EXAMPLE 33"); + +// 5kVA 400/200 V 50 Hz single phase transformer +//open ciruit and short circuit tests +//VARIABLE INITIALIZATION +va=5000; //apparent power +v1=400; //primary voltage in Volts +v2=200; //secondary voltage in Volts +f=50; +//no load parameters +Voc=400; +Io=1; +Woc=50; // watts HT side +//short circuit test +Vsc=12; +Isc=10; +Wc=40; // watts HT side +// +pf=0.8; +//SOLUTION +//no load condition +phi0=acos(Woc/(v1*Io)); +Ic=Io*cos(phi0); +Iphi=Io*sin(phi0); +Rc=v1/Ic; +X=v1/Iphi; +disp("SOLUTION (i)"); +disp(sprintf("The value of Ic is %f Amp",Ic)); +disp(sprintf("The value of IΦ is %f Amp",Iphi)); +//disp(sprintf("The value of Rc is %f Ohm",Rc)); +//disp(sprintf("The value of X is %fΩ",X)); +// +//short circuit +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Vsc*pf1/Isc; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp(sprintf("The value of Re1 is %.2f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %.2f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %.2fΩ",X_e1)); +// +I1=va/v1; +phi=acos(pf); +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R +%reg=(I1*R_e1*pf+I1*X_e1*sin(phi))*100/v1; +disp("SOLUTION (c(i))"); +disp(sprintf("The percent regulation at full load is %.3f",%reg)); +// +//full load output at pf=0.8 +Pout=va*pf; //output power +ironLoss=Woc; +cuLoss=Wc; +loss=ironLoss+cuLoss; +Pin=Pout+loss; // input power +eff=Pout*100/Pin; +disp("SOLUTION (c(ii))"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); // not calculated in the text book +disp(" "); +// +//END diff --git a/1445/CH7/EX7.34/Ex7_34.sce b/1445/CH7/EX7.34/Ex7_34.sce new file mode 100644 index 000000000..eaf48effe --- /dev/null +++ b/1445/CH7/EX7.34/Ex7_34.sce @@ -0,0 +1,41 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 35 + +disp("CHAPTER 7"); +disp("EXAMPLE 35"); + +//single phase 50 hz, 200kVA, 11kVA/230 V +//open circuit and short circuit tests +//VARIABLE INITIALIZATION +va=200000; //apparent power +v1=11000; //primary voltage in Volts +v2=230; //secondary voltage in Volts +Woc=1600; //watts also equals core losses +Wc=2600; //watts, also equals cu losses +f=50; +//no load parameters +//day cycle given +h1=8; // hours +load1=160000; //load in watts +pf1=0.8; //power factor +h2=6; +load2=100000; +pf2=1; +h3=10; +load3=0; +pf3=0; +//SOLUTION +//24 hr energy output +Pout=load1*h1*pf1+load2*h2*pf2+load3*h3*pf3; +Pc24=Woc*24; // 24 hours Pc loss +//cu loss= hours.(kva output/kva rated)^2.Full load Cu loss +Pcu24=h1*(load1/va)^2*Wc+h2*(load2/va)^2*Wc+h3*(load3/va)^2*Wc; +Pin=Pout+Pc24+Pcu24; +eff=Pout*100/Pin; +//disp(sprintf("The value Pout is %f",Pout)); +//disp(sprintf("The value Pc is %f",Pc24)); +//disp(sprintf("The value Pcu is %f",Pcu24)); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.35/Ex7_35.sce b/1445/CH7/EX7.35/Ex7_35.sce new file mode 100644 index 000000000..1d5f68a38 --- /dev/null +++ b/1445/CH7/EX7.35/Ex7_35.sce @@ -0,0 +1,46 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 36 + +disp("CHAPTER 7"); +disp("EXAMPLE 36"); + +// 100kVA 50 Hz 440/11000 V single phase transformer +//VARIABLE INITIALIZATION +va=100000; //apparent power +v1=440; //primary voltage in Volts +v2=11000; //secondary voltage in Volts +f=50; // efficiency +//loads +pf=1; //power factor at half load current +eff1=0.985; // at full load at 0.8pf +eff2=0.99; //at half full load at unity pf +pf1=0.8; // power factor at full load current +pf2=1; // +// +//SOLUTION +loss1=(1-eff1)*va*pf1/eff1; //=Pc+Pcu losses +loss2=(1-eff2)*va*(1/2)*pf2/eff2; //=Pc+Pcu losses +//simultaneous equation to be solved +//eq 1: Pc+Pcu=loss; +//fractipon of copper/ ohmic losses +f=(1/2)^2; // 60% of full load +//the 2nd equation is Pc+f*Pcu=loss +//now the matrix +M=[1,1;1,f]; //Pc+Pcu=loss1; Pc+(1/2)^2*Pcu=loss2: 1,1,; 1,f +A=[loss1,loss2]; +Mi=inv(M); +Ans=A*inv(M); +Pc=Ans(1,1); +Pcu=Ans(1,2); +disp(sprintf("The Pc is %.1f W",Pc)); +disp(sprintf("The Pcu is %.1f W",Pcu)); +// +//maximumefficiency at farction x times the full load;and then f.Pcu=Pc +x=sqrt(Pc/Pcu); +disp(sprintf("The maximum efficiency would occur at a load of %.0f kVA",x*va/1000)); +I1=va/v1; +I1maxEff=I1*x; +disp(sprintf("The current at maximum efficeincy is %.0f A",I1maxEff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.36/Ex7_36.sce b/1445/CH7/EX7.36/Ex7_36.sce new file mode 100644 index 000000000..860243a80 --- /dev/null +++ b/1445/CH7/EX7.36/Ex7_36.sce @@ -0,0 +1,46 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 36 + +disp("CHAPTER 7"); +disp("EXAMPLE 36"); + +//100kVA 50 Hz 440/1100 V single phase transformer +//VARIABLE INITIALIZATION +va=100000; //apparent power +v1=440; //primary voltage in Volts +v2=11000; //secondary voltage in Volts +f=50; // frequency +//loads +pf=1; //power factor unity +eff1=0.985; // at full load at 0.8pf +eff2=0.99; //at half full load at unity pf +pf1=0.8; // power factor +pf2=1; //power factor +// +//SOLUTION +loss1=(1-eff1)*va*pf1/eff1; //=Pc+Pcu losses +loss2=(1-eff2)*va*(1/2)*pf2/eff2; //=Pc+Pcu losses +//simultaneous equation to be solved +//eq 1: Pc+Pcu=loss; +//fractipon of copper/ ohmic losses +f=(1/2)^2; // 60% of full load +//the 2nd equation is Pc+f*Pcu=loss +//now the matrix +M=[1,1;1,f]; //Pc+Pcu=loss1; Pc+(1/2)^2*Pcu=loss2: 1,1,; 1,f +A=[loss1,loss2]; +Mi=inv(M); +Ans=A*inv(M); +Pc=Ans(1,1); +Pcu=Ans(1,2); +disp(sprintf("The Pc is %.1f W",Pc)); +disp(sprintf("The Pcu is %.1f W",Pcu)); +// +//maximumefficiency at farction x times the full load;and then f.Pcu=Pc +x=sqrt(Pc/Pcu); +disp(sprintf("The maximum efficiency would occur at a load of %.0f kVA",x*va/1000)); +I1=va/v1; +I1maxEff=I1*x; +disp(sprintf("The current at maximum efficeincy is %.0f A",I1maxEff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.37/Ex7_37.sce b/1445/CH7/EX7.37/Ex7_37.sce new file mode 100644 index 000000000..b4d21103f --- /dev/null +++ b/1445/CH7/EX7.37/Ex7_37.sce @@ -0,0 +1,40 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 37 + +disp("CHAPTER 7"); +disp("EXAMPLE 37"); + +//500 kVA 3300/500 V 50 hz single phase transformer +//VARIABLE INITIALIZATION +va=500000; //apparent power +v1=3300; //primary voltage in Volts +v2=500; //secondary voltage in Volts +f=50; +//loads +pf=1; //power factor unity +eff=0.97; // at 3/4 full load at unity pf +pf2=0.8; //power factor +// +//SOLUTION +I1=va/v1; +loss=(1-eff)*va*(3/4)*pf/eff; //=Pc+Pcu losses at 3/4 load +//since the eff value is maximum, Pcu=Pc; therefore, 2*Pc=loss +Pc=loss/2; +//(3/4)^2*Pcu=Pc; +f=(3/4)^2; //3/4 load +//Pcu=Pc/f +Pcu=Pc/f; +//disp(sprintf("The Pc is %f W",Pc)); +//disp(sprintf("The Pcu is %f W",Pcu)); +// +R_e1=Pcu/I1^2; +disp(sprintf("The value of Re1 is %.3f W",R_e1)); +//10% impedance +Z_e1=v1*0.1/I1; +X_e1=sqrt(Z_e1^2-R_e1^2); +phi=acos(0.8); +%reg=(I1*R_e1*cos(phi)+I1*X_e1*sin(phi))*100/v1; +disp(sprintf("The percent regulation at full load 0.8 pf is %.2f W",%reg)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.38/Ex7_38.sce b/1445/CH7/EX7.38/Ex7_38.sce new file mode 100644 index 000000000..080504a42 --- /dev/null +++ b/1445/CH7/EX7.38/Ex7_38.sce @@ -0,0 +1,31 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 38 + +disp("CHAPTER 7"); +disp("EXAMPLE 38"); + +//220/115 V 25 Hz single phase transformer +//VARIABLE INITIALIZATION +v1=220; //primary voltage in Volts +v2=115; //secondary voltage in Volts +f1=25; //frequency rating of the transformer in Hz +f2=50; //frequency of the connected load +//loads +V=440 // i Volts +We1=100; //in Watts at 220 V, eddy losses +Pc1=2*We1; //Total iron losses which equals We+Wh due to eddy and hysteresis +Wh1=Pc1-We1; +// +//SOLUTION +//since we know that We=kh.f.B^1.6 and Wh=Ke.Kf^2.f^2.B^2 +//since all being constant exept frequency, we may take We2/We1=f2^2/f1^2 +//and Wh2/Wh1=f2/f1 +//flux density in both cases is same as in second case voltage and frquency both are doubled +//find values for We2 and Wh2, whence Pc2=We2+Wh2 +We2=f2^2*We1/f1^2; +Wh2=f2*Wh1/f1; +Pc2=We2+Wh2; +disp(sprintf("The total no load losses at 400 V is %.0f W",Pc2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.39/Ex7_39.sce b/1445/CH7/EX7.39/Ex7_39.sce new file mode 100644 index 000000000..0d9677643 --- /dev/null +++ b/1445/CH7/EX7.39/Ex7_39.sce @@ -0,0 +1,41 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 39 + +disp("CHAPTER 7"); +disp("EXAMPLE 39"); + +//220/440 v 50 Hz transformer +//VARIABLE INITIALIZATION +v1=220; //primary voltage in Volts +v2=440; //secondary voltage in Volts +f1=50; //rated frequency in Hz + +//loads +V=110; +f2=25; //frquency of the applied load +//say, else computation may not be possible using computer +Pout1=100; //in watt, just assumed for computational purposes for the 220V supply +We1=0.01*Pout1; //in Watts at 220 V, eddy losses which are 1% of the output at 220V +Wh1=0.01*Pout1; //in Watts at 220 V, hysteresis losses which are 1% of the output at 220V +//Pc1=We1+Wh1; //Total iron losses which equals We+Wh due to eddy and hysteresis +Pcu1=0.01*Pout1; //copper losses +// +//SOLUTION +//since on connecting to half the power ie 110V, the output would get halved +Pout2=Pout1/2; +xPcu=Pcu1/Pout2; +disp(sprintf("The copper losses at 110 V would be %.0f percent of the output",xPcu*100)); +//now coming to frequency dependant losses ie eddy and hysteresis +//since we know that We=kh.f.B^1.6 and Wh=Ke.Kf^2.f^2.B^2 +//since all being constant exept frequency, we may take We2/We1=f2^2/f1^2 +//and Wh2/Wh1=f2/f1 +//find values for We2 and Wh2, whence Pc2=We2+Wh2 +We2=f2^2*We1/f1^2; +Wh2=f2*Wh1/f1; +xWe=We2/Pout2; +xWh=Wh2/Pout2; +disp(sprintf("The eddy losses at 110 V would be %.2f percent of the output",xWe*100)); +disp(sprintf("The hysteresis losses at 110 V would be %.2f percent of the output",xWh*100)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.4/Ex7_4.sce b/1445/CH7/EX7.4/Ex7_4.sce new file mode 100644 index 000000000..4f6586072 --- /dev/null +++ b/1445/CH7/EX7.4/Ex7_4.sce @@ -0,0 +1,38 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 4 + +disp("CHAPTER 7"); +disp("EXAMPLE 4"); + +//10kVA Transformer with 50 turns on primary and 10 turns on secondary +//connected to 440 V 50Haz supply +//VARIABLE INITIALIZATION +va=10*1000; //apparent power, converting kVA to VA +N1=50; //number of turns on primary side +N2=10; //number of turns on secondary side +v1=440; //primary voltage in Volts +f=50; //in Hertz + +//SOLUTION + +//solution (a) +//K=N2/N1=V2/V1 +v2=v1*(N2/N1); +disp(sprintf("(a) The secondary voltage on no load is %d V",v2)); + +//solution (b) +//Current on Full load +//primary side I1=VA/V1 +//secondary side I2=VA/V2 +I1=va/v1; +disp(sprintf("(b) The full load primary current is %.4f A",I1)); +I2=va/v2; +disp(sprintf("The full load secondary current is %.4f A",I2)); + +//solution (c) +//As per EMF equation +//E2=sqrt(2).pi.f.phimax.N2 +phi_m=v2/(sqrt(2)*%pi*f*N2); +disp(sprintf("(c) The maximum value of the flux is %.3f mWb",phi_m*1000)); + +//END diff --git a/1445/CH7/EX7.40/Ex7_40.sce b/1445/CH7/EX7.40/Ex7_40.sce new file mode 100644 index 000000000..a78c44b1d --- /dev/null +++ b/1445/CH7/EX7.40/Ex7_40.sce @@ -0,0 +1,22 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 40 + +disp("CHAPTER 7"); +disp("EXAMPLE 40"); + +//Given +//transformer on no load has a core loss 50W, draws a current of 2 A (RMS) and induced emf 220 V(RMS) +//VARIABLE INITIALIZATION +loss=50; //core loss in Watts +I0=2; //no load current in Amperes +v0=220; //induced emf in Volts + +//SOLUTION +pf=loss/(v0*I0); +I_c=I0*pf; //core loss component +I_phi=I0*sin(acos(pf)); //magnetizing component +disp(sprintf("The magnetizing component, I_c= %.4f A,",I_phi)); +disp(sprintf("The core loss component, I_Φ= %.4f A,",I_c)); + +//END + diff --git a/1445/CH7/EX7.41/Ex7_41.sce b/1445/CH7/EX7.41/Ex7_41.sce new file mode 100644 index 000000000..ffab26d2c --- /dev/null +++ b/1445/CH7/EX7.41/Ex7_41.sce @@ -0,0 +1,32 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 41 + +disp("CHAPTER 7"); +disp("EXAMPLE 41"); + +//3-phase 550/440 V star connected transformer supplies a load of 400kW +//VARIABLE INITIALIZATION +v1=550; //primary voltage in Volts +v2=440; //secondary voltage in Volts +p=400*1000; //load in Watts +pf=0.8; //power factor(lagging) + +//SOLUTION + +//solution (a) +I2=p/(sqrt(3)*v2*pf); //current on secondary side +I1=I2*(v2/v1); //since I1:I2=N2:N1 +I=I2-I1; //in sections Oa, Ob and Oc +disp(sprintf("(a) The current flowing in sections Oa, Ob and Oc is %.0f A",I)); +disp(sprintf("The current flowing in sections aA, bB and cC is %.0f A",I1)); + +//solution (b) +//power transferred by transformer action = Pin.(1-k) +p_o=p*(1-(v2/v1)); //k=v2/v1 +disp(sprintf("(b) The power transferred by transformer action %.0f kW",p_o/1000)); + +//solution (c) +p_d=p-p_o; +disp(sprintf("(c) The power conducted directly %d kW",p_d/1000)); + +//END diff --git a/1445/CH7/EX7.5/Ex7_5.sce b/1445/CH7/EX7.5/Ex7_5.sce new file mode 100644 index 000000000..cd6b7f3b3 --- /dev/null +++ b/1445/CH7/EX7.5/Ex7_5.sce @@ -0,0 +1,31 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 5 + +disp("CHAPTER 7"); +disp("EXAMPLE 5"); + +//single phase transformer +//350 primary and 1050 secondary turns +//VARIABLE INITIALIZATION +N1=350; //number of turns on primary side +N2=1050; //number of turns on secondary side +v1=400; //primary voltage in Volts +f=50; //in Hertz +ar=50/10000; //cross-sectional area of core in m^2 + +//SOLUTION + +//solution (i) +//emf1=sqrt(2).pi.f.Phimax.N1 +//Phimax=Bm.Area, Bm=flux density +//Bm=e1/sqrt(2).pi.A.f.N1 +Bm=v1/(sqrt(2)*%pi*ar*f*N1); +disp(sprintf("(i) The maximum flux density is %.4f Wb/m^2",Bm)); + +//solution (ii) +//e2/e1=n2/n1=K +K=N2/N1; +e2=K*v1; +disp(sprintf("(ii) The induced emf in the secondary winding is %d V",e2)); + +//END diff --git a/1445/CH7/EX7.6/Ex7_6.sce b/1445/CH7/EX7.6/Ex7_6.sce new file mode 100644 index 000000000..2abcb8cf9 --- /dev/null +++ b/1445/CH7/EX7.6/Ex7_6.sce @@ -0,0 +1,37 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 6 + +disp("CHAPTER 7"); +disp("EXAMPLE 6"); + +//2200/20V 50Hz single phase transformer +//VARIABLE INITIALIZATION +v1=2200; //primary voltage in Volts +v2=220; //secondary voltage in Volts +I=0.6; //exciting current in Amperes +p_c=361; //core loss in Watts +I2=60; //load current in Amperes +pf=0.8; //power factor + +//SOLUTION + +//solution (a) +//core loss components +I1=p_c/v1; //vertical component of I0 +I_phi=sqrt((I^2)-(I1^2)); //horizontal component of I0 +disp(sprintf("(a) The core loss component is %.3f A",I1)); +disp(sprintf("And the magnetising component is %.3f A",I_phi)); + +//solution (b) +//I1.N1=I2.N2 +I1_dash=(v2/v1)*I2; +theta=acos(pf); +I1_x=I1_dash*sin(theta)+I_phi; //horizontal component of I0 +I1_y=I1_dash*pf+I1; //vertical component of I0 +I1_res=sqrt((I1_x^2)+(I1_y^2)); //primary current +pf_p=I1_y/I1_res; //primary power factor +disp(sprintf("(b) The primary current is %.3f A",I1_res)); +disp(sprintf("And the power factor is %.3f A",pf_p)); + +//END + diff --git a/1445/CH7/EX7.8/Ex7_8.sce b/1445/CH7/EX7.8/Ex7_8.sce new file mode 100644 index 000000000..e53aed921 --- /dev/null +++ b/1445/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,66 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 8 + +disp("CHAPTER 7"); +disp("EXAMPLE 8"); + +//23 kVA 2300/230 V 60 Hz step down transformer + +//VARIABLE INITIALIZATION +va=23000; //apparent power +v1=2300; //primary voltage in Volts +v2=230; //secondary voltage in Volts +r1=4; //primary resistance in Ohms +r2=0.04; //secondary resistance in Ohms +X1=12; //leakage reactance primary in Ohms +X2=0.12; //leake reactance in secondary in Ohms +pf=0.866; //power factor(leading) + +//SOLUTION +//assume voltage across load be 230 V +//V'1=I2.(Re2+jXe2)+V2 +//Re2=R'1+R2 +//R'1=R1.(N2/N1)^2 +//Xe2=X'1+X2 +//X'1=X1.(N2/N1)^2 +//Ze2=Re2+j.Xe2 +r1_dash=r1*((v2/v1)^2); +r_e2=r1_dash+r2; +X1_dash=X1*((v2/v1)^2); +X_e2=X1_dash+X2; +// +//disp(sprintf("The value of Re2 %f and Xe2 %f",r_e2,X_e2)); +I2=0.75*(va/v2); //since transformer operates at 75% of its rated load +// +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[x,y]=pol2rect(I2,-30); +I_dash_2=x+y*%i; +//disp(sprintf("The value %f %f",real(I_dash_2),imag(I_dash_2))); +// +Z_e2=r_e2+X_e2*%i; //in rect coordinates +//disp(sprintf("The value %f %f",real(Z_e2),imag(Z_e2))); +// +V_dash_1=v2+I_dash_2*Z_e2; +//disp(sprintf("The value %f %f",real(V_dash_1),imag(V_dash_1))); +// +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +// +[magV1,angleV1]=rect2pol(real(V_dash_1),imag(V_dash_1)); +//disp(sprintf("The value %f <%f",magV1,angleV1)); +// +//Pin=V'1.I2.cos theta1 +//Pout=V2.I2.cos theta2 +Pin=magV1*I2*cos((30+angleV1)*%pi/180); +Pout=v2*I2*cos(30*%pi/180); +eff=Pout*100/Pin; +// +disp(sprintf("The efficiency of the transformer is %.2f",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.9/Ex7_9.sce b/1445/CH7/EX7.9/Ex7_9.sce new file mode 100644 index 000000000..4a53d3b70 --- /dev/null +++ b/1445/CH7/EX7.9/Ex7_9.sce @@ -0,0 +1,36 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 9 + +disp("CHAPTER 7"); +disp("EXAMPLE 9"); + +//11000/400 V distribution transformer +//VARIABLE INITIALIZATION +v1=11000; //primary voltage in Volts +v2=400; //secondary voltage in Volts +Io=1; //primary current in Amp +pf=0.24 //power factor lagging + +//SOLUTION +//core loss current +//Ic=Io.cos phi +//Ic=Io.pf +Ic=Io*pf; +disp("SOLUTION (a)"); +disp(sprintf("The value of core loss current is %.2f Amp",Ic)); +// +//magnetizing current +//Iphi=sqrt(Io^2-Ic^2) +Iphi=sqrt(Io^2-Ic^2); +disp("SOLUTION (b)"); +disp(sprintf("The value ofmagnetizing current is %.3f Amp",Iphi)); +// +//Iron Loss +//Iron loss=primary voltage X core loss current +IronLoss=v1*Ic; +disp("SOLUTION (c)"); +disp(sprintf("The iron loss is %.0f W",IronLoss)); +disp(" "); +// +//END + diff --git a/1445/CH8/EX8.1/Ex8_1.sce b/1445/CH8/EX8.1/Ex8_1.sce new file mode 100644 index 000000000..05b16b236 --- /dev/null +++ b/1445/CH8/EX8.1/Ex8_1.sce @@ -0,0 +1,23 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 1 + +disp("CHAPTER 8"); +disp("EXAMPLE 1"); + +//shunt generator +//VARIABLE INITIALIZATION +v_t=250; //terminal voltage in Volts +I_l=500; //load current in Amperes +r_a=0.04; //armature resistance in Ohms +r_f=50; //shunt field resistance in Ohms + +//SOLUTION +I_f=v_t/r_f; // current through the shunt field winding +I_a=I_l+I_f; //Armature Current +E_a=v_t+(I_a*r_a); //E_a=emf of generator +disp(sprintf("The generated emf is %.1f V",E_a)); + +//END + + + diff --git a/1445/CH8/EX8.10/Ex8_10.sce b/1445/CH8/EX8.10/Ex8_10.sce new file mode 100644 index 000000000..0189c399a --- /dev/null +++ b/1445/CH8/EX8.10/Ex8_10.sce @@ -0,0 +1,56 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 10 + +disp("CHAPTER 8"); +disp("EXAMPLE 10"); + +//6 pole DC machine with 400 conductors +//VARIABLE INITIALIZATION +P=6; //number of poles +I=80; //current per conductor in Amperes +Z=400; //total number of conductors +phi=0.020; //flux per pole in Wb +N=1800; //in rpm + +//SOLUTION + +//soluion (a): for wave connected +disp("(a) For Wave connected"); + +//(i) +A=2; //A=number of parallel paths =2 for wave connected conductors +I_a=I*A; +disp(sprintf("(i) The total current is %.0f A",I_a)); + +//(ii) +E_a=(phi*Z*N*P)/(60*A); +disp(sprintf("(ii) The emf is %.0f V",E_a)); + +//(iii) +p=E_a*I_a; +disp(sprintf("(iii) The power developed in armature is %.3f kW",p/1000)); +w=(2*%pi*N)/60; +T_e=p/w; +disp(sprintf("The electromagnetic torque is %.2f N-m",T_e)); + + +//soluion (b): for lap connected +disp("(b) For Lap connected"); + +//(i) +A=P; //P=6 is given +I_a=I*A; +disp(sprintf("(i) The total current is %.0f A",I_a)); + +//(ii) +E_a=(phi*Z*N*P)/(60*A); // induced emf +disp(sprintf("(ii) The emf is %.0f V",E_a)); + +//(iii) +p=E_a*I_a; //power developed in armature +disp(sprintf("(iii) The power developed in armature is %.1f kW",p/1000)); +w=(2*%pi*N)/60; //armature rotation in RPS +T_e=p/w; //Torque +disp(sprintf("The electromagnetic torque is %.2f N-m",T_e)); + +//END diff --git a/1445/CH8/EX8.11/Ex8_11.sce b/1445/CH8/EX8.11/Ex8_11.sce new file mode 100644 index 000000000..839d676d0 --- /dev/null +++ b/1445/CH8/EX8.11/Ex8_11.sce @@ -0,0 +1,26 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 11 + +disp("CHAPTER 8"); +disp("EXAMPLE 11"); + +//20 kW compound generator +//VARIABLE INITIALIZATION +p_o=20*1000; //output in W +v_t=250; //in Volts +r_a=0.05; //aramture resistance in Ohms +r_se=0.025; //series resistance in Ohms +r_sh=100; //shunt resistance in Ohms + +//SOLUTION +I_t=p_o/v_t; +v_se=I_t*r_se; //for series winding +v_sh=v_t+v_se; //for shunt winding +I_sh=v_sh/r_sh; //shunt curent +I_a=I_sh+I_t; //armature current +E_a=v_t+(I_a*r_a)+v_se; //induced emf +disp(sprintf("The total emf generated is %.3f V",E_a)); + +//END + + diff --git a/1445/CH8/EX8.12/Ex8_12.sce b/1445/CH8/EX8.12/Ex8_12.sce new file mode 100644 index 000000000..364e96eaf --- /dev/null +++ b/1445/CH8/EX8.12/Ex8_12.sce @@ -0,0 +1,29 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 12 + +disp("CHAPTER 8"); +disp("EXAMPLE 12"); + +//4 pole wave wound 750 RPM shunt generator +//VARIABLE INITIALIZATION +P=4; //number of poles +N=750; //in rpm +r_a=0.4; //in Ohms +r_f=200; //in Ohms +Z=720; +phi=2.895*(10^6)*(10^(-8)); //in Wb (1 line=10^(-8) Wb) +r_l=10; //load resistance in Ohms +A=2; //for wave winding + +//SOLUTION +E_a=(phi*Z*N*P)/(60*A); //induced emf +disp(sprintf("The induced emf is %.0f V",E_a)); +// E_a=v+(I_a*r_a) but I_a=I_l+I_f and I_l=v/r_l, I_f=v/r_f =>I_a=(v/r_l) + (v/r_f) +// =>E_a=v+(((v/r_l) + (v/r_f))*r_a) +// taking v common, the following equation is obtained +v=E_a/(1+(r_a/r_f)+(r_a/r_l)); +disp(sprintf("The terminal voltage of the machine is %.0f V",v)); + +//The answer is slightly different due to the precision of floating point numbers + +//END diff --git a/1445/CH8/EX8.13/Ex8_13.sce b/1445/CH8/EX8.13/Ex8_13.sce new file mode 100644 index 000000000..2e1e3d493 --- /dev/null +++ b/1445/CH8/EX8.13/Ex8_13.sce @@ -0,0 +1,31 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 13 + +disp("CHAPTER 8"); +disp("EXAMPLE 13"); + +//4 pole shunt generator +//VARIABLE INITIALIZATION +P=4; //number of poles +v_t=220; //in Volts +I_l=42; //load current in Amperes +r_a=0.1; //in Ohms +r_f=110; //in Ohms +drop=1; //contact drop per brush +//SOLUTION + +//solution (i) +A=P; //for lap winding +I_f=v_t/r_f; //I_f is same as I_sh +I_a=I_l+I_f; //induced emf +I_c=I_a/A; //conductor current +disp(sprintf("The current in each conductor of the armature is %d A",I_c)); + +//solution (ii) +v_a=I_a*r_a; //armature voltage drop +v_b=2*drop; //brush drop +emf=v_t+v_a+v_b; //total emf generated +disp(sprintf("The total emf generated is %.1f V",emf)); + +//END + diff --git a/1445/CH8/EX8.14/Ex8_14.sce b/1445/CH8/EX8.14/Ex8_14.sce new file mode 100644 index 000000000..f5d54ad55 --- /dev/null +++ b/1445/CH8/EX8.14/Ex8_14.sce @@ -0,0 +1,34 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 14 + +disp("CHAPTER 8"); +disp("EXAMPLE 14"); + +//shunt generator +//VARIABLE INITIALIZATION +v_t=220; //in Volts +I_l=196; //in Amperes +s_loss=720; //stray loss in Watts +r_f=55; //shunt field ressitance in Ohms +eff=88/100; //efficiency + +//SOLUTION +p_o=v_t*I_l; //output power +p_i=p_o/eff; //electrical input +tot_loss=p_i-p_o; +I_f=v_t/r_f; //field current +I_a=I_l+I_f; //armature current +cu_loss=v_t*I_f; //shunt field copper loss +c_loss=cu_loss+s_loss; //constant loss +arm_loss=tot_loss-c_loss; //armature copper loss +r_a=arm_loss/(I_a^2); //armature resistance +disp(sprintf("The armature resistance is %f Ω",r_a)); + +//for maximum efficiency, armature loss = constant loss =>(I_a^2)*r_a=c_loss +I_a=sqrt(c_loss/r_a); +disp(sprintf("The load current corresponding to maximum efficiency is %.1f A",I_a)); + +//END + + + diff --git a/1445/CH8/EX8.15/Ex8_15.sce b/1445/CH8/EX8.15/Ex8_15.sce new file mode 100644 index 000000000..f14132a94 --- /dev/null +++ b/1445/CH8/EX8.15/Ex8_15.sce @@ -0,0 +1,31 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 15 + +disp("CHAPTER 8"); +disp("EXAMPLE 15"); + +//230 V DC shunt motor +//VARIABLE INITIALIZATION +v_t=230; //in Volts +I_a1=3.33; //in Amperes +N1=1000; //in rpm +r_a=0.3; //armature resistance in Ohms +r_f=160; //field resistance in Ohms +I_l=40; //line current in Amperes +phi1=1; //in Wb (phi=1 is an assumption) +phi2=(1-(4/100)); //in Wb (phi2=0.96 of phi1), as armature reaction reduces no load flux by 4% + +//SOLUTION + +//At no load +E_a1=v_t-(I_a1*r_a); //counter emf +I_f=v_t/r_f; //field current + +//At full load +I_a2=I_l-I_f; +E_a2=v_t-(I_a2*r_a); +N2=(E_a2/E_a1)*(phi1/phi2)*N1; +N2=round(N2); //to round off the value +disp(sprintf("The full load speed is %d rpm",N2)); + +//END diff --git a/1445/CH8/EX8.16/Ex8_16.sce b/1445/CH8/EX8.16/Ex8_16.sce new file mode 100644 index 000000000..4ba0fd577 --- /dev/null +++ b/1445/CH8/EX8.16/Ex8_16.sce @@ -0,0 +1,47 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 16 + +disp("CHAPTER 8"); +disp("EXAMPLE 16"); + +//4 pole 250 V shunt motor +//VARIABLE INITIALIZATION +v_t=250; //in Volts +P=4; //number of poles +Z=500; //number of conductors +r_a=0.25; //in Ohms +r_f=125; //in Ohms +phi=0.02; //in Wb +I_l=14; //in Amperes +A=2; +rot_loss=300; //rotational loss in Watts + +//SOLUTION + +//solution (i) +I_f=v_t/r_f; // field current +I_a=I_l-I_f; //armature current +E_a=v_t-(I_a*r_a); // induced emf +N=(E_a*A*60)/(phi*Z*P); //RPM +N=round(N); //to round off the value of N +disp(sprintf("(i) The speed is %d rpm",N)); +p_e=E_a*I_a; //electromagnetic power +w=(2*%pi*N)/60; //speed in RPS +T1=p_e/w; // Internal torque +disp(sprintf("The internal torque developed is %.3f N-m",T1)); + +//solution (ii) +//shaft power +p_o=p_e-rot_loss; //power output +disp(sprintf("(ii)The shaft power is %.0f W",p_o)); +T2=p_o/w; //shaft torque +disp(sprintf("The shaft torque is %.2f N-m",T2)); +p_i=v_t*I_l; // power input +eff=(p_o/p_i)*100; //efficiency +disp(sprintf("The efficiency is %.2f %%",eff)); + +//END + + + + diff --git a/1445/CH8/EX8.17/Ex8_17.sce b/1445/CH8/EX8.17/Ex8_17.sce new file mode 100644 index 000000000..6e4141500 --- /dev/null +++ b/1445/CH8/EX8.17/Ex8_17.sce @@ -0,0 +1,58 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 17 + +disp("CHAPTER 8"); +disp("EXAMPLE 17"); + +//200 V DC shunt motor of 1000 rpm +//VARIABLE INITIALIZATION +v_t=200; //in Volts +I_l=22; //line current in Amperes +N1=1000; //in rpm +r_a=0.1; //armature resistancein Ohms +r_f=100; //field resistance in Ohms +N2=800; //new speed in rpm + +//SOLUTION + +//solution (i) +//load torque is independent of speed, the torque is constant at both speeds +//T dir prop phi1.Ia1 dir prop phi2.Ia2 +//Therefore we get +//phi1.Ia1=phi2.Ia2 (since phi1=phi2) +// or Ia1=Ia2 +I_f=v_t/r_f; // field current +I_a1=I_l-I_f; // armature current +E_a1=v_t-(I_a1*r_a); // counter emf +//on rearranging the equation E_a2:E_a1=N2:N1, where E_a2=v_t-I_a1*(r_a+r_s) and E_a1=v_t-(I_a1*r_a), we get, +r_s1=((v_t - ((N2*E_a1)/N1))/I_a1)-r_a; +disp(sprintf("(i) When the load torque is independent of speed, the additional resistance is %.2f Ω",r_s1)); + +//solution (ii) +//Load torque Tl is proportional to N +//But electromagnetic torque Te=k.phi.Ia +//therefore, +//k.phi1.Ia1 dir prop N1 +//k.phi2.Ia2 dir prop n2 +//hence we get (as phi1=phi2) +I_a2=(N2/N1)*I_a1; +//on rearranging the equation E_a2:E_a1=N2:N1, where E_a2=v_t-I_a2*(r_a+r_s) and E_a1=v_t-(I_a1*r_a), we get, +r_s2=((v_t - ((N2*E_a1)/N1))/I_a2)-r_a; +disp(sprintf("(ii)When the load torque is proportional to speed, the additional resistance is %.1f Ω",r_s2)); + +//solution (iii) +//The load Torque Tl dir prop N^2 dir prop phi.Ia +I_a2=(N2^2/N1^2)*I_a1; +//on rearranging the equation E_a2:E_a1=N2:N1, where E_a2=v_t-I_a2*(r_a+r_s) and E_a1=v_t-(I_a1*r_a), we get, +r_s3=((v_t - ((N2*E_a1)/N1))/I_a2)-r_a; +disp(sprintf("(iii)When the load torque varies as the square of speed, the additional resistance is %.2f Ω",r_s3)); + +//solution (iv) +//The load Torque Tl dir prop N^3 dir prop phi.Ia +I_a2=(N2^3/N1^3)*I_a1; +//on rearranging the equation E_a2:E_a1=N2:N1, where E_a2=v_t-I_a2*(r_a+r_s) and E_a1=v_t-(I_a1*r_a), we get, +r_s4=((v_t - ((N2*E_a1)/N1))/I_a2)-r_a; +disp(sprintf("(iv)When the load torque varies as the cube of speed, the additional resistance is %.2f Ω",r_s4)); + +//END + diff --git a/1445/CH8/EX8.18/Ex8_18.sce b/1445/CH8/EX8.18/Ex8_18.sce new file mode 100644 index 000000000..10b37b947 --- /dev/null +++ b/1445/CH8/EX8.18/Ex8_18.sce @@ -0,0 +1,29 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 18 + +disp("CHAPTER 8"); +disp("EXAMPLE 18"); + +//460 V 10 HP motor +//VARIABLE INITIALIZATION +v_t=460; //in Volts +p_o=10*736; //in Watts (1 metric H.P=735.5 W) +ratio=85/100; //as given in the question +eff=84/100; // efficiency +I_f=1.1; //in Amperes +r_a=0.2; //in Ohms + +//SOLUTION +p_i=p_o/eff; //power input +I_l=p_i/v_t; //line current +I_a=I_l-I_f; // armature current +E1=v_t-(I_a*r_a); //back emf +E2=E1*ratio; //E2:E1=N2:N1=ratio +v=v_t-E2; //voltage drop across r_a and r_s (r_s is the series resistance to be inserted) +r_s=(v/I_a)-r_a; // series resistance +disp(sprintf("The resistance required is %.2f Ω",r_s)); + +//The answer is different because ratio equals 85/100 and not 75/100 + +//END + diff --git a/1445/CH8/EX8.19/Ex8_19.sce b/1445/CH8/EX8.19/Ex8_19.sce new file mode 100644 index 000000000..a7376d7e8 --- /dev/null +++ b/1445/CH8/EX8.19/Ex8_19.sce @@ -0,0 +1,37 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 19 + +disp("CHAPTER 8"); +disp("EXAMPLE 19"); + +//250 V DC shunt motor +//VARIABLE INITIALIZATION +v_t=250; //in Volts +r_a=0.5; //in Ohms +r_f=250; //in Ohms +N1=600; //in rpm +I=21; //in Amperes +r_s=250; //in Ohms + +//SOLUTION +//when torque is constant T dir prop phi.Ia = constant +//assuming field is unsaturated , therefore, +//If dir prop phi +//therefore, If1.Ia1=If2.Ia2 +I_f1=v_t/r_f; // +I_f2=v_t/(r_f+r_s); +I_a1=I-I_f1; +// T is directly proportional to (Φ*I_a) +// I_f is directly proportional to Φ +// => I_f1*I_a1=I_f2*I_a2, therefore, +I_a2=(I_f1*I_a1)/I_f2; +E_b1=v_t-(I_a1*r_a); +E_b2=v_t-(I_a2*r_a); +// E_b is directly proportional to (Φ*N) +// (Φ*N) is directly proportinal to (I_f*N) +// =>E_b1:E_b2=(I_f1:I_f2)*(N1:N2) +N2=(I_f1/I_f2)*(E_b2/E_b1)*N1; +N2=round(N2); //to round off the value +disp(sprintf("The new speed of the motor is %.d rpm",N2)); + +//END diff --git a/1445/CH8/EX8.2/Ex8_2.sce b/1445/CH8/EX8.2/Ex8_2.sce new file mode 100644 index 000000000..0046becf5 --- /dev/null +++ b/1445/CH8/EX8.2/Ex8_2.sce @@ -0,0 +1,30 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 2 + +disp("CHAPTER 8"); +disp("EXAMPLE 2"); + +// 230 V DC shunt machine +//VARIABLE INITIALZATION +v_t=230; //terminal voltage in Volts +r_a=0.5; //armature resistance in Ohms +r_f=115; //shunt field resistance in Ohms +I_l=40; //line current in Amperes + +//SOLUTION + +//for generator +I_f=v_t/r_f; //current through the shunt field winding +I_a=I_l+I_f; //Armature Current +E_a=v_t+(I_a*r_a); //E_a=emf of generator + +//for motor +I_f=v_t/r_f; +I_a=I_l-I_f; +E_b=v_t-(I_a*r_a); //E_b=emf of motor +//ratio of speed as generator to speed as motor +ratio=E_a/E_b; //E_a:E_b=(k_a*flux*N_g):(k_a*flux*N_m) =>E_a:E_b=N_g:N_m (as flux is constant) +disp(sprintf("The ratio of speed as a generator to the speed as a motor is %.3f",ratio)); + +//END + diff --git a/1445/CH8/EX8.20/Ex8_20.sce b/1445/CH8/EX8.20/Ex8_20.sce new file mode 100644 index 000000000..a81f6f77c --- /dev/null +++ b/1445/CH8/EX8.20/Ex8_20.sce @@ -0,0 +1,59 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 20 + +disp("CHAPTER 8"); +disp("EXAMPLE 20"); + +//250 V DC shunt motor +//VARIABLE INITIALIZATION +v_t=250; //in Volts +I_a1=20; //in Amperes +N1=1000; //in rpm +r_a=0.5; //in Ohms +drop=1; //brush contact drop in Volts +ratio=1.5; //N2:N1=1.5 +phi1=1; //it is an assumption + +//SOLUTION +// equations have been renumbered differently than in the text book for better clarity +// Torque is constant +// T dir prop phi.Ia +// phi1.ia1=phi2.Ia2 (eq 1) +//similarly, E dir prop phi.N +//E1/E2 = phi1.n1/phi2.n2 +E_1=v_t-(I_a1*r_a)-(2*drop); +//speed raised by 50%. new speed 1.5 times the old one i.e n2=1.5N1 +// +//E1/E2 = Phi1.N1/phi2.N2 (eq 2) +//from eq 2 +//=>E1/E2=Phi1/1.5.phi2 (substituting N2=1.5N1) (eq 3) +//=>phi2/phi1=E2/1.5.E1 (eq 4) +//from eq 1 +//phi2/ph1=Ia2/Ia2=20/Ia2 -------------------(eq 5) +//substituting value of phi2/phi1 in eq 4 we get +//20/Ia2=E2/1.5E1 +//=>E1/E2=Ia2/30 (eq 6) +//further we know that +//E2=V-Ia2.Ra -2.drop where V=v_t=250, ra=R_a=0.5 and drop=1 +//=>E2=(V-2.drop) -Ra.Ia2 (eq 7) +//substituting value of E2 in eq 6, we get +//E1/[(V-2.drop)-ra.Ia2] = Ia2/30 (eq 8) +// we get quadratic equation +//Setting in an quadratic equation of type a.X^2 + b.X + c = 0 +//The constants are as given below: +a=1; // coefficient of Ia2^2 +b=-496; //coefficient of Ia2, = (V-2.drop).Ra=(v_t-2.drop).R_a +c=14280; // constant = E_1*30 +D=b^2-(4*a*c); +x1=(-b+sqrt(D))/(2*a); +x2=(-b-sqrt(D))/(2*a); +if(x1<40) +I_a2=x1; +else if(x2<40) +I_a2=x2; +end; +phi2=(I_a1/I_a2)*phi1; +phi=(1-phi2)*100; +disp(sprintf("The flux to be reduced is %.1f %% of the main flux",phi)); + +//END diff --git a/1445/CH8/EX8.21/Ex8_21.sce b/1445/CH8/EX8.21/Ex8_21.sce new file mode 100644 index 000000000..cd3275d33 --- /dev/null +++ b/1445/CH8/EX8.21/Ex8_21.sce @@ -0,0 +1,40 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 21 + +disp("CHAPTER 8"); +disp("EXAMPLE 21"); + +//10kW 6 pole DC generator +//VARIABLE INITIALIZATION +p_o=10*1000; //in Watts +P=6; //number of poles +E_g=200; //in Volts +N=1500; //in rpm +A=P; //since the armature is lap connected +B=0.9; //flux density in Tesla +l=0.25; //length of armature in m +dia=0.2; //diameter of armature in m + +//SOLUTION +//solution (a) +//pole pitch is defined as the periphery of armature divided by the number of poles or the area of armature between two adjacent poles +//area of armature = 2.pi. dia of armature. length of armature +area=2*%pi*(dia/2)*l; //area of armature +phi=B*area; //flux density over one pitch pole= flux per pole/area of armature between poles +disp(sprintf("(a) The flux per pole is %.4f Wb",phi)); + +//solution (b) +Z=(60*E_g)/(phi*N); // no of conductors in the armature + //induced emf = phi.Z.N.P/60.A + // = phi.Z.N/60 ( as A=P) +disp(sprintf("(b) The total number of active conductors is %d",Z)); + +//solution (c) +I_a=50; // armature current +p=E_g*I_a; //power developed +w=(2*%pi*N)/60; //speed in RPS +T=p/w; //Torque +disp(sprintf("(c) The torque developed when armature current is 50 A is %.2f N-m",T)); + +//END + diff --git a/1445/CH8/EX8.22/Ex8_22.sce b/1445/CH8/EX8.22/Ex8_22.sce new file mode 100644 index 000000000..7a554a6c8 --- /dev/null +++ b/1445/CH8/EX8.22/Ex8_22.sce @@ -0,0 +1,48 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 22 + +disp("CHAPTER 8"); +disp("EXAMPLE 22"); + +//230 V 600 rpm shunt motor +//VARIABLE INITIALIZATION +N1=600; //in rpm +v=230; //in Volts +I_l1=50; //line current in Amperes +r_a=0.4; //armature resistance in Ohms +r_f=104.5; //field resistance in Ohms +drop=2; //brush drop in Volts + +//SOLUTION + +//solution (i) +I_l2=5; // no load current +I_a1=I_l1-(v/r_f); // armature current +E_b1=v-(I_a1*r_a)-drop; // back emf +I_a2=I_l2-(v/r_f); +E_b2=v-(I_a2*r_a)-drop; +N2=(E_b2/E_b1)*N1; // speed at no load +N2=round(N2); +disp(sprintf("(i) The speed at no load is %d rpm",N2)); + +//solution (ii) +I_l2=50; +N2=500; +E_b2=(N2/N1)*E_b1; +dif=v-drop; //difference +I_a2=I_l2-(v/r_f); +r_se=((dif-E_b2)/I_a2)-r_a; +disp(sprintf("(ii) The additional resistance is %.3f Ω",r_se)); + +//solution (iii) +//Eb1/Eb2 = phi2.N2/Phi1.N1 +phi1=1; //it is an assumption +I_a3=30; +N2=750; +E_b3=v-(I_a3*r_a)-drop; +phi2=(E_b3/E_b1)*(N1/N2)*phi1; +red=((1-phi2)*100*phi1)/phi1; +disp(sprintf("(iii) The percentage reduction of flux per pole is %.1f %%",red)); + +//END + diff --git a/1445/CH8/EX8.23/Ex8_23.sce b/1445/CH8/EX8.23/Ex8_23.sce new file mode 100644 index 000000000..0f93e5d8a --- /dev/null +++ b/1445/CH8/EX8.23/Ex8_23.sce @@ -0,0 +1,36 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 23 + +disp("CHAPTER 8"); +disp("EXAMPLE 23"); + +//230 V DC shunt motor +//VARIABLE INITIALIZATION +v=230; //in Volts +r_a=0.4; //in Ohms +r_f1=115; //in Ohms +I_a=20; //in Amperes +N1=800; //in rpm +N2=1000; //in rpm + +//SOLUTION +//Eb1/Eb2 = phi1.N1/phi2.N2 (eq 1) +//Eb=Vt - Ia.Ra (eq 2) +//=> (Vt-Ia1.Ra)/(Vt-Ia2.Ra) = phi1.N1/phi2.N2 (eq 3) +I_f1=v/r_f1; //redundant step +E_b1=v-(I_a*r_a); // back emf +//Since terminal voltage Vt is constant, if dir prop phi dir prop 1/r_f +//=> phi1/phi2 = r_f2/r_f1 (eq 4) [r_f2 = field resistance at 10000 rpm] + //[r_f1 = field resistance at 800 rpm] +//Load torque is constant, so T dir prop phi.Ia +//=> phi1.Ia1=phi2.Ia2 +//=> Ia2=(phi1/phi2). Ia1 (eq 5) +//putting the value of Ia2 in eq 3 and +//rearranging the equation, we get, +r_f2=((E_b1*N2)/((v*N1)-(N1*I_a*r_a)))*r_f1; +r_f2_dash=r_f2-r_f1; +disp(sprintf("The external resistance is %.2f Ω",r_f2_dash));//text book answer is 29.93 ohm + +//The answer is slightly different due to the precision of floating point numbers + +//END diff --git a/1445/CH8/EX8.24/Ex8_24.sce b/1445/CH8/EX8.24/Ex8_24.sce new file mode 100644 index 000000000..e330f4a03 --- /dev/null +++ b/1445/CH8/EX8.24/Ex8_24.sce @@ -0,0 +1,28 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 24 + +disp("CHAPTER 8"); +disp("EXAMPLE 24"); + +//This example is same as example 19 + +//VARIABLE INITIALIZATION +v=250; //in Volts +r_a=0.5; //in Ohms +r_f=250; //in Ohms +N1=600; //in rpm +I_l=21; //in Amperes +r=250; //in Ohms + +//SOLUTION +I_f1=v/r_f; +I_a1=I_l-I_f1; +I_a2=2*I_a1; +E_b1=v-(I_a1*r_a); +E_b2=v-(I_a2*r_a); +ratio=(r+r_f)/r_f; +N2=(ratio*N1*E_b2)/E_b1; +N2=round(N2); +disp(sprintf("The new speed is %d rpm",N2)); + +//END diff --git a/1445/CH8/EX8.25/Ex8_25.sce b/1445/CH8/EX8.25/Ex8_25.sce new file mode 100644 index 000000000..a9088f41b --- /dev/null +++ b/1445/CH8/EX8.25/Ex8_25.sce @@ -0,0 +1,44 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 25 + +disp("CHAPTER 8"); +disp("EXAMPLE 25"); + +//24 slot 2 pole DC machine with 18 turns per coil +//VARIABLE INITIALIZATION +slot=24; //number of slots +P=2; //number of poles +N=18; //number of turns per coil +B=1; //in Webers +l=20/100; //effective length in meters +rad=10/100; //radius in meters +w=183.2; //angular velocity in rad/s + +//SOLUTION +A=2; // number of parallel paths +Z=slot*P*N; //total number of conductors +ar1=(2*%pi*rad*l)/P; // actual pole area +ar2=ar1*0.8; //since the magnetic poles 80% of the armature periphery +phi=B*ar2; //effective flux per pole + +//solution (a) +E_a=(P*Z*phi*w)/(2*%pi*A); +disp(sprintf("(a) The induced emf is %.1f V",E_a)); + +//solution (b) +coil=slot/P; //number of coils in each path = slots/path +E_coil=E_a/coil; //induced emf per coil +disp(sprintf("(b) The induced emf per coil is %.2f V",E_coil)); + +//solution (c) +E_turn=E_coil/N; //emf induced per turn +disp(sprintf("(c) The induced emf per turn is %.2f V",E_turn)); + +//solution (d) +E_cond=E_turn/A; // emf induced per conductor +disp(sprintf("(d) The induced emf per conductor is %.3f V",E_cond)); + +//The answers are slightly different due to the precision of floating point numbers + +//END + diff --git a/1445/CH8/EX8.27/Ex8_27.sce b/1445/CH8/EX8.27/Ex8_27.sce new file mode 100644 index 000000000..e6422663f --- /dev/null +++ b/1445/CH8/EX8.27/Ex8_27.sce @@ -0,0 +1,28 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 27 + +disp("CHAPTER 8"); +disp("EXAMPLE 27"); + +//DC series motor, 200V DC motor +//VARIABLE INITIALIZATION +v_t=200; //in volts +r_a=0.06; //in Ohms +r_se=0.04; //in Ohms +p_i=20*1000; //in Watts + +//SOLUTION + +//solution (a) +//Il=Ia=Ise= Pinput/Vt +I_a=p_i/v_t; // armature current +E_b=v_t-I_a*(r_a+r_se); // back emf +disp(sprintf("(a) The counter emf of the motor is %d V",E_b)); + +//solution (b) +p_a=E_b*I_a; // power developed in armature +p_a=p_a/1000; //from W to kW +disp(sprintf("(b) The power developed in the armature is %d kW",p_a)); + +//END + diff --git a/1445/CH8/EX8.28/Ex8_28.sce b/1445/CH8/EX8.28/Ex8_28.sce new file mode 100644 index 000000000..8cc1c1c85 --- /dev/null +++ b/1445/CH8/EX8.28/Ex8_28.sce @@ -0,0 +1,26 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 28 + +disp("CHAPTER 8"); +disp("EXAMPLE 28"); + +//series generator +//VARIABLE INITIALIZATION +E_a=120; //in Volts +r_se=0.03; //in Ohms +r_a=0.02; //in Ohms +v1=240; //in Volts +r=0.25; //in Ohms +I=300; //in Amperes + +//SOLUTION +v=I*(r_se+r_a+r); // voltage drop across Rse and ra and feeder +disp(sprintf("The voltage drop across the three resistances is %d V",v)); +//hence the voltage between far end and bus bar is: +v_t=v1+E_a-v; +disp(sprintf("The voltage between far end and the bus bar is %d V",v_t)); +disp(sprintf("The net increase of %d V may be beyond the desired limit",v_t-v1)); +disp("Hence, a field diverter resistance may be necessary to regulate the far-end terminal voltage"); + +//END + diff --git a/1445/CH8/EX8.29/Ex8_29.sce b/1445/CH8/EX8.29/Ex8_29.sce new file mode 100644 index 000000000..06477777a --- /dev/null +++ b/1445/CH8/EX8.29/Ex8_29.sce @@ -0,0 +1,22 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 29 + +disp("CHAPTER 8"); +disp("EXAMPLE 29"); + +//DC series motor +//VARIABLE INITIALIZATION +r_a=1; //in Ohms +N1=800; //in rpm +v_t=200; //in Volts +I_a=15; //in Amperes +r_s=5; //series resistance in Ohms + +//SOLUTION +E_b1=v_t-(I_a*r_a); // back emf +E_b2=v_t-I_a*(r_a+r_s); +N2=(E_b2/E_b1)*N1; //RPM +N2=round(N2); //to round off the value +disp(sprintf("The speed attained after connecting the series resistance is %d rpm",N2)); + +//END diff --git a/1445/CH8/EX8.3/Ex8_3.sce b/1445/CH8/EX8.3/Ex8_3.sce new file mode 100644 index 000000000..b08092d94 --- /dev/null +++ b/1445/CH8/EX8.3/Ex8_3.sce @@ -0,0 +1,39 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 3 + +disp("CHAPTER 8"); +disp("EXAMPLE 3"); + +//10 kW 250 V DC shunt generator +//VARIABLE INITIALIZATION +p_o=10*1000; //output of generator in Watts +v_t=250; //terminal voltage in Volts +N=1000; //speed in rpm +r_a=0.15; //armature resistance in Ohms +I_f=1.64; //field current in Amperes +rot_loss=540; //rotational loss in Watts + +//SOLUTION + +//solution (i) +I_l=p_o/v_t; //line current +I_a=I_l+I_f; // armature current +E_a=v_t+(I_a*r_a); //E_a=emf of generator +disp(sprintf("(i) The armature induced emf is %.2f V",E_a)); + +//solution (ii) +w=(2*%pi*N)/60; //in radian/sec +T_e=(E_a*I_a)/w; +disp(sprintf("(ii) The torque developed is %.2f N-m",T_e)); + +//solution (iii) +arm_loss=(I_a^2)*r_a; //armature loss +fld_loss=v_t*I_f; //field loss +tot_loss=rot_loss+arm_loss+fld_loss; +p_i=p_o+tot_loss; +eff=(p_o/p_i)*100; +disp(sprintf("(iii) The efficiency is %.3f %%",eff)); + +//END + + diff --git a/1445/CH8/EX8.30/Ex8_30.sce b/1445/CH8/EX8.30/Ex8_30.sce new file mode 100644 index 000000000..782ad08af --- /dev/null +++ b/1445/CH8/EX8.30/Ex8_30.sce @@ -0,0 +1,26 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 30 + +disp("CHAPTER 8"); +disp("EXAMPLE 30"); + +//Series DC motor 5 HP with 100 rpm +//VARIABLE INITIALIZATION +p=5*735.5; //in Watts (1 metric H.P.=735.5 W) +N=1000; //in rpm, given as 100 rpm but solved as 1000 rpm in the text book + //hence taken 1000 rpm +I=30; //in Amperes +I_s=45; //starting current in Amperes + +//SOLUTION +T=(p*60)/(2*%pi*1000); // Torque +//Torque dir prop phi.Ia +//=> since phi dir prop Ia +//=> torque dir prop Ia^2 +// starting torque T_s / T = Starting current Ia ^2 / I^2 +T_s=(T*(I_s^2))/(I^2); +disp(sprintf("The starting torque is %.0f N-m",T_s)); + +//The answer is slightly different due to precision of floating point numbers + +//END diff --git a/1445/CH8/EX8.31/Ex8_31.sce b/1445/CH8/EX8.31/Ex8_31.sce new file mode 100644 index 000000000..5e8349ca2 --- /dev/null +++ b/1445/CH8/EX8.31/Ex8_31.sce @@ -0,0 +1,34 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 31 + +disp("CHAPTER 8"); +disp("EXAMPLE 31"); + +//series motor +//VARIABLE INITIALIZATION +r_a=0.1; //combined resistance of armature & field resistance in Ohms +v_t=230; //in Volts +I_a1=100; //in Amperes +N1=1000; //in rpm +I_a2=200; //in Amperes +ratio=1.2; //ratio of Φ2:Φ1=1.2 + +//SOLUTION +//Eb1 dir prop phi1.N1 +//Eb1=Vt-Ia1.Ra +//=> (Vt-Ia1.Ra) dir prop ph1.N1 +//and +//=> (Vt-Ia2.Ra) dir prop ph1.N2 +//=> (Vt-Ia1.Ra)/ (Vt-Ia1.Ra) = phi1.N1/phi2.N2 +//given Phi2=1.2 Phi1 as flux is increased by 20% +E_b1=v_t-(I_a1*r_a); //numerator of LHS according to the book +E_b2=v_t-(I_a2*r_a); //denominator of LHS according to the book +N2=(E_b2/E_b1)*(1/ratio)*N1; +N2=round(N2); //to round off the value +disp(sprintf("The new speed of the armature is %d rpm",N2)); + +//END + + + + diff --git a/1445/CH8/EX8.32/Ex8_32.sce b/1445/CH8/EX8.32/Ex8_32.sce new file mode 100644 index 000000000..ff37b6767 --- /dev/null +++ b/1445/CH8/EX8.32/Ex8_32.sce @@ -0,0 +1,95 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 32 + +disp("CHAPTER 8"); +disp("EXAMPLE 32"); + +//250 V series motor at 1000 rpm +//VARIABLE INITIALIZATION +v_t=250; //in Volts +I=20; //in Amperes +N1=1000; //in rpm +P=4; //number of poles +r_p=0.05; //resistance of field coil on each pole in Ohms +r_a=0.2; //in Ohms + +//SOLUTION + +r_se=P*r_p; // series field resistance +r_m=r_a+r_se; //resistance of motor +E_b1=v_t-(I*r_m); // back emf +//Torque t1 dir prop phi1.Ia +//=> since phi dir prop Ia +//=> torque dir prop Ia^2 +T1=I^2; // torque + +//solution (a) +//10 ohm resistance in parallel with armature +//let I be input currnet then, drop in series field = r_a.I +//Voltage across the terminals = V = Vt-r_a.I +//=> current in 10 ohm resistance (=r) = (Vt-r_a.I)/r (eq 1) +// now, Armature current Ia +// Ia= I - (Vt-r_a.I)/r (eq 2) +//Torque developed t2 dir prop phi2.Ia +//=> since phi dir prop I +//=> torque dir prop I.Ia +//However, T2=T1, as torque developed in two cases is equal +//=> I.Ia = T1 +//substituting value of Ia from eq 2, we get +//I.(I - (Vt-r_a.I)/r) =T1 +//=>I. (I.r+r_a.I -Vt)/r = T1 +//=> (r+r_a).I^2 -Vt.I =T1.r +//=> (r+r_a).I^2 -Vt.I - T1.r =0 +//solving the quadratic equation directly, +r=10; //in Ohms +a=10.2; //(r+r_a). value 1.02 in text book, as it was divided by r=10 +b=-250; //Vt ; -25 in text book, as it was divided by r=10 +c=-4000; // T1.r; 400 in text book, as it was not multiplied by r=10 +D=b^2-(4*a*c); +x1=(-b+sqrt(D))/(2*a); +x2=(-b-sqrt(D))/(2*a); +//to extract the positive root out of the two +if (x1>0 & x2<0) +I1=x1; +else (x1<0 & x2>0) +I1=x2; +end; +I_a=((10.2*I1)-v_t)/r; // armature current +E_b2=v_t-(I_a*r_a); // back emf +N2=((E_b2/E_b1)*I*N1)/I1; +N2=round(N2); //to round off the value +disp(sprintf("(a) The speed with 10 Ω resistance in parallel with the armature is %d rpm",N2)); + +//solution (b) +//0.5 ohmic diverter resistance +//resistance in the field winding = 0.5/(0.5+r_a) +// since r_a=0.2,the value becomes 0.5/0.7 = 5/7 +//Torque T3 dir prop phi3.Ia +// => dir prop 5/7 . I. I. +//=> dir prop 5/7 I^2 +//since T3=T1 +//=> 5/7 I^2= T1 +//=> 5/7. I^2 - T1=0 +//solving the quadratic equation directly,with new values +a=5/7; +b=0; +c=-400; +D=b^2-(4*a*c); +y1=(-b+sqrt(D))/(2*a); +y2=(-b-sqrt(D))/(2*a); +//to extract the positive root out of the two +if (y1>0 & y2<0) +I2=y1; +else (y1<0 & y2>0) +I2=y2; +end; +E_b3=v_t-(I2*r_a); // back emf +N3=((E_b3/E_b1)*I*N1)/(I2*a); +N3=round(N3); //to round off the value +disp(sprintf("(b) The speed with 0.5 Ω resistance in parallel with series field is %d rpm",N3)); + +//The answers are slightly different due to the precision of floating point numbers + +//END + + diff --git a/1445/CH8/EX8.33/Ex8_33.sce b/1445/CH8/EX8.33/Ex8_33.sce new file mode 100644 index 000000000..aaf8cdd40 --- /dev/null +++ b/1445/CH8/EX8.33/Ex8_33.sce @@ -0,0 +1,48 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 33 + +disp("CHAPTER 8"); +disp("EXAMPLE 33"); + +//230 V DC series motor +//VARIABLE INITIALIZATION +v_t=230; //in Volts +N1=1500; //in rpm +I_a1=20; //in Amperes +r_a=0.3; //armature resistance in Ohms +r_se=0.2; //series field resistance in Ohms + +//SOLUTION + +//solution (a) +//for series motors, phi dir prop Ia +// therefore, Te dir prop Ia^2 +// at starting Eb=0 and Vt= Ia1.(r_a+r_se+r_ext) +//rearranging for r_ext, we get +// r_ext = (Vt-Ia1.(r_a+r_se))/ Ia1 +E_b=0; //back emf at starting +nr1=v_t-I_a1*(r_a+r_se); //value of numerator in the expression for r_ext +r_ext=nr1/I_a1; +disp(sprintf("(a) At starting, the resistance that must be added is %.0f Ω",r_ext)); + +//solution (b) +//Ia2=Ia1=20 A +//as phi dir prop Ia, we get +//Eb2/Eb1 = phi2.n2/ phi1. N1 = Ia2.N2/Ia1.N1 +//=> Eb2/Eb1=N2/N1 as Ia2=Ia1 (eq 1) +I_a2=I_a1; +N2=1000; +ratio=N2/N1; +// now, we know that Eb1=Vt-Ia1.(r_a+r_se) and +// Eb2 = Vt - Ia2.(r_a+r_se+r_ext) +//substituting values of Eb1 and Eb2 in eq 1 above, we get +//n2/n1 = (Vt - Ia2.(r_a+r_se+r_ext))/ (Vt-Ia1.(r_a+r_se)) +//since ia1=Ia2 (rated torque) +//we get +//r_ext = (N2/N1).(v_t-I_a1*(r_a+r_se))/Ia2 -(v_t-I_a2*(r_a+r_se))/Ia2 +// +nr2=v_t-I_a2*(r_a+r_se); +r_ext=((ratio*nr1)-nr2)/(-I_a2); +disp(sprintf("(b) At 1000 rpm, the resistance that must be added is %.3f Ω",r_ext)); + +//END diff --git a/1445/CH8/EX8.34/Ex8_34.sce b/1445/CH8/EX8.34/Ex8_34.sce new file mode 100644 index 000000000..00c7d76f7 --- /dev/null +++ b/1445/CH8/EX8.34/Ex8_34.sce @@ -0,0 +1,31 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 34 + +disp("CHAPTER 8"); +disp("EXAMPLE 34"); + +//COMPOUND MACHINE +//VARIABLE INITIALIZATION +r_a=0.06; //armature resistance in Ohms +r_se=0.04; //series resistance in Ohms +r_sh=25; //shunt resistance in Ohms +v_t=110; //in Volts +I_l=100; //in Amperes + +//SOLUTION + +//solution (a) +I_sh=v_t/r_sh; // shunt current +I_a=I_sh+I_l; // armature current +E_g=v_t+I_a*(r_a+r_se); // emf generated +disp("(a) When the machine is connected as long shunt compound generator-"); +disp(sprintf("The armature current is %f A and the total emf is %.2f V",I_a,E_g)); + +//solution (b) +I_sh=(v_t/r_sh)+(I_l*r_se/r_sh); +I_a=I_sh+I_l; +E_g=v_t+(I_a*r_a)+(I_l*r_se); +disp("(b) When the machine is connected as short shunt compound generator-"); +disp(sprintf("The armature current is %f A and the total emf is %.1f V",I_a,E_g)); + +//END diff --git a/1445/CH8/EX8.35/Ex8_35.sce b/1445/CH8/EX8.35/Ex8_35.sce new file mode 100644 index 000000000..fcf1b5461 --- /dev/null +++ b/1445/CH8/EX8.35/Ex8_35.sce @@ -0,0 +1,31 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 35 + +disp("CHAPTER 8"); +disp("EXAMPLE 35"); + +//Exercise 34, motor working as DC motor +//VARIABLE INITIALIZATION +r_a=0.06; //armature resistance in Ohms +r_se=0.04; //series resistance in Ohms +r_sh=25; //shunt resistance in Ohms +v_t=110; //in Volts +I_l=100; //in Amperes + +//SOLUTION + +//solution (a) +I_sh=v_t/r_sh; // shunt current +I_a=I_l-I_sh; // armature current +E_g=v_t-I_a*(r_a+r_se); // generated emf +disp("(a) When the machine is connected as long shunt compound generator-"); +disp(sprintf("The armature current is %f A and the total emf is %.1f V",I_a,E_g)); + +//solution (b) +I_sh=(v_t/r_sh)-(I_l*r_se/r_sh); +I_a=I_l-I_sh; +E_g=v_t-(I_a*r_a)-(I_l*r_se); +disp("(b) When the machine is connected as short shunt compound generator-"); +disp(sprintf("The armature current is %f A and the total emf is %.2f V",I_a,E_g)); + +//END diff --git a/1445/CH8/EX8.36/Ex8_36.sce b/1445/CH8/EX8.36/Ex8_36.sce new file mode 100644 index 000000000..6ea9e53b5 --- /dev/null +++ b/1445/CH8/EX8.36/Ex8_36.sce @@ -0,0 +1,38 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 36 + +disp("CHAPTER 8"); +disp("EXAMPLE 36"); + +//250 long shunt compound generator +//VARIABLE INITIALIZATION +v_t=250; //in Volts +I_l=150; //in Amperes +loss1=1200; //core loss at full load in Watts +loss2=800; //mechanical loss in Watts +r_b=0.08; //brush resistance in Ohms +r_sh=62.5; //shunt field resistance in Ohms +r_se=0.03; //series field resistance in Ohms +r_ip=0.02; //interpole resistance in Ohms + +//SOLUTION + +//solution (a) +p_o=v_t*I_l; // power output +I_sh=v_t/r_sh; // shunt current +I_a=I_l+I_sh; // armature current +r_tot=r_b+r_se+r_ip; // total armature circuit resistance +arm_loss=(I_a^2)*r_tot; //armature circuit copper loss +cu_loss=v_t*I_sh; //shunt field copper loss +c_loss=cu_loss+loss1+loss2; //constant loss +disp(sprintf("(a) The constant loss is %.0f W",c_loss)); + +//solution (b) +tot_loss=arm_loss+c_loss; //total loss +p_i=p_o+tot_loss; // power input +eff=(p_o/p_i)*100; // efficiency +disp(sprintf("(b) The full load efficiency is %.0f %%",eff)); + +//END + + diff --git a/1445/CH8/EX8.37/Ex8_37.sce b/1445/CH8/EX8.37/Ex8_37.sce new file mode 100644 index 000000000..7cadef348 --- /dev/null +++ b/1445/CH8/EX8.37/Ex8_37.sce @@ -0,0 +1,44 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 37 + +disp("CHAPTER 8"); +disp("EXAMPLE 37"); + +//250 V DC machine +//VARIABLE INITIALIZATION +p_o=50*1000; //in Watts +v_t=250; //in Volts +loss1=5000; //total core loss in Watts +loss2=2000; //total core loss in Watts (when speed is reduced to half) +speed=125/100; + +//SOLUTION + +//solution (a) + +//W_h=A*N, where W_h=hysteresis loss, A=constant and N=speed +//W_e=B*(N^2), where W_e=eddy current loss, B=constant and N=speed +//W_h+(W_e^2)=loss1 =>W_h+W_e=5000 +//(W_h/2)+(W_e/4)=loss2 =>(0.5*W_h)+(0.25*W_e)=2000 (when speed reduces to half) +//So, we get two equations +//W_h+W_e=5000.......................eq(i) +//(0.5*W_h)+(0.25*W_e)=2000..........eq(ii) +//solving the equations by matrix method +A=[1 1;0.5 0.25]; +b=[5000;2000]; +x=inv(A)*b; +W_h1=x(1,:); //to access the 1st row of 2X1 matrix +W_e1=x(2,:); //to access the 2nd row of 2X1 matrix +disp("Solution (a)"); +disp(sprintf("The hysteresis loss at full speed is %d W",W_h1)); +disp(sprintf("The eddy current loss at full speed is %d W",W_e1)); + +//solution (b) +W_h2=speed*W_h1; +W_e2=(speed^2)*W_e1; +disp("Solution (b)"); +disp(sprintf("The hysteresis loss at 125%% of the full speed is %d W",W_h2)); +disp(sprintf("The eddy current loss at 125%% of the full speed is %d W",W_e2)); + +//END + diff --git a/1445/CH8/EX8.38/Ex8_38.sce b/1445/CH8/EX8.38/Ex8_38.sce new file mode 100644 index 000000000..ce64d0ef1 --- /dev/null +++ b/1445/CH8/EX8.38/Ex8_38.sce @@ -0,0 +1,31 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 38 + +disp("CHAPTER 8"); +disp("EXAMPLE 38"); + +//215 V DC machine supplying 5kW at 1000 rpm +//VARIABLE INITIALIZATION +v_t=215; //in Volts +r_a=0.4; //in Ohms +p=5*1000; //in Watts +N_g=1000; //speed as generator in rpm +ratio=1.1; //according to the solution, Φ_b:Φ_a=1.1 + +//SOLUTION + +//As generator +I_ag=p/v_t; // as generator induced current +E_a=v_t+(I_ag*r_a); // induced emf + +//As motor +I_am=p/v_t; // current as motor +E_b=v_t-(I_am*r_a); // back emf +N_m=(1/ratio)*N_g*(E_b/E_a); // speed of machine +N_m=round(N_m); //to round off the value +disp(sprintf("The speed of the machine as motor is %d rpm",N_m)); + +//END + + + diff --git a/1445/CH8/EX8.4/Ex8_4.sce b/1445/CH8/EX8.4/Ex8_4.sce new file mode 100644 index 000000000..afdaa2c0a --- /dev/null +++ b/1445/CH8/EX8.4/Ex8_4.sce @@ -0,0 +1,35 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 4 + +disp("CHAPTER 8"); +disp("EXAMPLE 4"); + +//240 Volt Shunt Generator +//VARIABLE INITIALIZATION +v_t=240; //in Volts +I_l=200; //full load current in Amperes +r_f=60; //shunt field resisatnce in Ohms +eff=90; //percentage full load efficiency +s_loss=800; //stray(iron + friction) loss in Watts + +//SOLUTION + +//solution (a) +p_o=v_t*I_l; //output +eff=eff/100; +p_i=p_o/eff; //input +tot_loss=p_i-p_o; //since input=output+loss +I_f=v_t/r_f; //field current +I_a=I_l+I_f; //armature current +cu_loss=(I_f^2)*r_f; //copper loss +c_loss=cu_loss+s_loss; //constant loss +arm_loss=tot_loss-c_loss; //armature loss ((I_a^2)*r_a) +r_a=arm_loss/(I_a^2); //armature resistance +disp(sprintf("(a) The armature resisatnce is %.4f Ω",r_a)); + +//solution (b) +//for maximum efficiency, armature loss = constant loss =>(I_a^2)*r_a=c_loss +I_a=sqrt(c_loss/r_a); +disp(sprintf("(b) The load current corresponding to maximum efficiency is %.1f A",I_a)); + +//END diff --git a/1445/CH8/EX8.5/Ex8_5.sce b/1445/CH8/EX8.5/Ex8_5.sce new file mode 100644 index 000000000..52b22ec32 --- /dev/null +++ b/1445/CH8/EX8.5/Ex8_5.sce @@ -0,0 +1,45 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 5 + +disp("CHAPTER 8"); +disp("EXAMPLE 5"); + +//200 V shunt generator +//VARIABLE INITIALIZATION +v_t=200; //in Volts +I_l=50; //in Amperes +r_a=0.1; //armature resistance in Ohms +r_f=100; //field resistance in Ohms +s_loss=500; //core and iron loss in Watts + +//SOLUTION + +//solution (a) +//Shunt field current, Armature current and induced emf +//I_sh is same as I_f and r_sh is same as r_f +I_f=v_t/r_f; //Field current +I_a=I_f+I_l; //armature current +E_a=v_t+(I_a*r_a); //Emf of generator +disp(sprintf("(a) The induced emf is %.1f V",E_a)); + +//solution (b) +arm_loss=(I_a^2)*r_a; //armature copper loss +sh_loss=(I_f^2)*r_f; //shunt field copper loss +tot_loss=arm_loss+sh_loss+s_loss; +p_o=v_t*I_l; //output power +p_i=p_o+tot_loss; //input power +bhp=p_i/735.5; //1 metric horsepower= 735.498 W +disp(sprintf("(b) The Break Horse Power(B.H.P.) of the prime mover is %.1f H.P.(metric)",bhp)); + +//solution (c) +c_eff=(p_o/p_i)*100; //Commercial efficiency = Output/Input +p_EE=E_a*I_a; //electrical power developed +m_eff=(p_EE/p_i)*100; //Mechanical efficiency = electrical power/Input power +e_eff=(p_o/p_EE)*100; //Electrical efficiency = output power/electrical power +disp(sprintf("(c) The commercial efficiency is %.1f %%",c_eff)); +disp(sprintf("(c) The mechanical efficiency is %.1f %%",m_eff)); +disp(sprintf("(c) The electrical efficiency is %.1f %%",e_eff)); + +//END + + diff --git a/1445/CH8/EX8.6/Ex8_6.sce b/1445/CH8/EX8.6/Ex8_6.sce new file mode 100644 index 000000000..67e4601b2 --- /dev/null +++ b/1445/CH8/EX8.6/Ex8_6.sce @@ -0,0 +1,52 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 6 + +disp("CHAPTER 8"); +disp("EXAMPLE 6"); + +//VARIABLE INITIALIZATION +p_o=20*746; //output power from H.P. to Watts (1 H.P.=745.699 or 746 W) +v_t=230; //in Volts +N=1150; //speed in rpm +P=4; //number of poles +Z=882; //number of armature conductors +r_a=0.188; //armature resistance in Ohms +I_a=73; //armature current in Amperes +I_f=1.6; //field current in Amperes + +//SOLUTION + +//solution (i) +E_b=v_t-(I_a*r_a); //Back emf +w=(2*%pi*N)/60; //in radian/sec +T_e=(E_b*I_a)/w; //electromagnetic torque +disp(sprintf("(i) The electromagnetic torque is %.0f N-m",T_e)); + +//solution (ii) +A=P; //since it is lap winding, so A=P and A=number of parallel paths +phi=(E_b*60*A)/(P*N*Z); +disp(sprintf("(ii) The flux per pole is %.3f Wb",phi)); + +//solution (iii) +//Rotational power= Power developed on rotor - Pshaft.(=Pout) +p_rotor=E_b*I_a; //power developed on rotor +p_rot=p_rotor-p_o; //p_shaft=p_out +disp(sprintf("(iii) The rotational power is %.4f W",p_rot)); //text book answer is 870 W + +//solution (iv) +tot_loss=p_rot+((I_a^2)*r_a)+(v_t*I_f); +p_i=p_o+tot_loss; //input power +eff=(p_o/p_i)*100; +disp(sprintf("(iv) The efficiency is %.2f %%",eff)); + +//solution (v) +T=p_o/w; //shaft torque +disp(sprintf("(v) The shaft torque is %.0f N-m",T)); + +//The answers are slightly different due to the precision of floating point numbers +//END + + + + + diff --git a/1445/CH8/EX8.7/Ex8_7.sce b/1445/CH8/EX8.7/Ex8_7.sce new file mode 100644 index 000000000..20e434a5a --- /dev/null +++ b/1445/CH8/EX8.7/Ex8_7.sce @@ -0,0 +1,34 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 7 + +disp("CHAPTER 8"); +disp("EXAMPLE 7"); + +//Contnuation of the Example 6 +//shaft load/ load torque remains fixed, and field flux is reduced to 80% by using field rheostat +//VARIABLE INITIALIZATION +p_o=20*746; //output power from H.P. to Watts (1 H.P.=745.699 or 746 W) +v_t=230; //in Volts +N1=1150; //speed in rpm +P=4; //number of poles +Z=882; //number of armature conductors +r_a=0.188; //armature resistance in Ohms +I_a1=73; //armature current in Amperes +I_f=1.6; //field current in Amperes +ratio=0.8; //phi2:phi1=0.8 (here phi=flux) + +//SOLUTION +//Eb2/Eb1= phi2.W2/phi1.W1 = phi2.N2/phi1.N1 +E_b1=v_t-(I_a1*r_a); // +I_a2=I_a1/ratio; //(phi2*I_a2)=(phi1*I_a1) +E_b2=v_t-(I_a2*r_a); +N2=(E_b2/E_b1)*(1/ratio)*N1; //N2:N1=(E_b2/E_b1)*(phi1/phi2) +N2=round(N2); //to round off the value of N2 (before rounding off N2=1414.695516 rpm) +disp(sprintf("The new operating speed is %d rpm",N2)); + +//The answer is slightly different due to the precision of floating point numbers + +//END + + + diff --git a/1445/CH8/EX8.8/Ex8_8.sce b/1445/CH8/EX8.8/Ex8_8.sce new file mode 100644 index 000000000..0eb7a9dd1 --- /dev/null +++ b/1445/CH8/EX8.8/Ex8_8.sce @@ -0,0 +1,50 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 8 + +disp("CHAPTER 8"); +disp("EXAMPLE 8"); + +//250 V DC shunt machine +//VARIABLE INITIALIZATION +v_t=250; //in Volts +r_a=0.1; //armature resistance in Ohms +r_f=125; //field resistance in Ohms +p_o=20*1000; //output power in Watts +N_g=1000; //speed as generator in rpm + +//SOLUTION + +//machine as a generator +I_l=p_o/v_t; //load current +I_f=v_t/r_f; //field current, I_f is same as I_sh +I_ag=I_l+I_f; //Output current as generator +E_a=v_t+(I_ag*r_a); //induced emf = E_a = E_g + +//machine as a motor +I_l=p_o/v_t; //full load current +I_f=v_t/r_f; +I_am=I_l-I_f; //output current as motor +E_b=v_t-(I_am*r_a); //back emf = E_b = E_m + +//solution (a) +N_m=(N_g*E_b)/E_a; //Speed of motor in RPM +N_m=round(N_m); //to round off the value of N_m +disp(sprintf("(a) The speed of the same machine as a motor is %d rpm",N_m)); + +//solution (b) +//internal power developed as generator +//(i) +//total power developed in the armature +//=Eg.Iag +p_g=(E_a*I_ag)/1000; //to express the answer in kW divide by 1000 +disp(sprintf("(b) (i) The internal power developed as generator is %.1f kW",p_g)); + +//(ii) +//internal power developed as motor +// is total power developed in armature +//=Em.Iam +p_m=(E_b*I_am)/1000; +disp(sprintf("(b) (ii) The internal power developed as motor is %.1f kW",p_m)); + +//END + diff --git a/1445/CH8/EX8.9/Ex8_9.sce b/1445/CH8/EX8.9/Ex8_9.sce new file mode 100644 index 000000000..fa24acd41 --- /dev/null +++ b/1445/CH8/EX8.9/Ex8_9.sce @@ -0,0 +1,31 @@ +//CHAPTER 8- DIRECT CURRENT MACHINES +//Example 9 + +disp("CHAPTER 8"); +disp("EXAMPLE 9"); + +//4 Pole 230 V lap wound shunt motor with 600 conductors. RPM 1800 +//VARIABLE INITIALIZATION +P=4; //number of poles +v_t=230; //in Volts +I_l=52; //in Amperes +Z=600; //tottal number of conductors +r_f=115; //in Ohms +d=30/100; //airgap diameter from cm to m +l=20/100; //effective length of pole +B=4100/10000; //flux density from Gauss to Wb/m^2 + +//SOLUTION + +I_f=v_t/r_f; //I_f is same as I_sh +I_a=I_l-I_f; // armature current +ar=(%pi*d*l)/P; //area of pole +phi=ar*B; //phi = flux +A=P; //for lap winding +T=(phi*Z*I_a)/(2*%pi*A); //Torque developed +disp(sprintf("The torque developed in the motor is %.4f N-m",T)); + +//The answer is different as 'A' has not been included in the denominator(in the book) + +//END + |