{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Appendix - Solved problems"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2 Page 340"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Voltage Gradients :\n",
" for A : 1622 V/cm\n",
" for B : 1216 V/cm\n",
" for C : 811 V/cm\n",
"\n",
"Energy stored :\n",
" for A : 21.9 uJ\n",
" for B : 41.1 uJ\n",
" for C : 38.3 uJ\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"# Given\n",
"t1=2# # mm \n",
"t2=5# # mm \n",
"t3=7# # mm \n",
"eps1=3 # dielectric constant\n",
"eps2=4 # dielectric constant\n",
"eps3=6# # dielectric constant\n",
"eps0=1/36/pi*10**-9# # dielectric constant\n",
"d=10/100 # m\n",
"V=1500 # V \n",
"#E1*t1+E2*t2+E3*t3=V\n",
"#Voltage Gradients : \n",
"# using eps1*E1=eps2*E2=eps3*E3\n",
"E1=V/(t1+(eps1/eps2)*t2+(eps1/eps3)*t3)# V/mm \n",
"E1=E1*10 # V/cm\n",
"E2=eps1*E1/eps2 # V/cm\n",
"E3=eps1*E1/eps3 # V/cm\n",
"print \"Voltage Gradients :\\n for A : %.f V/cm\\n for B : %.f V/cm\\n for C : %.f V/cm\"%(E1,E2,E3)\n",
"\n",
"A = pi*d**2\n",
"W1=1/2*eps0*eps1*E1**2*10**4*A*t1*10**-3# # J\n",
"W2=1/2*eps0*eps2*E2**2*10**4*A*t2*10**-3# # J\n",
"W3=1/2*eps0*eps3*E3**2*10**4*A*t3*10**-3# # J\n",
"W1=W1*10**6 # # uJ\n",
"W2=W2*10**6 # # uJ\n",
"W3=W3*10**6 # # uJ\n",
"print \"\\nEnergy stored :\\n for A : %.1f uJ\\n for B : %.1f uJ\\n for C : %.1f uJ\"%(W1,W2,W3)\n",
"\n",
"\n",
"# Answer in the textbook are not accurate"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3 Page 341"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current required = 1.95 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"\n",
"# Given\n",
"N=680# # turns\n",
"fi=1.6*10**3 # Wb\n",
"d1=4/100 # m\n",
"d2=24/100 # m\n",
"l=0.6 # m\n",
"mu0=4*pi/10**7 # constant\n",
"\n",
"\n",
"# For air gap : \n",
"A=d1**2 # m**2\n",
"Bg=fi/A # weber/m**2\n",
"Hg=Bg/mu0 # AT/m\n",
"mmf1=0.001/mu0 # AT\n",
"\n",
"# For central limb : \n",
"A=d1**2 # m**2\n",
"Bc=fi/A # weber/m**2\n",
"Hc=900 # AT/m (from magnetization curve)\n",
"mmf2=Hc*d2 # AT\n",
"\n",
"\n",
"# For side limb : \n",
"fi=1/2*fi # Wb\n",
"A=d1**2 # m**2\n",
"Bc=fi/A # weber/m**2\n",
"Hc=520 # AT/m (from magnetization curve)\n",
"mmf3=Hc*l # AT\n",
"\n",
"mmf_total = mmf1+mmf2+mmf3 # AT\n",
"i=mmf_total/N # A\n",
"print \"Current required = %0.2f A\"%(i)\n",
"\n",
"\n",
"# Answer in the textbook are not accurate"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 4 Page 343"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\t\t\tWithout air gap With air gap\n",
"\n",
"Exciting current 3.75 A 11.7 A\n",
"\n",
"Inductance 5.3 mH 1.7 mH\n",
"\n",
"Stored Energy 0.375 J 1.17 J\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"\n",
"# Given\n",
"\n",
"D=15/100 # m\n",
"A=10/10**-4 # m**2\n",
"N=200# # turns\n",
"fi=1.6*10**3 # Wb\n",
"B=1 # weber/m**2\n",
"mu0=4*pi/10**7 # constant\n",
"mur=500 # constant\n",
"lg=2/1000 # m\n",
"\n",
"\n",
"# without air gap\n",
"l=pi*D # m\n",
"R=l/mu0/mur/A # A/Wb\n",
"fi=B*A # Wb\n",
"mmf=fi*R # AT\n",
"I=mmf/N # A\n",
"L=N**2/R/10**6 # mH\n",
"E=1/2*L*I**2/100 # J\n",
"\n",
"\n",
"# with air gap\n",
"Rg=lg/mu0/A # A/Wb\n",
"Rt=R+Rg # A/Wb\n",
"fi=B*A # Wb\n",
"mmf=fi*Rt # AT\n",
"I2=mmf/N # A\n",
"L2=N**2/Rt/10**6 # mH\n",
"E2=1/2*L2*I2**2/100 # J\n",
"\n",
"print \"\\t\\t\\tWithout air gap With air gap\"\n",
"print \"\\nExciting current %.2f A %.1f A\"%(I,I2)\n",
"print \"\\nInductance %.1f mH %.1f mH\"%(L,L2)\n",
"print \"\\nStored Energy %.3f J %.2f J\"%(E,E2)\n",
"\n",
"\n",
"# Answer in the textbook are not accurate"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 5 Page 344"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Voltage acroos 100 ohm = -72.0 V\n",
"\n",
"R=37.5 ohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"from numpy import array\n",
"\n",
"# Given\n",
"\n",
"VA=60 # V\n",
"I=0.6 # A\n",
"# (VB-VA)/20+(VB-VC)/20+VB/20-I=0\n",
"#3*VB-VC=72 for node B eqn(1)\n",
"#(VC-VA)/50+(VC-VB)/30+(VC-12)/50+VC/100=0\n",
"#-5*VB+10*VC=144 eqn(2)\n",
"A=array([[3, -1],[-5 ,10]])\n",
"B=array([[72],[144]])\n",
"X=A**-1*B#\n",
"VB=X[0,0] # V\n",
"VC=X[0,1] # V\n",
"print \"Voltage acroos 100 ohm = %.1f V\"%(VC)\n",
"VC=24 # V\n",
"VB=(72+VC)/3 # from eqn(1)\n",
"# Node C \n",
"# (VC-VA)/50+(VC-VB)/20+(VC-12)/50+VC/100+VC/R=0 eqn(3)\n",
"R=100*VC/(144+5*VB-10*VC) # ohm\n",
"print \"\\nR=%.1f ohm\"%(R)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 6 Page 346"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"at f = 2.34 kHz, the above filter will have required attenuation.\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,cosh\n",
"\n",
"# Given\n",
"\n",
"Ro=600 # ohm\n",
"fc=2*1000 # Hz\n",
"alfa=10 # dB\n",
"\n",
"\n",
"L=Ro/pi/fc*1000 # mH\n",
"C=1/(pi*Ro*fc)*10**6 # uF\n",
"alfa=alfa/8.686 # nepers\n",
"f=fc*cosh(alfa/2)/1000 # kHz\n",
"print \"\\nat f = %.2f kHz, the above filter will have required attenuation.\"%(f)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 7 Page 347"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"equation for instant current:\n",
"i=2.13*sin(314*t+1.01)\n",
"Power consumed = 56.6 W\n",
"Voltage across capacitor = 73.3 V(+ve & -ve)\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,atan,sqrt,asin,sin\n",
"\n",
"# Given\n",
"#v=100*sin(314*t)\n",
"R=25 # ohm\n",
"C=80 # uF\n",
"omega=314 # radian\n",
"Vm=100 # V\n",
"\n",
"Xc=1/omega/(C*10**-6) # ohm\n",
"Z=sqrt(R**2+Xc**2) # ohm\n",
"Im=Vm/Z # A\n",
"theta=atan(Xc/R) # radian\n",
"print \"equation for instant current:\"\n",
"print \"i=%.2f*sin(%d*t+%.2f)\"%(Im,omega,theta)\n",
"P=(Im/sqrt(2))**2*R # W\n",
"print \"Power consumed = %.1f W\"%(P)\n",
"Vcm=Im*Xc # V \n",
"#(when i=Im/2)\n",
"i=0.5*Im # A\n",
"#vc=Vcm*sin(314*t+theta-pi/2)\n",
"#i=Im*sin(314*t+theta)\n",
"tt=asin(i/Im) # radian tt=314*t+theta\n",
"vcm=Vcm*sin(tt-pi/2)\n",
"print \"Voltage across capacitor = %.1f V(+ve & -ve)\"%(abs(vcm))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 8 Page 348"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Capacitance of XC = 318 uF\n",
"Circuit current = 10 A and power = 1 kW\n"
]
}
],
"source": [
"from __future__ import division\n",
"from numpy import pi,roots\n",
"\n",
"# Given\n",
"\n",
"Z1=(6.25+1J*1.25) # ohm\n",
"Z2=(5+1J*0) # ohm\n",
"#Z3=(5-1J*XC) # ohm\n",
"V=100 # V\n",
"f=50 # Hz\n",
"#Z23=(250+5*Xc**2)/(100+Xc**2)-1J*(25*Xc)/(100+Xc**2)\n",
"#for in phase condition imag part must be zero\n",
"#5*Xc**2-100*Xc+5*100=0\n",
"A=[5 ,-100, 500] # polynomal \n",
"XC=roots(A)#\n",
"XC=XC[0] # ohm\n",
"C=1/(2*pi*f*XC)*10**6 # uF\n",
"print \"Capacitance of XC = %.f uF\"%(C)\n",
"Z=XC # ohm\n",
"I=V/Z # A\n",
"P=I**2*Z/1000 # kW\n",
"print \"Circuit current = %.f A and power = %.f kW\"%(I,P)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 9 Page 349"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"L = 10.4 mH\n",
" C=267 uF\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"\n",
"# Given\n",
"\n",
"omega_o=600 # rad/s\n",
"omega=400 # rad/s\n",
"R=3 # ohm\n",
"IBYIo=1/2 # ratio\n",
"\n",
"\n",
"fo=omega_o/2/pi # Hz\n",
"f=omega/2/pi # Hz\n",
"#I/Io=1/(sqrt(1+Q**2*(f/fo-fo/f)**2))\n",
"Q=sqrt(1/IBYIo**2-1)/(fo/f-f/fo)\n",
"#Q=1/omega_0/R/C\n",
"C=1/omega_o/R/Q*10**6 # uF\n",
"#Q=omega_0*L/R\n",
"L=Q*R/omega_o*1000 # mH\n",
"print \"L = %.1f mH\\n C=%.f uF\"%(L,C)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 10 Page 350"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Star Connection : P=1.6 kW\n",
"Delta Connection : P=4.8 kW\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"\n",
"# Given\n",
"\n",
"V=400 # V\n",
"f=50 # Hz\n",
"n=3 # no of phase\n",
"R=100 # ohm\n",
"\n",
"#Star connection\n",
"Vph=V/sqrt(n) # V\n",
"Iph=Vph/R # A\n",
"IL=Iph # A\n",
"cos_fi=1 # for only resitor load\n",
"P=sqrt(3)*V*IL*cos_fi/1000 # kW\n",
"print \"Star Connection : P=%.1f kW\"%(P)\n",
"#Delta Connection\n",
"\n",
"Vph=V # V\n",
"Iph=Vph/R # A\n",
"IL=sqrt(3)*Iph # A\n",
"VL=Vph # V\n",
"P=sqrt(3)*VL*IL*cos_fi/1000 # kW\n",
"print \"Delta Connection : P=%.1f kW\"%(P)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 11 Page 351"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Phase Current:\n",
"Iab=10 angle=-53.13 degree \n",
"Ibc=10 angle=-156.87 degree \n",
"Ica=20 angle=156.87 degree \n",
"\n",
"\n",
" Line Current:\n",
"Iaa=29 angle=-33.03 degree \n",
"Ibb=10 angle=165.00 degree \n",
"Icc=15 angle=127.97 degree \n",
"\n",
"\n",
" Total Power, W=3 kW\n"
]
}
],
"source": [
"from __future__ import division\n",
"from numpy import exp,pi\n",
"import cmath as cm\n",
"# Given\n",
"Rab=6;Rbc=8;Rca=4 # ohm\n",
"Vab=100*exp(1J*0) # V\n",
"Vbc=100*exp(1J*-120*pi/180) # V\n",
"Vca=100*exp(1J*120*pi/180) # V\n",
"Zab=6+1J*8 # ohm\n",
"Zbc=8+1J*6 # ohm\n",
"Zca=4-1J*3 # ohm\n",
"\n",
"#Phase current\n",
"Iab=Vab/Zab # A\n",
"Ibc=Vbc/Zbc # A\n",
"Ica=Vca/Zca # A\n",
"print \"Phase Current:\"\n",
"print \"Iab=%.f angle=%.2f degree \"%(abs(Iab),cm.phase(Iab)*180/pi)\n",
"print \"Ibc=%.f angle=%.2f degree \"%(abs(Ibc),cm.phase(Ibc)*180/pi)\n",
"print \"Ica=%.f angle=%.2f degree \"%(abs(Ica),cm.phase(Ica)*180/pi)\n",
"#Line current\n",
"Iaa=Iab-Ica # A\n",
"Ibb=Ibc-Iab # A\n",
"Icc=Ica-Ibc # A\n",
"print \"\\n\\n Line Current:\"\n",
"print \"Iaa=%.f angle=%.2f degree \"%(abs(Iaa),cm.phase(Iaa)*180/pi)\n",
"print \"Ibb=%.f angle=%.2f degree \"%(abs(Iab),cm.phase(Ibb)*180/pi)\n",
"print \"Icc=%.f angle=%.2f degree \"%(abs(Icc),cm.phase(Icc)*180/pi)\n",
"#Power Consumed\n",
"Wab=abs(Iab)**2*Rab # W\n",
"Wbc=abs(Ibc)**2*Rbc # W\n",
"Wca=abs(Ica)**2*Rca # W\n",
"W=Wab+Wbc+Wca # W\n",
"W=W/1000 # kW\n",
"print \"\\n\\n Total Power, W=%.f kW\"%(W)\n",
"#Answer wrong for line current in the textbook."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 12 Page 353"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wattmeter W1 reading=0 W\n",
"Wattmeter W2 reading=8000 W or 8 kW\n"
]
}
],
"source": [
"from __future__ import division\n",
"from numpy import exp,pi\n",
"import cmath as cm\n",
"\n",
"# Given\n",
"VRY=200*exp(1J*0) # V\n",
"VYB=200*exp(1J*-120*pi/180) # V\n",
"VBR=200*exp(1J*120*pi/180) # V\n",
"\n",
"\n",
"ZA=10*exp(1J*60*pi/180) # ohm\n",
"ZB=10*exp(1J*0*pi/180) # ohm\n",
"ZC=10*exp(1J*60*pi/180) # ohm\n",
"\n",
"#Phase current\n",
"IRY=VRY/ZA # A\n",
"IYB=VYB/ZB # A\n",
"IBR=VBR/ZC # A\n",
"\n",
"IR=IRY-IBR # A\n",
"PVA=(VRY).conjugate()*IR # W\n",
"print \"Wattmeter W1 reading=%.f W\"%((PVA.real))\n",
"IB=IBR-IYB # A\n",
"PVB=(-VYB).conjugate()*IB # W\n",
"print \"Wattmeter W2 reading=%.f W or %.f kW\"%((PVB.real),(PVB.real)/1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 13 Page 354"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"expression for current:\n",
"i = 9.83*sin(omega*t--38.1)+1.0*sin(3*omega*t-7.0)+0.25*sin(5*omega*t-74.3)\n",
"Irms=7 A\n",
" Vrms=181 V\n",
"Total Power, P=977 W\n",
"Power factor = 0.77\n"
]
}
],
"source": [
"from __future__ import division\n",
"from numpy import exp,pi,sqrt\n",
"import cmath as cm\n",
"# Given\n",
"#v=250*sin(omega*t)+50*sin(3*omega*t+pi/3)+20*sin(5*omega*t+5*pi/6)\n",
"V1=250;V3=50;V5=20 # V\n",
"fi1=0;fi3=60;fi5=150 # degree\n",
"R=20 # omh\n",
"L=0.05 # H\n",
"omega=314 # rad/s\n",
"\n",
"X1=omega*L # ohm\n",
"Z1=R+1J*X1 # ohm\n",
"X3=3*omega*L # ohm\n",
"Z3=R+1J*X3 # ohm\n",
"X5=5*omega*L # ohm\n",
"Z5=R+1J*X5 # ohm\n",
"r1=abs(Z1);t1=cm.phase(Z1)\n",
"r3=abs(Z3);t3=cm.phase(Z3)\n",
"r5=abs(Z5);t5=cm.phase(Z5)\n",
"print \"expression for current:\"\n",
"print \"i = %.2f*sin(omega*t-%.1f)+%.1f*sin(3*omega*t%.1f)+%.2f*sin(5*omega*t-%.1f)\"%(V1/r1,fi1-t1*180/pi,V3/r3,fi3-t3*180/pi,V5/r5,fi5-t5*180/pi)\n",
"\n",
"I1m=V1/r1 # A\n",
"I3m=V3/r3 # A\n",
"I5m=V5/r5 # A\n",
"Irms=sqrt(I1m**2/2+I3m**2/2+I5m**2/2) # A\n",
"Vrms=sqrt(V1**2/2+V3**2/2+V5**2/2) # A\n",
"print \"Irms=%.f A\\n Vrms=%.f V\"%(Irms,Vrms)\n",
"P=Irms**2*R # W\n",
"print \"Total Power, P=%.f W\"%(P)\n",
"cosfi=P/Vrms/Irms # Power factor\n",
"print \"Power factor = %.2f\"%(cosfi)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 14 Page 355"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"expression for current:\n",
"i = 12.1*sin(314*t-1.263)+0.95*e**(-100*t)\n",
"current after 0.02 sec is : -11.4 A\n",
"transient component is : 1.56 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,exp,sin,atan\n",
"\n",
"# Given\n",
"f=50 # Hz\n",
"Vm=400 # V\n",
"R=10 # ohm\n",
"L=0.1 # H\n",
"t=0.02 # sec\n",
"XL=2*pi*f*L # ohm\n",
"Z=R+1J*XL # ohm\n",
"Im=Vm/abs(Z) # A\n",
"fi=atan(XL/R) # degree\n",
"lamda=L/R # sec\n",
"print \"expression for current:\"\n",
"print \"i = %.1f*sin(314*t-%.3f)+0.95*e**(-100*t)\"%(Im,fi)\n",
"i = Im*sin(314*t-fi)+0.95*exp(-100*t) # A\n",
"print \"current after 0.02 sec is : %0.1f A\"%(i)\n",
"i2=Im*(0.95*exp(-100*t)) # A\n",
"print \"transient component is : %0.2f A\"%(i2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 15 Page 356"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Since R<2sqrt(L/C), the circuit is originally oscillatory.\n",
"Expression for current :\n",
" i = 0.000*exp(-50t)*sin(312.2t)\n",
"\n",
"\n",
" Additional resistance required = 1064 ohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt,asin,exp,sin\n",
"from sympy import Symbol,solve\n",
"from scipy.misc import derivative\n",
"\n",
"# Given\n",
"C=5*10**-6 # F\n",
"L=2 # H\n",
"R=200 # ohm\n",
"\n",
"if R<2*sqrt(L/C):\n",
" print \"Since R<2sqrt(L/C), the circuit is originally oscillatory.\"\n",
"\n",
"\n",
"a=R/2/L\n",
"omega = sqrt(1/L/C-R**2/4/L**2) # rad/s\n",
"#i=Im*exp(-a*t)*sin(omega*t+fi)\n",
"#at t=0 sec\n",
"i0=0 # A\n",
"vc=10 # V\n",
"fi=asin(i0) # degree\n",
"#L*di/dt=vc at t=0\n",
"Im=Symbol('Im')\n",
"def current(t):\n",
" i=Im*exp(-a*t)*sin(omega*t+fi)\n",
" return i\n",
"#i=Im*expm(-a*t)*sin(omega*t+fi)\n",
"\n",
"\n",
"LdiBYdt=L*derivative(current,0)\n",
"#temp = coeff(LdiBYdt)\n",
"Im=solve(LdiBYdt,Im)[0]\n",
"#vc/temp(2)\n",
"print \"Expression for current :\\n i = %.3f*exp(-%dt)*sin(%.1ft)\"%(Im,a,omega)\n",
"Rn=2*sqrt(L/C) # ohm\n",
"Rad=Rn-R # ohm\n",
"print \"\\n\\n Additional resistance required = %d ohm\"%(Rad)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 16 Page 357"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reading of hot wire instrument = 0.548 A\n",
"Reading of electrostatic voltmeter acroos 1000 ohm = 547 V\n",
"Reading of electrostatic voltmeter acroos 1 mH inductor = 353 V\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"\n",
"# Given\n",
"#i=0.5+0.3*sin(omega*t)-0.2*sin(2*omega*t)\n",
"I0=0.5;I1m=0.3;I2m=-0.2 # from above expression\n",
"Iav=I0 # A\n",
"R=1000 # ohm\n",
"L=1/1000 # H\n",
"\n",
"Irms=sqrt(I0**2+(I1m/sqrt(2)**2+(I2m/sqrt(2)**2))) # A\n",
"print \"Reading of hot wire instrument = %.3f A\"%(Irms)\n",
"VR=Irms*R # V\n",
"print \"Reading of electrostatic voltmeter acroos 1000 ohm = %d V\"%(VR)\n",
"#vl_dash=L*di/dt=300*cos(w*t)-400*cos(2*w*t)\n",
"vl1=300;vl2=4 # V\n",
"vl=sqrt((300/sqrt(2))**2+(400/sqrt(2))**2)\n",
"print \"Reading of electrostatic voltmeter acroos 1 mH inductor = %d V\"%(vl)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 17 Page 358"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The limit of error = 48.6 uV\n",
"Deflection = 8.2 mm\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"R=80 # ohm\n",
"V=2 # V\n",
"l=50 # cm\n",
"vd=.1 # V\n",
"emf=1.43 # V\n",
"Rc=850 # ohm\n",
"sg=17.5 # mm/uA\n",
"df=1 # mm\n",
"\n",
"\n",
"I=R/V # A\n",
"Rw=vd/I # ohm (Resistance of side wire)\n",
"Id=df/sg*10**-6 # A (current for 1mm deflection)\n",
"el=1/sg*Rc # uV\n",
"print \"The limit of error = %.1f uV\"%(el)\n",
"Rw1=0.2/l*Rw # ohm (for 2cm slide wire)\n",
"dV=I*Rw1*1000 # mV (Change in voltage from null point)\n",
"r1=emf/I # ohm (tapped portion) \n",
"r2=r1*22.8/R # ohm\n",
"Ig=dV/1000/(Rc+r2) # A\n",
"d=dV/1000/(Rc+r2)/Id # mm\n",
"print \"Deflection = %.1f mm\"%(d)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 18 Page 359"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"reading of hot wire ammeter = 0.56 A\n",
"reading of moving coil ammeter = 0.30 A\n",
"\n",
"\n",
" Power taken from the mains = 83.3 W\n",
"Power dissipated in rectifying device = 67 W\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"from sympy.mpmath import quad\n",
"\n",
"# Given\n",
"R=50 # ohm\n",
"Vrms=100 # V\n",
"Rd1=50 # ohm\n",
"Rd2=100 # ohm \n",
"\n",
"Vm=Vrms/sqrt(2) # V\n",
"#v=Vm*sin(theta)\n",
"Rf=R+Rd1 # ohm\n",
"Rb=R+Rd2 # ohm\n",
"#i_f=v/Rf # A\n",
"#i_b=v/Rb # A\n",
"Irms=1/2/pi*(quad(lambda theta:(sqrt(2)*sin(theta))**2,[0,pi])+quad(lambda theta:(sqrt(2)/3*sin(theta))**2,[pi,2*pi]))\n",
"Iav=1/2/pi*(quad(lambda theta:sqrt(2)*sin(theta),[0,pi])+quad(lambda theta:sqrt(2)/3*sin(theta),[pi,2*pi]))\n",
"print \"reading of hot wire ammeter = %.2f A\"%(Irms)\n",
"print \"reading of moving coil ammeter = %.2f A\"%(Iav)\n",
"P=1/2*(Vrms**2/Rf+Vrms**2/Rb) # W\n",
"print \"\\n\\n Power taken from the mains = %.1f W\"%(P)\n",
"Pc=Irms**2*R # W\n",
"Pd=P-Pc # W\n",
"print \"Power dissipated in rectifying device = %d W\"%(Pd)\n",
"#Answer wrong in the textbook."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 19 Page 361"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Required potential difference = 500 V\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt,sin\n",
"\n",
"# Given\n",
"d=1/100 # m\n",
"S=-1/100 # m\n",
"Ve=2 # kV\n",
"theta=30 # degree\n",
"e=1.6*10**-19 # C\n",
"m=9.67*10**-31 # kg\n",
"\n",
"u=sqrt(2*e*Ve*1000/m) # m/s\n",
"uy=u*sin(pi/180*theta) # m/s\n",
"vy=0 # since final velocity =0\n",
"#vy**2-uy**2=2*ay*S\n",
"ay=(vy**2-uy**2)/2/S # m**2/s\n",
"#ay=e/m*V/d\n",
"V=ay*m*d/e # V\n",
"print \"Required potential difference = %.f V\"%(V)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 20 Page 361"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Amplification factor, mu = -40\n",
"Mutual conductance, gm = 2.74 S\n",
"Plate resistance, ra = 14.6 kohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"#Ia=0.0004*(Va+40*Vg)**(3/2) # mA --eqn(1)\n",
"Va=250 # V\n",
"Vg=-3 # V\n",
"#mu=delVa/delVg\n",
"#differenciation wrt Vg eqn(1)\n",
"#(4*10**-6*3/2*(Va+40*Vg))**(1/2)*(mu+40)=0\n",
"mu=-40 # constant\n",
"print \"Amplification factor, mu = %.f\"%(mu)\n",
"#differenciation wrt Va eqn(1)\n",
"#delIa/delVa=(4*10**-6*3/2*(Va+40*Vg))**(1/2)*(0+40)\n",
"gm=(4*10**-6*3/2)*(Va+40*Vg)**(1/2)*(0+40)*1000 # mA/V or S\n",
"print \"Mutual conductance, gm = %.2f S\"%(gm)\n",
"#differenciation wrt Ia eqn(1) keeping Vg constant\n",
"#1=(4*10**-6)*3/2*(Va+40*Vg)**(1/2)*(delVa/delIa+0)\n",
"#ra=delVa/delIa\n",
"ra=1/((4*10**-6)*3/2*(Va+40*Vg)**(1/2))\n",
"print \"Plate resistance, ra = %.1f kohm\"%(ra/1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 21 Page 363"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"General equation of FM wave is:\n",
"v=4*sin(1.57e+08*t+25*sin(2513*t)\n",
"\n",
"\n",
" General equation of PM wave is:\n",
"v=4*sin(1.57e+08*t+25*sin(2513*t)\n",
"\n",
"\n",
" Now equation of FM wave is:\n",
"v=4*sin(1.57e+08*t+25*sin(12566*t)\n",
"\n",
"\n",
" Now equation of PM wave is:\n",
"v=4*sin(1.57e+08*t+25*sin(12566*t)\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"\n",
"# Given\n",
"fc=25*10**6 # Hz\n",
"fm=400 # Hz\n",
"Vm=4 # V\n",
"Del=10*10**3 # Hz\n",
"wc=2*pi*fc # rad/s\n",
"wm=2*pi*fm # rad/s\n",
"m=Del/fm # modulation index\n",
"mf=m;mp=m # modulation index\n",
"print \"General equation of FM wave is:\"\n",
"print \"v=%d*sin(%.2e*t+%d*sin(%d*t)\"%(Vm,wc,mf,wm)\n",
"print \"\\n\\n General equation of PM wave is:\"\n",
"print \"v=%d*sin(%.2e*t+%d*sin(%d*t)\"%(Vm,wc,mp,wm)\n",
"# Changing modulating frequency\n",
"fm_new=2*10**3 # Hz\n",
"a=fm_new/fm # increase in angular frequency\n",
"print \"\\n\\n Now equation of FM wave is:\"\n",
"print \"v=%d*sin(%.2e*t+%d*sin(%d*t)\"%(Vm,wc,mf,a*wm)\n",
"print \"\\n\\n Now equation of PM wave is:\"\n",
"print \"v=%d*sin(%.2e*t+%d*sin(%d*t)\"%(Vm,wc,mp,a*wm)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 22 Page 363"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"modulation index = 0.5\n",
"carrier power under modulated condition = 5.06 kW\n",
"plate circuit efficiency = 75 percent\n",
"plate dissipation under unmodulated condition = 1.5 kW\n",
"plate dissipation under modulated condition = 1.69 kW\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"Ebb=300 # V\n",
"Ibb=20 # A\n",
"Emm=150 # V\n",
"Po=4.5*10**3 # W\n",
"\n",
"m=Emm/Ebb # modulation index\n",
"Pbb=Ebb*Ibb\n",
"eta=Po/Pbb*100 # %\n",
"P=Po*(1+m**2/2) # W\n",
"Pdo=Pbb-Po # W\n",
"Pd=Pdo*(1+m**2/2) # W\n",
"print \"modulation index = %.1f\"%(m)\n",
"print \"carrier power under modulated condition = %0.2f kW\"%(P/1000)\n",
"print \"plate circuit efficiency = %.f percent\"%(eta)\n",
"print \"plate dissipation under unmodulated condition = %.1f kW\"%(Pdo/1000)\n",
"print \"plate dissipation under modulated condition = %.2f kW\"%(Pd/1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 23 Page 364"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Series equivalent circuit:\n",
"Rs = 77.7 ohm\n",
"Xs = 34.3 ohm\n",
"\n",
"\n",
" Parallel equivalent circuit:\n",
"Rp = 92.8 ohm\n",
"Xp = 211 ohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import cos,pi,sin\n",
"# Given\n",
"Zo=50 # ohm\n",
"VSWR=2 # ratio\n",
"#lm=0.2*lamda\n",
"lmBYlamda=0.2\n",
"betaINTOlamda=2*pi\n",
"rho=(VSWR-1)/(VSWR+1) # reflection coefficient\n",
"theta=2*betaINTOlamda*lmBYlamda # radian\n",
"#exp(j*theta)=cos(theta)+1J*sin(theta)\n",
"ZL=Zo*(1-rho*(cos(theta)+1J*sin(theta)))/(1+rho*(cos(theta)+1J*sin(theta))) # ohm\n",
"Rs=(ZL.real) # ohm\n",
"Xs=abs((ZL.imag)) # ohm(capacitive)\n",
"print \"Series equivalent circuit:\"\n",
"print \"Rs = %0.1f ohm\"%(Rs)\n",
"print \"Xs = %0.1f ohm\"%(Xs)\n",
"YL=(1/ZL)*1000 # mS\n",
"Rp=1000/(YL.real) # ohm\n",
"Xp=1000/(YL.imag) # ohm\n",
"print \"\\n\\n Parallel equivalent circuit:\"\n",
"print \"Rp = %0.1f ohm\"%(Rp)\n",
"print \"Xp = %0.f ohm\"%(Xp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 24 Page 366"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For TE10 mode:\n",
"cutoff wavelength = 9 cm\n",
"guide wavelength = 3.59 cm\n",
"Group velocity = 2.8e+08 m/s\n",
"Phase velocity = 3.2e+08 m/s\n",
"Characteristic wave impedence = 406 ohm\n",
"\n",
"\n",
" For TM11 mode:\n",
"cutoff wavelength = 5 cm\n",
"guide wavelength = 4.48 cm\n",
"Group velocity = 2.2e+08 m/s\n",
"Phase velocity = 4.0e+08 m/s\n",
"Characteristic wave impedence = 281 ohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"\n",
"# Given\n",
"b=3 # cm\n",
"a=4.5 # cm\n",
"f=9*10**9 # Hz\n",
"v=3*10**10 # cm/s\n",
"lamda=v/f # cm\n",
"\n",
"print \"For TE10 mode:\"\n",
"m=1 # for TE10 mode\n",
"lamda_c = 2*a/m # cm\n",
"rho=sqrt(1-(lamda/lamda_c)**2)\n",
"lamda_g=lamda/rho # cm\n",
"vg=rho*v # cm/s\n",
"vp=v/rho # cm/s\n",
"ZTE=120*pi/rho # ohm\n",
"\n",
"print \"cutoff wavelength = %.f cm\"%(lamda_c)\n",
"print \"guide wavelength = %.2f cm\"%(lamda_g)\n",
"print \"Group velocity = %.1e m/s\"%(vg/100)\n",
"print \"Phase velocity = %.1e m/s\"%(vp/100)\n",
"print \"Characteristic wave impedence = %.f ohm\"%(ZTE)\n",
"\n",
"print \"\\n\\n For TM11 mode:\"\n",
"m=1;n=1# for TE10 mode\n",
"lamda_c = 2/sqrt((m/a)**2+(n/b)**2) # cm\n",
"rho=sqrt(1-(lamda/lamda_c)**2)\n",
"lamda_g=lamda/rho # cm\n",
"vg=rho*v # cm/s\n",
"vp=v/rho # cm/s\n",
"ZTM=120*pi*rho # ohm\n",
"print \"cutoff wavelength = %.f cm\"%(lamda_c)\n",
"print \"guide wavelength = %.2f cm\"%(lamda_g)\n",
"print \"Group velocity = %.1e m/s\"%(vg/100)\n",
"print \"Phase velocity = %.1e m/s\"%(vp/100)\n",
"print \"Characteristic wave impedence = %.f ohm\"%(ZTM)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 25 Page 367"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"part(a):\n",
"For fo>fs, the range of fo : 965 to 2065 kHz\n",
"frequency ratio = 2.14\n",
"capacitance ratio = 4.58\n",
"\n",
"\n",
" part(b):\n",
"For fo>fs, the range of fo : 35 to 1135 kHz\n",
"frequency ratio = 32.4\n",
"capacitance ratio = 1051.6\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"fs_max=1600 # kHz\n",
"fs_min=500 # kHz\n",
"IF=465 # kHz\n",
"\n",
"fr=fs_max/fs_min # ratio\n",
"C_ratio = fr**2 # Cs_max/Cs_min\n",
"#Part (a)\n",
"fo_min=IF+fs_min # kHz\n",
"fo_max=IF+fs_max # kHz\n",
"fr_o=fo_max/fo_min # frequency ratio for oscillator\n",
"C_ratio_o = fr_o**2 # Cs_max/Cs_min\n",
"print \"part(a):\"\n",
"print \"For fo>fs, the range of fo : %.f to %.f kHz\"%(fo_min,fo_max)\n",
"print \"frequency ratio = %.2f\"%(fr_o)\n",
"print \"capacitance ratio = %.2f\"%(C_ratio_o)\n",
"\n",
"#Part (b)\n",
"fo_min=-IF+fs_min # kHz\n",
"fo_max=-IF+fs_max # kHz\n",
"fr_o=fo_max/fo_min # frequency ratio for oscillator\n",
"C_ratio_o = fr_o**2 # Cs_max/Cs_min\n",
"print \"\\n\\n part(b):\"\n",
"print \"For fo>fs, the range of fo : %.f to %.f kHz\"%(fo_min,fo_max)\n",
"print \"frequency ratio = %.1f\"%(fr_o)\n",
"print \"capacitance ratio = %.1f\"%(C_ratio_o)\n",
"#ans wrong for part b in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 26 Page 368"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Resistor values are : \n",
"RL=1.60 kohm\n",
"Re=0.40 kohm\n",
"R1=55.60 kohm\n",
"R2=9.34 kohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"Ic=3 # mA\n",
"hfe=45 # unitless\n",
"Vcc=12 # V\n",
"VBE=0.5 # V\n",
"S=0.05 # stability factor\n",
"Beta=45 # unitless\n",
"\n",
"RR=Vcc/2/(Ic*10**-3) # ohm (let RL+Re=RR)\n",
"#Re=20% of (Re+Rl)\n",
"Re=RR*20/100 # ohm\n",
"RL=RR-Re # ohm\n",
"Ve=(Ic+Ic/Beta)*10**-3*Re # V\n",
"Vb=Ve+VBE # V\n",
"#S=Re/Rb=0.5 => Rb=Re/S\n",
"R1=Vcc*Re/S/Vb/1000 # kohm\n",
"# Vb/Vcc = R2/(R2+R1)\n",
"R2=Vb*R1/(Vcc-Vb) # kohm\n",
"print \"Resistor values are : \"\n",
"print \"RL=%.2f kohm\"%(RL/1000)\n",
"print \"Re=%.2f kohm\"%(Re/1000)\n",
"print \"R1=%.2f kohm\"%(R1)\n",
"print \"R2=%.2f kohm\"%(R2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 27 Page 369"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"load presented by transformer = 11.8 ohm\n",
"load power output = 67.6 W\n",
"conversion efficiency = 62.8 percent\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"\n",
"# Given\n",
"Vcc=50 # V\n",
"Vmin=10 # V\n",
"Pd=40 # W\n",
"\n",
"\n",
"Vo=Vcc-Vmin # V\n",
"K=Vo/Vcc # constant\n",
"Rdash=2*Vcc**2/pi/Pd*(K-pi*K**2/4) # ohm\n",
"Po=K**2*Vcc**2/2/Rdash # W\n",
"eta=pi*K/4*100 # %\n",
"\n",
"print \"load presented by transformer = %.1f ohm\"%(Rdash)\n",
"print \"load power output = %.1f W\"%(Po)\n",
"print \"conversion efficiency = %.1f percent\"%(eta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 28 Page 370"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"for 2nd stage(CC stage)\n",
"current gain = 48.57\n",
"Input impedence = 97.14 kohm\n",
"Voltage gain = 1.00\n",
"\n",
"\n",
" for 1st stage(CE stage)\n",
"current gain = -47.66\n",
"Input impedence = 1.08 kohm\n",
"Voltage gain = -86.76\n",
"Output impedence = 68.57 kohm\n",
"Output impedence taking Rc1 into account = 1.94 kohm\n",
"\n",
"\n",
" for overall amplifier\n",
"Output impedence = 34.81 ohm\n",
"Output impedence taking Re2 into account = 33.65 ohm\n",
"current gain = -46.70\n",
"Voltage gain = -86.76\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"Rs=1000 # ohm\n",
"Rc1=2*1000 # ohm\n",
"Re2=2*1000 # ohm\n",
"#CE configuration\n",
"hie=1100 # ohm\n",
"hre=2.5*10**-4#\n",
"hfe=50#\n",
"hoe=25*10**-6 # s\n",
"#CC configuration\n",
"hic=1.1 # kohm\n",
"hrc=1#\n",
"hfc=-51#\n",
"hoc=25*10**-6 # s\n",
"\n",
"print \"for 2nd stage(CC stage)\"\n",
"AI2=-hfc/(1+hoe*Re2) # current gain\n",
"Ri2=hic+hrc*AI2*Re2 # kohm\n",
"Av2=AI2*Re2/Ri2 # Voltage Gain\n",
"print \"current gain = %0.2f\"%(AI2)\n",
"print \"Input impedence = %0.2f kohm\"%(Ri2/1000)\n",
"print \"Voltage gain = %0.2f\"%(Av2)\n",
"\n",
"print \"\\n\\n for 1st stage(CE stage)\"\n",
"RL1=Rc1*Ri2/(Rc1+Ri2) # kohm\n",
"AI1=-hfe/(1+hoe*RL1) # current gain\n",
"print \"current gain = %.2f\"%(AI1)\n",
"Ri1=hie+hre*AI1*RL1 # kohm\n",
"print \"Input impedence = %0.2f kohm\"%(Ri1/1000)\n",
"Av1=AI1*RL1/Ri1 # Voltage gain\n",
"print \"Voltage gain = %0.2f\"%(Av1)\n",
"Ro1=1/(hoe-hfe*hre/(hie+100)) # ohm\n",
"print \"Output impedence = %.2f kohm\"%(Ro1/1000)\n",
"Ro1dash=Ro1*Rc1/(Ro1+Rc1) # /ohm\n",
"print \"Output impedence taking Rc1 into account = %.2f kohm\"%(Ro1dash/1000)\n",
"\n",
"print \"\\n\\n for overall amplifier\"\n",
"Ro=1/(hoc*100-hfc*hrc/(hic+Ro1dash)) # ohm\n",
"print \"Output impedence = %.2f ohm\"%(Ro)\n",
"Rodash=Ro*Re2*1000/(Ro1+Re2*1000) # /ohm\n",
"print \"Output impedence taking Re2 into account = %.2f ohm\"%(Rodash)\n",
"AI=AI1*AI2*Rc1/(Ri2+Rc1) # current gain\n",
"print \"current gain = %.2f\"%(AI)\n",
"Av=Av1*Av2 # voltage gain\n",
"print \"Voltage gain = %.2f\"%(Av)\n",
"#answer is wrong for overall amplifier in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 29 Page 372"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Voltage gain upper BW frequency = 0.37 MHz\n",
"Current gain = -13.51\n",
"Voltage gain = -27.03\n",
"Voltage gain BW product = 9.90 MHz\n",
"Current gain BW product = 4.95 MHz\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"\n",
"# Given\n",
"fT=6*10**6 # Hz\n",
"hfe=50#\n",
"Rs=500 # ohm\n",
"gm=0.04 # S\n",
"rbb_dash=100 # ohm\n",
"Cc=10*10**-12 # F\n",
"RL=1 # kohm\n",
"\n",
"rbe=hfe/gm # ohm\n",
"Ce=gm/2/pi/fT # F\n",
"C=Ce+Cc*(1+gm*RL) # F\n",
"hie=rbb_dash+rbe # ohm\n",
"R=(Rs+rbb_dash)*rbe/((Rs+rbb_dash)+rbe) # ohm\n",
"f2=1/2/pi/R/C # Hz\n",
"print \"Voltage gain upper BW frequency = %.2f MHz\"%(f2/10**6)\n",
"AIS=-hfe*Rs/(Rs+hie) # current gain\n",
"print \"Current gain = %.2f\"%(AIS)\n",
"AVS=-hfe*RL*1000/(Rs+hie) # voltage gain\n",
"print \"Voltage gain = %.2f\"%(AVS)\n",
"AVSf2=AVS*f2 # Hz\n",
"print \"Voltage gain BW product = %.2f MHz\"%(abs(AVSf2/10**6))\n",
"AISf2=AIS*f2 # Hz\n",
"print \"Current gain BW product = %.2f MHz\"%(abs(AISf2/10**6))\n",
"\n",
"#answer in the textbook are wrong."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 30 Page 373"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"VGS=0.05 V\n",
"gm = -13.23 mS\n",
"Rs = -49 ohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"\n",
"# Given\n",
"VP=-2 # V\n",
"IDSS=1.75/1000 # A\n",
"VDD=24 # V\n",
"ID=1/1000 # A\n",
"VP=0.2 # V (pinch off voltage)\n",
"\n",
"VGS=(1-sqrt(ID/IDSS))*VP # V\n",
"gmo=-2*IDSS/VP # S\n",
"gm=gmo*(1-VGS/VP) # S\n",
"Rs=-VGS/ID # ohm\n",
"\n",
"print \"VGS=%.2f V\"%(VGS)\n",
"print \"gm = %.2f mS\"%(gm*1000)\n",
"print \"Rs = %.f ohm\"%(Rs)\n",
"#Ans are wrong in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 31 Page 374"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Bandwidth of redesigned aplifier, BW=101 kHz\n"
]
}
],
"source": [
"from math import sqrt\n",
"from __future__ import division\n",
"# Given\n",
"G=37 # dB\n",
"f1=50 # Hz\n",
"f2=18.7*1000 # Hz\n",
"BW1=f2 # Hz (f2-f1~=f2)\n",
"\n",
"\n",
"A1=10**(G/20) # Gain\n",
"A3=sqrt(A1) # Gain\n",
"RL1BYRL2=A1/A3 # ratio\n",
"RL2BYRL1=A3/A1 # ratio\n",
"#BW=2*pi*Cd*RL\n",
"BW1BYBW2=RL2BYRL1#\n",
"BW2BYBW1=RL1BYRL2#\n",
"f2dash=f2*sqrt(sqrt(2)-1)#\n",
"BW2=BW2BYBW1*f2dash # Hz\n",
"print \"Bandwidth of redesigned aplifier, BW=%.f kHz\"%(BW2/1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 32 Page 375"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ripple factor = 0.4 percent\n",
"Critical inductance, Lc=8.5 H\n"
]
}
],
"source": [
"from math import sqrt\n",
"from __future__ import division\n",
"\n",
"# Given\n",
"L=30 # H\n",
"C=10*10**-6 # F\n",
"RL=8*10**3 # ohm\n",
"f=50 # Hz\n",
"\n",
"r=sqrt(2)/12/(2*pi*f)**2/L/C*100 # %\n",
"Lc=2*RL/6/(2*pi*f) # H\n",
"print \"ripple factor = %.1f percent\"%(r)\n",
"print \"Critical inductance, Lc=%.1f H\"%(Lc)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 33 Page 376"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current supplied by the main generator = 7000 A\n",
"Current supplied on +ve side = 6000 A\n",
"Current supplied on -ve side = 8000 A\n",
"out-off balance Current = 2000 A\n",
"Current in each armature = 1000 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"# Given\n",
"V=500 # V\n",
"Pp=1500*10**3 # W (+ve side)\n",
"Pn=2000*10**3 # W (-ve side)\n",
"\n",
"P=Pp+Pn # W\n",
"I=P/V # A\n",
"Ip=Pp/(V/2) # A\n",
"In=Pn/(V/2) # A\n",
"Iob=In-Ip # A\n",
"Ia=Iob/2 # A\n",
"print \"Current supplied by the main generator = %.f A\"%(I)\n",
"print \"Current supplied on +ve side = %.f A\"%(Ip)\n",
"print \"Current supplied on -ve side = %.f A\"%(In)\n",
"print \"out-off balance Current = %.f A\"%(Iob)\n",
"print \"Current in each armature = %.f A\"%(Ia)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 34 Page 377"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"regulation = 17 percent\n",
"Efficiency = 94 percent\n",
"\n",
"\n",
" regulation = 13.4 percent\n",
"Efficiency = 96 percent\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"# Given\n",
"l=20 # km\n",
"P=10000 # kW\n",
"V=11 # kV\n",
"pf=0.707 # lagging\n",
"R=0.02 # ohm/km/phase\n",
"X=0.07 # ohm/km/phase\n",
"\n",
"#for pf = 0.707\n",
"\n",
"IL=P*10**3/sqrt(3)/(V*1000)/pf # A\n",
"VRphase=V*1000/sqrt(3) # V\n",
"R_phase=l*R # ohm\n",
"X_phase=l*X # ohm\n",
"Z_phase=R_phase+1J*X_phase # ohm\n",
"Vd_phase=IL*(pf-1J*pf)*Z_phase # V\n",
"VS=(Vd_phase+VRphase) # V\n",
"regulation=(VS-VRphase)/VRphase*100 # %\n",
"print \"regulation = %.f percent\"%abs(regulation)\n",
"PL=3*IL**2*R_phase/1000 # kW\n",
"Po=P+PL # kW\n",
"eta=P/Po*100 # %\n",
"print \"Efficiency = %.f percent\"%(eta)\n",
"\n",
"#for pf2=0.9 # lagging\n",
"pf=0.9 # lagging\n",
"IL=P*10**3/sqrt(3)/(V*1000)/pf # A\n",
"VRphase=V*1000/sqrt(3) # V\n",
"R_phase=l*R # ohm\n",
"X_phase=l*X # ohm\n",
"Z_phase=R_phase+1J*X_phase # ohm\n",
"Vd_phase=IL*(pf-1J*.435)*Z_phase # V\n",
"VS=(Vd_phase+VRphase) # V\n",
"regulation=(VS-VRphase)/VRphase*100 # %\n",
"print \"\\n\\n regulation = %.1f percent\"%abs(regulation)\n",
"PL=3*IL**2*R_phase/1000 # kW\n",
"Po=P+PL # kW\n",
"eta=P/Po*100 # %\n",
"print \"Efficiency = %.f percent\"%(eta)\n",
"#ans wrong for 2nd part in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 35 Page 378"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"lamp1 : Total cost/hour = 0.488 paise\n",
"lamp2 : Total cost/hour = 0.61 paise\n",
"on comparing cost it is clear lamp1 will be more economical. \n",
"\n",
"\n",
" load factor = 28 percent\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"C1=1.2 # Rs\n",
"C2=5 # Rs\n",
"P1=100 # W\n",
"P2=30 # W\n",
"t=1000 # hours\n",
"Ce=60 # Rs/kW/annum for max demand\n",
"Cee=3 # paise/unit for extra\n",
"\n",
"#first lamp\n",
"Cl1=C1*100/t # paise / hour\n",
"dmax1=P1/1000 # kW/hour\n",
"Cmax1=Ce*100*dmax1/(24*365) # paise/hour\n",
"CE1=Cee*dmax1 # /paise / hour\n",
"CT1=Cl1+Cmax1+CE1 # paise (total cost per hour)\n",
"print \"lamp1 : Total cost/hour = %.3f paise\"%(CT1)\n",
"#second lamp\n",
"Cl2=C2*100/t # paise / hour\n",
"dmax2=P2/1000 # kW/hour\n",
"Cmax2=Ce*100*dmax2/(24*365) # paise/hour\n",
"CE2=Cee*dmax2 # /paise / hour\n",
"CT2=Cl2+Cmax2+CE2 # paise (total cost per hour)\n",
"print \"lamp2 : Total cost/hour = %.2f paise\"%(CT2)\n",
"print \"on comparing cost it is clear lamp1 will be more economical. \"\n",
"#let load factor = x\n",
"#Cl1+Cmax1/x+CE1=Cl2+Cmax2/x+CE2\n",
"x=(Cmax1-Cmax2)/(Cl2+CE2-Cl1-CE1)*100 # % load factor\n",
"print \"\\n\\n load factor = %.f percent\"%(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 36 Page 379"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a) extra shunt field turns required = 104\n",
"(b) extra shunt field turns required = 52\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"p=4 # pole\n",
"I1=143 # A\n",
"Z=492 # armature conductors\n",
"theta=10 # degree\n",
"I2=10 # A\n",
"\n",
"Ia=I1+I2 # A\n",
"Iw=Ia/2 # A for wave sound\n",
"Il=Ia/4 # for lap sound\n",
"#part(a)\n",
"ATw=Z*Iw*theta/360 # AT\n",
"nw=ATw/theta # turns \n",
"print \"(a) extra shunt field turns required = %d\"%(nw)\n",
"\n",
"#part(b)\n",
"ATl=Z*Il*theta/360 # AT\n",
"nl=ATl/theta # turns \n",
"print \"(b) extra shunt field turns required = %d\"%(nl)\n",
"#answer wrong for part(a) in the boko."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 37 Page 380"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"New speed will be 570 rpm\n"
]
}
],
"source": [
"from __future__ import division\n",
"from numpy import roots\n",
"# Given\n",
"Wh=250 # W\n",
"We=100 # W\n",
"N=1000/60 # rps\n",
"\n",
"A=Wh/N # constant\n",
"B=We/N**2 # constant\n",
"Wnew=1/2*(Wh+We) # W\n",
"#Wnew=A*N1+B*N1**2\n",
"p=[B,A,-Wnew] # polynomial for N1\n",
"N1=roots(p) # rps\n",
"N1=N1[1]*60 # rpm#discarding -ve vealue\n",
"print \"New speed will be %.f rpm\"%(N1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 38 Page 381"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Speed of the machine running as shunt motor = 381 rpm\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"P=50 # kW\n",
"V=250#V\n",
"N1=400 # rpm\n",
"Ra=0.02 # ohm\n",
"Rf=50 # ohm\n",
"Pi=50 # kW\n",
"Vin=250 # V\n",
"Vd=1 # V per Brush\n",
"\n",
"I=P*10**3/V#A\n",
"Ish=V/Rf # A\n",
"Ia=I+Ish # A\n",
"Va=Ia*Ra # V\n",
"Vbd=2*Vd # V\n",
"Eb1=V+Va+Vbd # V\n",
"\n",
"\n",
"#as motor\n",
"I=P*10**3/V#A\n",
"Ish=V/Rf # A\n",
"Ia=I-Ish # A\n",
"\n",
"Va=Ia*Ra # V\n",
"Vbd=2*Vd # V\n",
"Eb2=V-Va-Vbd # V\n",
"N2=(Eb2/Eb1)*N1 # rpm\n",
"print \"Speed of the machine running as shunt motor = %.f rpm\"%(N2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 39 Page 383"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Motor efficiency = 92 percent\n",
"Generator efficiency = 92 percent\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"VL=250 # V\n",
"Is=50 # A\n",
"Ia=380 # A\n",
"If1=5 # A\n",
"If2=4.2 # A\n",
"ra=0.02 # ohm\n",
"\n",
"#Machine Losses:\n",
"ma_cu_loss=Ia**2*ra # W (motor armature cu loss)\n",
"ga_cu_loss=(Ia-Is)**2*ra # W (generator armature cu loss)\n",
"P=VL*Is # W\n",
"stray_loss=P-ma_cu_loss-ga_cu_loss # W\n",
"stray_loss_per_machine=stray_loss/2 # W\n",
"\n",
"#Motor efficiency\n",
"field_cu_loss=VL*If2 # W\n",
"total_loss=ma_cu_loss+field_cu_loss+stray_loss_per_machine # W\n",
"Pin_motor=(VL*Ia)+(VL*ra) # W\n",
"Pout_motor=Pin_motor-total_loss # W\n",
"Eff=Pout_motor/Pin_motor*100 # %\n",
"print \"Motor efficiency = %.f percent\"%(Eff)\n",
"\n",
"\n",
"#Generator efficiency\n",
"field_cu_loss=VL*If1 # W\n",
"total_loss=ga_cu_loss+field_cu_loss+stray_loss_per_machine # W\n",
"Pout_generator=VL*(Ia-Is) # W\n",
"Pin_generator=Pout_generator+total_loss # W\n",
"Eff=Pout_motor/Pin_motor*100 # %\n",
"print \"Generator efficiency = %.f percent\"%(Eff)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 40 Page 384"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Full load efficiency : \n",
"at unity power factor = 96.8 percent\n",
"at 0.8 power factor = 96.0 percent\n",
"\n",
"\n",
" Voltage drop at unity pf = 393.8 V\n",
"Voltage drop at 0.8 pf lagging = 384.0 V\n",
"Voltage drop at 0.8 pf leading = 406 V\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"# Given\n",
"KVA=4 # kVA\n",
"V1=200#V\n",
"V2=400#V\n",
"f=50 # Hz\n",
"Io1=0.8 # A\n",
"P1=70 # W\n",
"Vs2=17.5 # V\n",
"Is2=9 # A\n",
"P2=50 # W\n",
"\n",
"#full load\n",
"I_loss=P1 # W\n",
"I2=KVA*1000/V2 # A\n",
"Cu_loss=(I2/Is2)**2*P2 # W\n",
"Zo2=Vs2/Is2 # ohm\n",
"Ro2=P2/Is2**2 # ohm\n",
"Xo2=sqrt(Zo2**2-Ro2**2) # ohm\n",
"\n",
"#(a) \n",
"print \"Full load efficiency : \"\n",
"#unity pf\n",
"pf=1 # power factor\n",
"Output=KVA*pf # kW\n",
"Losses=Cu_loss+I_loss # W\n",
"eta=Output*1000/(Output*1000+Losses)*100 # %\n",
"print \"at unity power factor = %.1f percent\"%(eta)\n",
"#0.8 pf\n",
"pf=0.8 # power factor\n",
"Output=KVA*pf # kW\n",
"eta=Output*1000/(Output*1000+Losses)*100 # %\n",
"print \"at 0.8 power factor = %.1f percent\"%(eta)\n",
"\n",
"#(b)\n",
"#(i) unity pf\n",
"Vd=I2*Ro2 # V\n",
"V22=V2-Vd # V\n",
"print \"\\n\\n Voltage drop at unity pf = %.1f V\"%(V22)\n",
"#(i) 0.8 pf lagging\n",
"pf=0.8 # power factor\n",
"Vd=I2*(Ro2*pf+Xo2*sqrt(1-pf**2)) # V\n",
"V22=V2-Vd # V\n",
"print \"Voltage drop at 0.8 pf lagging = %.1f V\"%(V22)\n",
"#(i) 0.8 pf leading\n",
"pf=0.8 # power factor\n",
"Vd=I2*(Ro2*pf-Xo2*sqrt(1-pf**2)) # V\n",
"V22=V2-Vd # V\n",
"print \"Voltage drop at 0.8 pf leading = %.f V\"%(V22)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 41 Page 385"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"All day efficiency = 97 percent\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"KVA=15 # kVA\n",
"pf=1#\n",
"eff=98/100 # efficiency\n",
"\n",
"L1=2 # kW\n",
"pf1=0.5 # lagging\n",
"t1=12 # hours\n",
"L2=12 # kW\n",
"pf2=0.8 # lagging\n",
"t2=6 # hours\n",
"L3=18 # kW\n",
"pf3=0.9 # lagging\n",
"t3=6 # hours\n",
"\n",
"Po=KVA*pf # kW\n",
"Pin=Po/eff # kW\n",
"Losses=Pin-Po # kW\n",
"Cu_loss=Losses/2 # kW\n",
"I_loss=Losses/2 # kW\n",
"\n",
"KVA1=L1/pf1 # kVA\n",
"KVA2=L2/pf2 # kVA\n",
"KVA3=L3/pf3 # kVA\n",
"Cu_loss1=Cu_loss*(KVA1/KVA2)**2 # kW\n",
"Cu_loss2=Cu_loss*(KVA2/KVA2)**2 # kW\n",
"Cu_loss3=Cu_loss*(KVA3/KVA2)**2 # kW\n",
"\n",
"Cu_loss_t1=Cu_loss1*t1 # kW\n",
"Cu_loss_t2=Cu_loss2*t2 # kW\n",
"Cu_loss_t3=Cu_loss3*t3 # kW\n",
"Cu_loss_total=Cu_loss_t1+Cu_loss_t2+Cu_loss_t3 # kW\n",
"I_loss24=I_loss*24 # Wh\n",
"\n",
"Po24=L1*t1+L2*t2+L3*t3 # kWh\n",
"Pi24=Po24+Cu_loss_total+I_loss24 # kWh\n",
"eff_allday=Po24/Pi24*100 # %\n",
"print \"All day efficiency = %.f percent\"%(eff_allday)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 42 Page 386"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current drawn by the transformer=42.67 A\n",
"power factor = 0.9 lagging\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"# Given\n",
"V1=250 # V\n",
"V2=150 # V\n",
"Vs1=200 # V\n",
"Load1=5 # kW\n",
"pf1=0.8 # lagging\n",
"Load2=2 # kW\n",
"pf2=1 # unity\n",
"Vs2=100 # V\n",
"\n",
"I1=Load1*1000/V1/pf1 # A\n",
"t1_ratio=V1/Vs1 # \n",
"Ip1=I1*t1_ratio # A at 0.8 pf (current drawn by primary)\n",
"\n",
"I2=Load2*1000/Vs2/pf2 # A\n",
"t2_ratio=Vs2/V2 # \n",
"Ip2=I2*t2_ratio # A at 0.8 pf (current drawn by primary)\n",
"\n",
"Ipx=Ip1*pf1+Ip2 # A\n",
"Ipy=Ip1*sqrt(1-pf1**2) # A\n",
"I3=sqrt(Ipx**2+Ipy**2) # A\n",
"print \"Current drawn by the transformer=%.2f A\"%(I3)\n",
"pf=Ipx/I3 # power factor\n",
"print \"power factor = %.1f lagging\"%(pf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 43 Page 387"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Percentage reduction in stator voltage = 23 percent\n",
"power factor = 0.3\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,atan,cos\n",
"# Given\n",
"R2=0.03 # ohm\n",
"X2=0.18 # ohm\n",
"Ns=100 # rpm\n",
"s1=3 # %\n",
"\n",
"\n",
"Nfl=(100-s1) # rpm (full load speed)\n",
"N2=Nfl/2 # rpm\n",
"s2=(Ns-N2)/Ns*100 # %\n",
"V1BYV2=sqrt(s2/s1*(R2**2+(s1/100*X2)**2)/(R2**2+(s2/100*X2)**2)) # from torque equation\n",
"#let V1=V12BYV1 V2=1\n",
"V1=V1BYV2 # V\n",
"V2=1 # V\n",
"V12BYV1=(V1-1)/V1*100 # % reduction in the stator (V12=V1-V2)\n",
"print \"Percentage reduction in stator voltage = %.f percent\"%(V12BYV1)\n",
"fi=atan(s2/100*X2/R2) # radian\n",
"pf=cos(fi) # power factor\n",
"print \"power factor = %.1f\"%(pf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 44 Page 388"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a) at standstill, To:Ti = 40:1\n",
"(b) at s=0.05, To:Ti = 0.4:1\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"\n",
"# Given\n",
"zo=1+1J*1 # ohm\n",
"zi=0.2+1J*4 # ohm\n",
"Ri=zi.real # ohm\n",
"Ro=(zo).real # ohm\n",
"\n",
"#at standstill\n",
"s=1 # % at standstill\n",
"Zo=sqrt((zo).real**2+(zo).imag**2) # ohm\n",
"Zi=sqrt((zi).real**2+(zi).imag**2) # ohm\n",
"ToBYTi=Ro/Ri*(Zi/Zo)**2 # torque ratio\n",
"print \"(a) at standstill, To:Ti = %d:1\"%(ToBYTi)\n",
"\n",
"#at s=0.5\n",
"s=0.05 # %\n",
"Zo=sqrt((zo).real**2/s**2+(zo).imag**2) # ohm\n",
"Zi=sqrt((zi).real**2/s**2+(zi).imag**2) # ohm\n",
"ToBYTi=Ro/Ri*(Zi/Zo)**2 # torque ratio\n",
"print \"(b) at s=0.05, To:Ti = %.1f:1\"%(ToBYTi)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 45 Page 389"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"no. of turns in primary = 582\n",
"no. of turns in secondary = 18\n",
"\n",
"cross section of primary winding=5.24e-04 m**2\n",
"cross section of secondary winding=1.7e-05 m**2\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"# Given\n",
"Edc=500 # V\n",
"fim=.085 # Wb\n",
"f=50 # Hz\n",
"E1=11000 # V\n",
"P=1500 # kW\n",
"p=8 # pole\n",
"pf=0.9\n",
"V=500 # V\n",
"J=3 # A/mm**2\n",
"\n",
"E2=Edc/sqrt(2)#V\n",
"N2=E2/4.44/f/fim # no. of turns\n",
"N1=E1/E2*N2 # no. of turns\n",
"print \"no. of turns in primary = %d\"%(N1)\n",
"print \"no. of turns in secondary = %d\"%(N2)\n",
"Idc=P*10**3/V # A\n",
"eta=1 # because of no loss\n",
"ISR=0.472*Idc/(eta*pf)\n",
"A1=ISR/J*10**-6 # m**2 (cross section area)\n",
"I1=N2/N1*ISR # A\n",
"A2=I1/J*10**-6 # m**2 (cross section area of primary winding)\n",
"print \"\\ncross section of primary winding=%.2e m**2\"%(A1)\n",
"print \"cross section of secondary winding=%.1e m**2\"%(A2)\n",
"#ans in the book are not accurate."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 46 Page 391"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Suitable auto transformation ratio = 77.5\n",
"Starting torque Tst = 15 percent of full-load torque\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"\n",
"# Given\n",
"IscBYIfl=5 # as Isc=5*Ifl\n",
"ILByIfl=3 # as IL <= 3*Ifl\n",
"sf=5 # %\n",
"\n",
"#IL=K**2*ISC\n",
"#dividing by Ifl\n",
"K=sqrt(ILByIfl/IscBYIfl)*100 # %\n",
"TstBYTf=(K/100)**2*IscBYIfl*sf/100*100 # % #ratio of torque\n",
"print \"Suitable auto transformation ratio = %.1f\"%(K)\n",
"print \"Starting torque Tst = %.f percent of full-load torque\"%(TstBYTf)\n",
"#ans wrong in the textbook."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 47 Page 391"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"no of studs = 5 and no. of section = 4\n",
"\n",
"Resistance of 1st section = 2.24 ohm\n",
"Resistance of 2nd section = 1.49 ohm\n",
"Resistance of 3rd section = 0.99 ohm\n",
"Resistance of 4th section = 0.68 ohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import log\n",
"\n",
"# Given\n",
"V=500 # V\n",
"ns=60 # slots\n",
"nc=20 # conductor/slot\n",
"ra=1.31 # ohm\n",
"Tmax=218 # N-m\n",
"fi=23*10**-3 # Wb\n",
"\n",
"Tmin=Tmax/1.5#N-m\n",
"Z=ns*nc # no of conductors\n",
"Ia=Tmax/(.159*fi*Z) # A\n",
"Imax=1.5*Ia # A\n",
"I1=Imax # A\n",
"I2=Ia # A\n",
"R1=V/I1 # ohm\n",
"n= log(R1/ra)/log(I1/I2)+1 # no of studs\n",
"N=n-1 # no of section\n",
"print \"no of studs = %d and no. of section = %d\"%(n,N)\n",
"R2=R1*(I2/I1) # ohm\n",
"R3=R2*(I2/I1) # ohm\n",
"R4=R3*(I2/I1) # ohm\n",
"R1s=R1-R2 # ohm\n",
"R2s=R2-R3 # ohm\n",
"R3s=R3-R4 # ohm\n",
"R4s=R4-ra # ohm\n",
"print \"\\nResistance of 1st section = %.2f ohm\"%(R1s)\n",
"print \"Resistance of 2nd section = %.2f ohm\"%(R2s)\n",
"print \"Resistance of 3rd section = %.2f ohm\"%(R3s)\n",
"print \"Resistance of 4th section = %.2f ohm\"%(R4s)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 48 Page 393"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"temperature rise after 2 hours full load = 55 degree C\n",
"temperature rise of cold water after 1 hour = 28 degree C\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import log,exp\n",
"\n",
"# Given\n",
"theta1=20 # degree C\n",
"theta2=35 # degree C\n",
"t1=0.5 # hour\n",
"t2=1 # hour\n",
"theta_m_dashBYthetam=80/100 # temperature rise\n",
"\n",
"#theta=theta_m*(1-e**(-t/alfa))\n",
"#theta1/theta2=(1-exp(-t1/alfa))/(1-exp(-t2/alfa))\n",
"ee1=theta2/theta1-1 # let ee1=exp(-1/2/alfa)\n",
"theta_m=theta1/(1-ee1) # degree C\n",
"theta_2=theta_m*(1-ee1**4) # degree C (after 2 hours)\n",
"print \"temperature rise after 2 hours full load = %.f degree C\"%(theta_2)\n",
"alfa=-1/2/log(ee1) # hour\n",
"alfa_dash=theta_m_dashBYthetam*alfa # hour\n",
"theta_m_dash=theta_m_dashBYthetam*theta_m\n",
"theta_dash=theta_m_dash*(1-exp(-t2/alfa))\n",
"print \"temperature rise of cold water after 1 hour = %.f degree C\"%(theta_dash)\n",
"#ans of 2nd part is wrong in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 49 Page 394"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Regulation at no load voltage = 6.7 percent\n",
"Regulation at full load voltage = 7.2 percent\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,cos,pi,sin\n",
"\n",
"# Given\n",
"u=30 # degree \n",
"m=3 # no of phases\n",
"\n",
"#Id=sqrt(2)*Vs*X*(1-cosd(u))*sin(pi/m)\n",
"IdBYVs_dash=m/2/pi*(1-cos(pi/180*u))*sin(pi/m)*sqrt(2) # load current/Vs\n",
"#where IdBYVs_dash = m/pi*IdX/2\n",
"EdoBYVs=sqrt(2)*m/pi*sin(pi/m) # dc output voltage/Vs with no overlap\n",
"EduBYVs=EdoBYVs-IdBYVs_dash # dc output voltage/Vs with overlap\n",
"#part (a)\n",
"Reg1=(EdoBYVs-EduBYVs)/EdoBYVs*100 # % (regulation)\n",
"print \"Regulation at no load voltage = %.1f percent\"%(Reg1)\n",
"#part (b)\n",
"Reg2=(EdoBYVs-EduBYVs)/EduBYVs*100 # % (regulation)\n",
"print \"Regulation at full load voltage = %.1f percent\"%(Reg2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 50 Page 395"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current for each machine = 370 A & 1630 A \n",
"Power output for each machine = 162.3 kW & 716.3 kW\n"
]
}
],
"source": [
"from __future__ import division\n",
"from numpy import array\n",
"# Given\n",
"I12=2000 # A (I12=I1+I2)\n",
"R1=0.04 # ohm\n",
"R2=0.025 # ohm\n",
"rf1=25 # ohm\n",
"rf2=20 # ohm\n",
"E1=440 # V\n",
"E2=420 # V\n",
"\n",
"#E-Vad=V where Vad=I1+V/rf1\n",
"#V*(1+R1/rf1)+R1*I1=E1#eqn(1)\n",
"#V*(1+R2/rf2)-I1*R2=E2-I12*R2# eqn(2)\n",
"A=array([[(1+R1/rf1),R1],[(1+R2/rf2),-R2]])# # matrix for solution\n",
"B=array([[E1],[E2-I12*R2]]) # matrix for solution\n",
"X=A**-1*B # solution\n",
"V=X[0,0] # V\n",
"I1=X[1,0] # A\n",
"I2=I12-I1 # A\n",
"print \"Current for each machine = %.f A & %.f A \"%(I1,I2)\n",
"Po1=V*I1 # W\n",
"Po2=V*I2 # W\n",
"print \"Power output for each machine = %.1f kW & %.1f kW\"%(Po1/1000,Po2/1000)\n",
"#ans in the book are wrong."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 51 Page 396"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"pf transformer A = 0.82 lag\n",
"pf transformer B = 0.78 lag\n",
"power output transformer A = 6535 W\n",
"power output transformer B = 4925 W\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import atan,pi,cos,degrees\n",
"# Given\n",
"ZA=0.15+0.5*1J # ohm\n",
"ZB=0.1+0.6*1J # ohm\n",
"EA=207 # V\n",
"EB=205 # V\n",
"ZL=2+1.5*1J # ohm\n",
"\n",
"IA=(EA*ZB+(EA-EB)*ZL)/(ZA*ZB+ZL*(ZA+ZB)) # A\n",
"IB=(EB*ZA-(EA-EB)*ZL)/(ZA*ZB+ZL*(ZA+ZB)) # A\n",
"V2=(IA+IB)*ZL # V\n",
"fi_A=degrees(atan((V2).imag/(V2).real)-(atan((IA.imag)/(IA.real))))\n",
"pf_A=cos(pi/180*fi_A) # lag\n",
"print \"pf transformer A = %.2f lag\"%(pf_A)\n",
"fi_B=degrees(atan((V2.imag)/(V2.real))-(atan((IB.imag)/(IB.real))))\n",
"pf_B=cos(pi/180*fi_B) # lag\n",
"print \"pf transformer B = %.2f lag\"%(pf_B)\n",
"PA=abs(V2*IA*pf_A) # W\n",
"print \"power output transformer A = %.f W\"%(PA)\n",
"PB=abs(V2*IB*pf_B) # W\n",
"print \"power output transformer B = %.f W\"%(PB)\n",
"#Power output ans are wrong in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 52 Page 397"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"filament length = 1.26 m\n",
"filament diameter = 20 um\n"
]
}
],
"source": [
"from __future__ import division\n",
"# Given\n",
"d1=0.05*10**-3 # mm\n",
"l1=100*10**-2 # m\n",
"i2BYi1=1/4 # current ratio\n",
"#(d2/d1)**(3/2)=i2BYi1\n",
"d2=(i2BYi1)**(2/3)*d1*10**6 # um\n",
"l2=1/2*l1*d1/d2*10**6 # m\n",
"print \"filament length = %.2f m\"%(l2)\n",
"print \"filament diameter = %.f um\"%(d2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 53 Page 398"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"filament length = 1.6 m\n",
"filament diameter = 48 um\n"
]
}
],
"source": [
"from __future__ import division\n",
"# Given\n",
"d1=0.10*10**-3 # mm\n",
"l1=150*10**-2 # m\n",
"i2BYi1=1/3 # current ratio\n",
"#(d2/d1)**(3/2)=i2BYi1\n",
"d2=(i2BYi1)**(2/3)*d1*10**6 # um\n",
"l2=1/2*l1*d1/d2*10**6 # m\n",
"print \"filament length = %.1f m\"%(l2)\n",
"print \"filament diameter = %.f um\"%(d2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 54 Page 398"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a) at standstill, To:Ti = 8:1\n",
"(b) at s=0.05, To:Ti = 3:10\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"# Given\n",
"zo=2+1J*2 # ohm\n",
"zi=0.5+1J*4 # ohm\n",
"Ri=(zi).real # ohm\n",
"Ro=(zo).real # ohm\n",
"\n",
"#at standstill\n",
"s=1 # % at standstill\n",
"Zo=sqrt((zo.real)**2+(zo.imag)**2) # ohm\n",
"Zi=sqrt((zi.real)**2+(zi.imag)**2) # ohm\n",
"ToBYTi=Ro/Ri*(Zi/Zo)**2 # torque ratio\n",
"print \"(a) at standstill, To:Ti = %d:1\"%(ToBYTi)\n",
"\n",
"#at s=0.5\n",
"s=0.05 # %\n",
"Zo=sqrt((zo.real)**2/s**2+(zo.imag)**2) # ohm\n",
"Zi=sqrt((zi.real)**2/s**2+(zi.imag)**2) # ohm\n",
"ToBYTi=Ro/Ri*(Zi/Zo)**2 # torque ratio\n",
"print \"(b) at s=0.05, To:Ti = %.f:10\"%(ToBYTi*10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 55 Page 400"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"no. of turns in primary = 415\n",
"no. of turns in secondary = 12\n",
"\n",
"cross section of primary winding=6.56e-04 m**2\n",
"cross section of secondary winding=1.9e-05 m**2\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"\n",
"# Given\n",
"Edc=250 # V\n",
"fim=.065 # Wb\n",
"f=50 # Hz\n",
"E1=6000 # V\n",
"P=1500 # kW\n",
"p=8 # pole\n",
"pf=0.9\n",
"V=400 # V\n",
"J=3 # A/mm**2\n",
"\n",
"E2=Edc/sqrt(2)#V\n",
"N2=E2/4.44/f/fim # no. of turns\n",
"N1=E1/E2*N2 # no. of turns\n",
"print \"no. of turns in primary = %d\"%(N1)\n",
"print \"no. of turns in secondary = %d\"%(N2)\n",
"Idc=P*10**3/V # A\n",
"eta=1 # because of no loss\n",
"ISR=0.472*Idc/(eta*pf)\n",
"A1=ISR/J*10**-6 # m**2 (cross section area)\n",
"I1=N2/N1*ISR # A\n",
"A2=I1/J*10**-6 # m**2 (cross section area of primary winding)\n",
"print \"\\ncross section of primary winding=%.2e m**2\"%(A1)\n",
"print \"cross section of secondary winding=%.1e m**2\"%(A2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 56 Page 400"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Suitable auto transformation ratio = 86.6\n",
"Starting torque Tst = 12 percent of full-load torque\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"# Given\n",
"IscBYIfl=4 # as Isc=5*Ifl\n",
"ILByIfl=3 # as IL <= 3*Ifl\n",
"sf=4 # %\n",
"\n",
"#IL=K**2*ISC\n",
"#dividing by Ifl\n",
"K=sqrt(ILByIfl/IscBYIfl)*100 # %\n",
"TstBYTf=(K/100)**2*IscBYIfl*sf/100*100 # % #ratio of torque\n",
"print \"Suitable auto transformation ratio = %.1f\"%(K)\n",
"print \"Starting torque Tst = %.f percent of full-load torque\"%(TstBYTf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 57 Page 401"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"temperature rise after 2 hours full load = 56 degree C\n",
"temperature rise of cold water after 1 hour = 27 degree C\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import log,exp\n",
"# Given\n",
"theta1=30 # degree C\n",
"theta2=45 # degree C\n",
"t1=0.5 # hour\n",
"t2=1 # hour\n",
"theta_m_dashBYthetam=60/100 # temperature rise\n",
"\n",
"#theta=theta_m*(1-e**(-t/alfa))\n",
"#theta1/theta2=(1-exp(-t1/alfa))/(1-exp(-t2/alfa))\n",
"ee1=theta2/theta1-1 # let ee1=exp(-1/2/alfa)\n",
"theta_m=theta1/(1-ee1) # degree C\n",
"theta_2=theta_m*(1-ee1**4) # degree C (after 2 hours)\n",
"print \"temperature rise after 2 hours full load = %.f degree C\"%(theta_2)\n",
"alfa=-1/2/log(ee1) # hour\n",
"alfa_dash=theta_m_dashBYthetam*alfa # hour\n",
"theta_m_dash=theta_m_dashBYthetam*theta_m\n",
"theta_dash=theta_m_dash*(1-exp(-t2/alfa))\n",
"print \"temperature rise of cold water after 1 hour = %.f degree C\"%(theta_dash)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 58 Page 401"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"at slip=0, To:Ti = 7:1\n",
"at s=0.05, To:Ti = 3:10\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"# Given\n",
"zo=2+1J*3 # ohm\n",
"zi=0.5+1J*5 # ohm\n",
"Ri=(zi.real) # ohm\n",
"Ro=(zo.real) # ohm\n",
"\n",
"#at standstill\n",
"s=1 # % at standstill\n",
"Zo=sqrt((zo.real)**2+(zo.imag)**2) # ohm\n",
"Zi=sqrt((zi.real)**2+(zi.imag)**2) # ohm\n",
"ToBYTi=Ro/Ri*(Zi/Zo)**2 # torque ratio\n",
"print \"at slip=0, To:Ti = %d:1\"%(ToBYTi)\n",
"\n",
"#at s=0.5\n",
"s=0.05 # %\n",
"Zo=sqrt((zo.real)**2/s**2+(zo.imag)**2) # ohm\n",
"Zi=sqrt((zi.real)**2/s**2+(zi.imag)**2) # ohm\n",
"ToBYTi=Ro/Ri*(Zi/Zo)**2 # torque ratio\n",
"print \"at s=0.05, To:Ti = %.f:10\"%(ToBYTi*10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 59 Page 402"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"part(a) Regulation at no load voltage = 15 percent\n",
"part(b) Regulation at full load voltage = 17 percent\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,sin,cos\n",
"\n",
"# Given\n",
"u=45 # degree \n",
"m=3 # no of phases\n",
"\n",
"#Id=sqrt(2)*Vs*X*(1-cosd(u))*sin(pi/m)\n",
"IdBYVs_dash=m/2/pi*(1-cos(pi/180*u))*sin(pi/m)*sqrt(2) # load current/Vs\n",
"#where IdBYVs_dash = m/pi*IdX/2\n",
"EdoBYVs=sqrt(2)*m/pi*sin(pi/m) # dc output voltage/Vs with no overlap\n",
"EduBYVs=EdoBYVs-IdBYVs_dash # dc output voltage/Vs with overlap\n",
"#part (a)\n",
"Reg1=(EdoBYVs-EduBYVs)/EdoBYVs*100 # % (regulation)\n",
"print \"part(a) Regulation at no load voltage = %.f percent\"%(Reg1)\n",
"#part (b)\n",
"Reg2=(EdoBYVs-EduBYVs)/EduBYVs*100 # % (regulation)\n",
"print \"part(b) Regulation at full load voltage = %.f percent\"%(Reg2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 60 Page 402"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"length of filament = 1.89 m\n",
"diameter of filament = 60 um\n"
]
}
],
"source": [
"from __future__ import division\n",
"\n",
"# Given\n",
"d1=0.15*10**-3 # mm\n",
"l1=150*10**-2 # m\n",
"i2BYi1=1/4 # current ratio\n",
"#(d2/d1)**(3/2)=i2BYi1\n",
"d2=(i2BYi1)**(2/3)*d1*10**6 # um\n",
"l2=1/2*l1*d1/d2*10**6 # m\n",
"print \"length of filament = %.2f m\"%(l2)\n",
"print \"diameter of filament = %.f um\"%(d2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 61 Page 403"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Potential difference = 1875 V\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,sin,pi\n",
"# Given\n",
"d=5/100 # m\n",
"S=-4/100 # m\n",
"Ve=3 # kV\n",
"theta=45 # degree\n",
"e=1.6*10**-19 # C\n",
"m=9.67*10**-31 # kg\n",
"\n",
"u=sqrt(2*e*Ve*1000/m) # m/s\n",
"uy=u*sin(pi/180*theta) # m/s\n",
"vy=0 # since final velocity =0\n",
"#vy**2-uy**2=2*ay*S\n",
"ay=(vy**2-uy**2)/2/S # m**2/s\n",
"#ay=e/m*V/d\n",
"V=ay*m*d/e # V\n",
"print \"Potential difference = %.f V\"%(V)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 62 Page 403"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"reading of ammeter 1= 0.56 A\n",
"reading of ammeter 2 = 0.30 A\n",
"\n",
"\n",
"Power taken from the mains = 162.0 W\n",
"Power dissipated in rectifying device = 115 W\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"from sympy.mpmath import quad\n",
"# Given\n",
"R=150 # ohm\n",
"Vrms=200 # V\n",
"Rd1=65 # ohm\n",
"Rd2=140 # ohm \n",
"\n",
"Vm=Vrms/sqrt(2) # V\n",
"#v=Vm*sin(theta)\n",
"Rf=R+Rd1 # ohm\n",
"Rb=R+Rd2 # ohm\n",
"#i_f=v/Rf # A\n",
"#i_b=v/Rb # A\n",
"Irms=1/2/pi*(quad(lambda theta:(sqrt(2)*sin(theta))**2,[0,pi])+quad(lambda theta:(sqrt(2)/3*sin(theta))**2,[pi,2*pi]))\n",
"Iav=1/2/pi*(quad(lambda theta:sqrt(2)*sin(theta),[0,pi])+quad(lambda theta:sqrt(2)/3*sin(theta),[pi,2*pi]))\n",
"print \"reading of ammeter 1= %.2f A\"%(Irms)\n",
"print \"reading of ammeter 2 = %.2f A\"%(Iav)\n",
"P=1/2*(Vrms**2/Rf+Vrms**2/Rb) # W\n",
"print \"\\n\\nPower taken from the mains = %.1f W\"%(P)\n",
"Pc=Irms**2*R # W\n",
"Pd=P-Pc # W\n",
"print \"Power dissipated in rectifying device = %d W\"%(Pd)\n",
"#Answer wrong in the textbook."
]
}
],
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