{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 4 - Potentiometers"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1 - pg 256"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Unknown resistor (ohm) = 0.08275\n"
]
}
],
"source": [
"#pg 256\n",
"#Example 4.1: Unknown resistor\n",
"#calculate the Unknown resistor\n",
"#given data :\n",
"Vd=0.83942;# volt-drop in V\n",
"emf=23*10**-6;# in V\n",
"Vds=1.01575;# volt-drop in V\n",
"Rs=0.10014;# in ohm\n",
"#calculations\n",
"Vdt=Vd-emf;# in V\n",
"I=Vds/Rs;\n",
"R=Vdt/I;\n",
"#results\n",
"print \"Unknown resistor (ohm) = \",round(R,5)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2 - pg 257"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a). emf of the cell,(V) = 1.42562\n",
"(b). % error (high),(%) = 1.98\n",
"(c). % error (high),(%) = 1.59\n"
]
}
],
"source": [
"#pg 257\n",
"#Example 4.2: emf and % error \n",
"#calculate the emf and % error \n",
"#given data :\n",
"l=50;# in cm\n",
"l1=70;# in cm\n",
"l2=65;# in cm\n",
"l3=43.5;# in cm\n",
"I=0.45;# in A\n",
"V=1.0183;# in V\n",
"V1=1.35;# in V\n",
"R=2;# in ohm\n",
"#calculations\n",
"Vpl=V/l;# in V/cm\n",
"emf=Vpl*l1;\n",
"Vr=Vpl*l2;\n",
"P_error1=((V1-Vr)/Vr)*100;\n",
"Ir=(Vpl*l3)/R;# in A\n",
"P_error2=((I-Ir)/Ir)*100;\n",
"#results\n",
"print \"(a). emf of the cell,(V) = \",emf\n",
"print \"(b). % error (high),(%) = \",round(P_error1,2)\n",
"print \"(c). % error (high),(%) = \",round(P_error2,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3 - pg 258"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"part a \n",
"current is (A)= 0.02\n",
"resistance is (ohm)= 100.0\n",
"part b\n",
"current is (mA)= 7.078\n",
"resistance is (k-ohm)= 2035.32\n",
"resistance is calculated wrong in the textbook\n"
]
}
],
"source": [
"#pg 258\n",
"#Example 4.3.a: current and resistance\n",
"#calculate the current and resistance\n",
"#given\n",
"import numpy\n",
"from numpy import linalg\n",
"e1=1.0191;#V\n",
"r1=100.;#ohms\n",
"l=2;#m\n",
"e2=4;#V\n",
"#calculations and results\n",
"I=l/r1;#A\n",
"rh=(e2/I)-r1;#\n",
"print 'part a '\n",
"print \"current is (A)=\",I\n",
"print \"resistance is (ohm)=\",rh\n",
"e1=4;#V\n",
"e2=1.0191;#V\n",
"R1=100;#OHM\n",
"R2=49.045;#OHMS\n",
"r3=R1-R2;#ohms\n",
"rg=50;#ohms\n",
"r4=200;#ohms\n",
"A=numpy.matrix([[r4, -r3],[-r3, (r4+rg+r3)]]);#\n",
"B=numpy.matrix([[e1],[e2]]);#\n",
"X=numpy.dot(numpy.linalg.inv(A),B)\n",
"I2=X[1,0]*10**3;#\n",
"I1=((e1+(r3*10**-5))/r4);#mA\n",
"rp=((e2+(r3*I1)-(r4+rg+r3)*10**-5)/10**-5);#\n",
"#results\n",
"print 'part b'\n",
"print \"current is (mA)=\",round(I2,3)\n",
"print \"resistance is (k-ohm)=\",round(rp*10**-2,2)\n",
"print 'resistance is calculated wrong in the textbook'\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4 - pg 259"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"internal resistance,Ri(ohm) = 176.689\n"
]
}
],
"source": [
"#pg 259\n",
"#Example 4.4: Resistance\n",
"#calculate the internal resistance\n",
"#given data :\n",
"emf=1.01892;# in V\n",
"R=1;# in M-ohm\n",
"V=1.01874;# in V\n",
"#calculations\n",
"Ic=V/R;\n",
"Vd=emf-V;\n",
"Ri=Vd/(Ic*10**-6);\n",
"#results\n",
"print \"internal resistance,Ri(ohm) = \",round(Ri,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5 - pg 259"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Internal resistance,Ri(ohm) = 3.636\n"
]
}
],
"source": [
"#pg 259\n",
"#Example 4.5: Resistance\n",
"#calculate the resistance\n",
"#given data :\n",
"l=65;# in cm\n",
"V=0.1;# in V\n",
"V1=5.5;# in V\n",
"R=20;# in ohm\n",
"#calculations\n",
"E=V*l;\n",
"I=V1/R;\n",
"Ri=(E-V1)/I;\n",
"#results\n",
"print \"Internal resistance,Ri(ohm) = \",round(Ri,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6 - pg 259"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"resistance is (k-ohm)= 50.0\n"
]
}
],
"source": [
"#pg 259\n",
"#Example 4.6: Resistance\n",
"#calculate the resistance\n",
"#given\n",
"vr=5.;#V\n",
"r=10.;#k-ohm\n",
"#calculations\n",
"x=vr*r*10**3;#\n",
"R=x;#\n",
"#results\n",
"print \"resistance is (k-ohm)=\",R*10**-3\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 7 - pg 260"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The length of slide wire (cm) = 200.0\n"
]
}
],
"source": [
"#pg 260\n",
"#Example 4.7: Length\n",
"#calculate the length of the slide wire\n",
"#given data :\n",
"l=40.;# in cm\n",
"r=0.5;# ion ohm\n",
"V=1.2;# in V\n",
"V1=6;# in V\n",
"#calculations\n",
"R=r*l/1;# in ohm\n",
"I=V/R;\n",
"x=V1/(r*I);\n",
"#results\n",
"print \"The length of slide wire (cm) = \",x\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 8 - pg 260"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"resistance R is (ohm)= 20.0\n",
"resistance R1 is (ohm)= 2.0\n",
"resistance R2 is (ohm)= 4.0\n",
"resistance per cm of slide wire is (ohm/cm)= 0.02\n"
]
}
],
"source": [
"#pg 260\n",
"#Example 4.8: design\n",
"#calculate the resistance in all cases\n",
"#given\n",
"vab=1.;#V\n",
"i=50.;#mA\n",
"n=10.;#\n",
"l=100.;#cm\n",
"#calculations\n",
"vr=2-vab;#V\n",
"R=vr/(i*10**-3);#ohm\n",
"R1=(vr/10)/(i*10**-3);#ohm\n",
"tr1=n*R1;#ohm\n",
"r2=2*R1;#\n",
"x=R1/l;#\n",
"#results\n",
"print \"resistance R is (ohm)=\",R\n",
"print \"resistance R1 is (ohm)=\",R1\n",
"print \"resistance R2 is (ohm)=\",r2\n",
"print \"resistance per cm of slide wire is (ohm/cm)=\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9 - pg 261"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"resistance is (ohm) = 39.5\n",
"resolution of the instrument is (micro-V) = 20.0\n",
"error is (micro-V) = 2.5\n"
]
}
],
"source": [
"#pg 261\n",
"#Example 4.9.a:resistance\n",
"#calculate the resistance, resolution and error\n",
"#given\n",
"st=15.;#steps\n",
"r=5.;#ohm\n",
"rsw=5.5;#ohm\n",
"vr=1.61;#V\n",
"e2=1.61;#V\n",
"e1=2.40;#V\n",
"trn=11.;#turns\n",
"dv=100.;#divisions\n",
"ig=0.05;#micro-A\n",
"vlt=1.1;#V\n",
"ir=50.;#ohm\n",
"#calculations\n",
"tr=(st*r)+rsw;#ohm\n",
"i=vr/tr;#A\n",
"rh=(e1-e2)/i;#ohm \n",
"slwr=rsw/trn;#ohm\n",
"vd=slwr*i;#V\n",
"vedv=(1/dv)*vd;#\n",
"rs=vedv/5;#\n",
"em=((ig*ir));#\n",
"#results\n",
"print \"resistance is (ohm) = \",rh\n",
"print \"resolution of the instrument is (micro-V) = \",rs*10**6\n",
"print \"error is (micro-V) = \",em\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 10 - pg 262"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"power dissipated in the resistor is (mW)= 0.4176\n",
"power dissipated in the coil is (mW)= 0.264\n",
"power dissipated in the capacitor is (mW)= 0.036\n",
"energy stored in the coil is (micro-J)= 0.61\n",
"energy stored in capacitor is (micro-J)= 0.42\n"
]
}
],
"source": [
"#pg 262\n",
"#Example 4.10:power dissipated\n",
"#calculate the power dissipated and energy stored\n",
"#given\n",
"import math,cmath\n",
"r1=0.6-1j*0.24;#V\n",
"r2=0.6+1j*0.4;#V\n",
"r3=-0.1-1j*0.4;#V\n",
"f=50;#Hx\n",
"ir=1000;#ohm\n",
"#calculations\n",
"i1=r1/ir;#A\n",
"pdr=(r1.real*i1.real)+(r1.imag*i1.imag);#W\n",
"pdC=(r1.real*i1.real)+(r2.imag*i1.imag);#W\n",
"pdc=(r3.real*i1.real)-(r2.imag*i1.imag);#W\n",
"imp=(r2/r1)*10**3;#ohm\n",
"rc=imp.imag;#ohm\n",
"indu=rc/(2*math.pi*f);#H\n",
"ersl=(1./2)*(i1.imag**2+i1.real**2)*indu;#joules\n",
"admc=(r1*10**-3)/r3;#ohm**-1\n",
"C=admc.imag/(2*math.pi*f);#\n",
"ersc=(1./2)*(r3.imag**2+r3.real**2)*C;#\n",
"#results\n",
"print \"power dissipated in the resistor is (mW)=\",pdr*10**3\n",
"print \"power dissipated in the coil is (mW)=\",pdC*10**3\n",
"print \"power dissipated in the capacitor is (mW)=\",pdc*10**3\n",
"print \"energy stored in the coil is (micro-J)=\",round(ersl*10**6,2)\n",
"print \"energy stored in capacitor is (micro-J)=\",round(ersc*10**6,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 11 - pg 263"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"measuring range of the potentiometer is (V)= 1.9\n",
"resolution is (mV)= 0.5\n",
"current through the dial is (mA)= 10.0\n",
"setting of the rheostat is (ohm)= 410.0\n"
]
}
],
"source": [
"#pg 263\n",
"#Example 4.11:measuring range,resulution,working current,setting of the rheostat\n",
"#calculate the measuring range,resulution,working current,setting of the rheostat\n",
"#given\n",
"sd=18.;#steps\n",
"v1=0.1;#V\n",
"dv=100;#divisions\n",
"dr=10;#ohm\n",
"wbc=6;#V\n",
"#calculations\n",
"mr=(sd*v1)+v1;#V\n",
"rs=(v1/dv)*(1./2);#mV\n",
"cdd=v1/dr;#A\n",
"rsv=wbc-mr;#V\n",
"sh=rsv/cdd;#ohm\n",
"#results\n",
"print \"measuring range of the potentiometer is (V)=\",mr\n",
"print \"resolution is (mV)=\",rs*10**3\n",
"print \"current through the dial is (mA)=\",cdd*10**3\n",
"print \"setting of the rheostat is (ohm)=\",sh\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 12 - pg 263"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"true value of drop across the resistance is (V)= 0.6529\n",
"percentage error is (%)= 0.06\n"
]
}
],
"source": [
"#pg 263\n",
"#Example 4.12:voltage and percentage error\n",
"#calculate the voltage and percentage error\n",
"#given\n",
"st=15;#steps\n",
"r1=10;#ohm\n",
"v1=0.1;#V\n",
"r2=10;#ohm\n",
"r3=9.9;#ohm\n",
"v2=0.0185;#V\n",
"v3=1.0185;#V\n",
"n=6;#\n",
"vg=0.6525;#\n",
"#calculations\n",
"acr=(r1*r3)+((r2*v2)/v1);#ohm\n",
"I=v3/acr;#\n",
"acr1=(n*r3)+(r2*0.0525)/v1;#ohm\n",
"tvr=I*acr1;#V\n",
"er=((tvr-vg)/tvr)*100;#\n",
"#results\n",
"print \"true value of drop across the resistance is (V)=\",round(tvr,4)\n",
"print \"percentage error is (%)=\",round(er,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 13 - pg 264"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"reactance is (ohm)= 1.28\n",
"inductance of the coil is (mH)= 30.0\n",
"The answer is a bit different due to rounding off error in textbook\n"
]
}
],
"source": [
"#pg 264\n",
"#Example 4.13:resistance and reactance\n",
"#calculate the resistance and reactance\n",
"#given\n",
"import math,cmath\n",
"from math import sqrt,atan,sin\n",
"r1=2.;#ohm\n",
"r2=9.;#\n",
"vm=85.;#V\n",
"va=40.;#degree\n",
"vm1=90.;#V\n",
"va1=45.;#degree\n",
"f=50.;#Hz\n",
"#calculations\n",
"imp=r1+1j*r2;#ohm\n",
"mg=sqrt(r1**2+r2**2);#\n",
"th=atan(r2/r1) *57.3;#\n",
"ccm=vm/mg;#A\n",
"cca=va-th;#degree\n",
"impm=vm1/ccm;#ohm\n",
"impa=va1-cca;#degree\n",
"reac=impm*sin(impa/57.3);#ohm\n",
"rc=sqrt(impm**2-reac**2);#ohm\n",
"ind=reac/(2*math.pi*f);#\n",
"#results\n",
"print \"reactance is (ohm)=\",round(rc,2)\n",
"print \"inductance of the coil is (mH)=\",math.floor(ind*10**3)\n",
"print 'The answer is a bit different due to rounding off error in textbook'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 14 - pg 265"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"limit of error in the reading is 48.6 micro-V\n",
"deflection of the galvanometer is (mm)= 8.1\n"
]
}
],
"source": [
"#pg 265\n",
"#Example 4.14:limit of error,deflection\n",
"#calculate the limit of error and deflection of galvanometer\n",
"#given\n",
"x=17.5;#mm/micro-A\n",
"r1=850.;#ohm\n",
"v1=2.;#V\n",
"r2=80.;#\n",
"v3=1.43;#V\n",
"v2=0.1;#V\n",
"l=50.;#cm\n",
"l1=2.;#mm\n",
"fr1=22.784;#\n",
"#calculations\n",
"lr=r1*(1./x);#micro V\n",
"i1=v1/r2;#A\n",
"r3=v2/i1;#ohm\n",
"r4=v3/i1;#ohm\n",
"r5=((l1/10.)/l)*r3;#ohm\n",
"fr=r4+r5;#ohm\n",
"R=(fr*fr1)/r2;#ohm\n",
"e=i1*fr;#V\n",
"ig=(e-v3)/(r1+R);#A\n",
"dg=ig*x*10**6;#mm\n",
"#results\n",
"print \"limit of error in the reading is \",round(lr,1),\" micro-V\"\n",
"print \"deflection of the galvanometer is (mm)=\",round(dg,1)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15 - pg 266"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current in one direction,I1(mA) = 10.0\n",
"Current in another direction,I2(mA) = 10.34\n"
]
}
],
"source": [
"#pg 266\n",
"#Example 4.15: Current \n",
"#calculate the Current \n",
"#given data :\n",
"V1=4.2;# in V\n",
"V2=1.43;# in V\n",
"r1=21.0;# in ohm\n",
"r2=1.;# in ohm\n",
"r3=15.;# in ohm\n",
"#calculations\n",
"I=V1/r1;# in A\n",
"R=V2/I;# in ohm\n",
"R1=R+r2;\n",
"R2=R-r2;\n",
"R3=round(R1*(r1-R1)/r1);\n",
"R4=R2*(r1-R2)/r1;\n",
"e1=R1*I;\n",
"e2=R2*I;\n",
"I1=(e1-V2)*10**3/(R3+r3);\n",
"I2=(V2-e2)*10**3/(R4+r3);\n",
"#results\n",
"print \"Current in one direction,I1(mA) = \",I1\n",
"print \"Current in another direction,I2(mA) = \",round(I2,2)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}