{
"metadata": {
"name": "",
"signature": "sha256:9a66201b8d7233d025725f77699aa3bd8f73ea293b76d05e7eed8e99adada086"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter - 7 : Inductance and Capacitance Measurements"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.1 - Page No : 178"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"Z1= 100 # in \u03a9\n",
"theta1= 30 # in \u00b0\n",
"Z2= 50 # in \u03a9\n",
"theta2= 0 # in \u00b0\n",
"Z3= 200 # in \u03a9\n",
"theta3= -90 # in \u00b0\n",
"Z4= 100 # in \u03a9\n",
"theta4= 30 # in \u00b0\n",
"if Z1*Z4 == Z2*Z3 :\n",
" print \"The first condition is satisfied\"\n",
"if theta1+theta4 == theta2+theta3 :\n",
" print \"The second condiiton is also satisfied, So it is possible to balance the bridge under the given condition\"\n",
"else:\n",
" print \"The second condition is not satisfied.\"\n",
" print \"So balance is not possible under given condition\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The first condition is satisfied\n",
"The second condition is not satisfied.\n",
"So balance is not possible under given condition\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.2 - Page No : 178"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"Z1= 1000 # in \u03a9\n",
"theta1= -90 # in \u00b0\n",
"Z2= 500 # in \u03a9\n",
"theta2= 0 # in \u00b0\n",
"Z3= 1000 # in \u03a9\n",
"theta3= 0 # in \u00b0\n",
"R4= 100 # in \u03a9\n",
"XL4= 500 # in \u03a9\n",
"i_XL4= 500j # imaginary part\n",
"Z4=(R4+i_XL4) # in \u00b0\n",
"theta4= math.atan2(Z4.imag,Z4.real)*180/pi # in \u00b0\n",
"if theta1+theta4 == theta2+theta3 :\n",
" print \"The first condiiton is satisfied.\"\n",
"else :\n",
" print \"Balance is not possible with given configuration\"\n",
"\n",
"# 1/Z1=1/R1+j*omega*C1 (i)\n",
"# According to figure 1/Z1= R4/(Z2*Z3)+%i*XL4/(Z2*Z3) (ii) \n",
"# Comparing real and j-components of Eqn (i) and (ii)\n",
"R1= Z2*Z3/R4 # in \u03a9\n",
"OmegaC1= Z2*Z3/XL4 # in \u03a9\n",
"print \"\\nSince X_C1 is already equal to \",int(OmegaC1),\" \u03a9, the bridge can be balanced simply by placing a \"\n",
"print \"resistance of \",int(R1),\" \u03a9 across the capacitor arm 1\"\n",
"# Z3= R3-j*X_C3 (iii)\n",
" #Z3= Z1*expm(%i*theta1*pi/180)*Z4*expm(%i*theta4*pi/180)/(Z2*expm(%i*theta2*pi/180)) # (iv)\n",
"# Comparing real and j-components of Eqn (iii) and (iv)\n",
"R3= 1000 # in \u03a9\n",
"XC3= 200 # in \u03a9\n",
"print \"\\nSince R3 is already of \",int(R3),\" \u03a9, the bridge can be balanced simply by adding a\"\n",
"print \"capacitor of reactance X_C3 of \",int(XC3),\" \u03a9 in series with the resistor R3 in arm 3.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Balance is not possible with given configuration\n",
"\n",
"Since X_C1 is already equal to 1000 \u03a9, the bridge can be balanced simply by placing a \n",
"resistance of 5000 \u03a9 across the capacitor arm 1\n",
"\n",
"Since R3 is already of 1000 \u03a9, the bridge can be balanced simply by adding a\n",
"capacitor of reactance X_C3 of 200 \u03a9 in series with the resistor R3 in arm 3.\n"
]
}
],
"prompt_number": 47
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.3 - Page No : 180"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"#Given data\n",
"C2= 0.2 # in micro F\n",
"Ratio21= 10/1 # resistance ratio R2/R1\n",
"C1= C2*Ratio21 # in micro F\n",
"Ratio21_desh= 1/10 \n",
"C1_desh= C2*Ratio21_desh # in micro F\n",
"print \"The range of measurement of unknown capacitance = \",round(C1_desh,2),\"\u00b5F to\",int(round(C1)),\"\u00b5F\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The range of measurement of unknown capacitance = 0.02 \u00b5F to 2 \u00b5F\n"
]
}
],
"prompt_number": 51
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.4 - Page No : 182"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from numpy import pi\n",
"#Given data\n",
"R2= 5 # in ohm\n",
"R3= 2000 # in ohm\n",
"R4= 2950 # in ohm\n",
"C2= 0.5 # in micro F\n",
"C2=C2*10**-6 # in F\n",
"r2=0.4 # in ohm\n",
"f=450 # in Hz\n",
"omega= 2*pi*f \n",
"# Under Balace Condition Z1*Z4=Z2*Z3\n",
"# [r1+1/(j*omega*C1)]*R4= [r2+R2+1/(j*omega*C2)]*R3\n",
"# Equating the real parts we have, r1*R4= (r2+R2)*R3\n",
"r1= (r2+R2)*R3/R4 # in ohm\n",
"print \"Value of r1 = %0.3f ohm\" %r1\n",
"# Equating imaginary parts we have R4/(j*omega*C1)= R3/(j*omega*C2)\n",
"C1= R4/R3*C2 # in F\n",
"print \"Value of C1 = %0.4f micro F\" %(C1*10**6) \n",
"Tan_toh= omega*C1*r1 \n",
"print \"Dissipation Factor = %0.3e\" %Tan_toh"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of r1 = 3.661 ohm\n",
"Value of C1 = 0.7375 micro F\n",
"Dissipation Factor = 7.634e-03\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.5 - Page No : 183"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f=1000 #in Hz\n",
"R1=1000 #in ohm\n",
"R2=1000 # in ohm\n",
"R3=2000 #in ohm\n",
"R4=2000 #in ohm\n",
"C1=1*10**-6 #in F\n",
"r1= 10 # in ohm\n",
"omega=2*pi*f \n",
"C2=C1*R1/R2 #in F\n",
"print \"Unknown capacitance = %0.f \u00b5F \"%(C2*10**6) \n",
"\n",
"r2=(R2*(R3+r1)-R1*R4)/R1 #in ohm \n",
"del_1=omega*r1*C1 #in radian\n",
"del_1=del_1*180/pi # in \u00b0\n",
"print \"Phase angle error1 = %0.1f degree\" %del_1 \n",
"del_2=omega*r2*C2 #in radian\n",
"del_2=del_2*180/pi # in degree\n",
"print \"Phase angle error2 = %0.1f degree\" %del_2 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Unknown capacitance = 1 \u00b5F \n",
"Phase angle error1 = 3.6 degree\n",
"Phase angle error2 = 3.6 degree\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.6 - Page No :183"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f=500 #in Hz\n",
"R2=4.8 #in ohm\n",
"R3=2*10**3 # in ohm\n",
"R4=2.85*10**3 #in ohm\n",
"C2=0.5*10**-6 #in F\n",
"r2= 0.4 # in ohm \n",
"omega=2*pi*f \n",
"C1=C2*R4/R3 #in F\n",
"print \"The value of unknown capacitance = %0.4f micro F\" %(C1*10**6) \n",
"r1=(R3*(R2+r2))/R4 #in ohm \n",
"print \"Resistance of unknown capacitance = %0.3f ohm\" %r1\n",
"Tan_del_1= omega*C1*r1 \n",
"print \"Dissipation factor = %0.5f\" %Tan_del_1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of unknown capacitance = 0.7125 micro F\n",
"Resistance of unknown capacitance = 3.649 ohm\n",
"Dissipation factor = 0.00817\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.7 - Page No : 184"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f=50 #in Hz\n",
"R2=330*10**3 #in ohm\n",
"R3=15*10**3 # in ohm\n",
"R4=22*10**3 #in ohm\n",
"C2=0.12*10**-6 #in F\n",
"omega=2*pi*f \n",
"R1= R2*R3/R4 # in ohm\n",
"print \"Resistive component of unknown resistance = %0.f kohm\" %(R1*10**-3)\n",
"C1= C2*R4/R3 # in F\n",
"print \"Capacitive component of unknown capacitor = %0.3f micro F\" %(C1*10**6)\n",
"D=1/(omega*C1*R1) \n",
"print \"Dissipation factor = %0.2f\" %D"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistive component of unknown resistance = 225 kohm\n",
"Capacitive component of unknown capacitor = 0.176 micro F\n",
"Dissipation factor = 0.08\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.8 - Page No : 191"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f=50 #in Hz\n",
"R4=309 #in ohm\n",
"R2=100 # in ohm\n",
"C3=109*10**-12 #in F\n",
"C4=0.5*10**-6 #in F\n",
"omega=2*pi*f \n",
"Cx= C3*R4/R2 # in F\n",
"print \"Equivalent series capacitance = %0.2f \u00b5\u00b5F\" %(Cx*10**12)\n",
"Rx= C4*R2/C3 # in ohm\n",
"# Power factor of the specimen\n",
"Tan_delta= omega*Cx*Rx \n",
"print \"Power factor of the specimen = %0.4f\" %Tan_delta"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equivalent series capacitance = 336.81 \u00b5\u00b5F\n",
"Power factor of the specimen = 0.0485\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.9 - Page No : 192"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import cos, tan \n",
"from numpy import pi\n",
"#Given data\n",
"f=50 #in Hz\n",
"R4=1000 #in ohm\n",
"C3=50*10**-12 #in F\n",
"delta=9 # in \u00b0\n",
"epsilon_r= 2.3 \n",
"epsilon_0= 8.854*10**-12 \n",
"d= 0.3*10**-2 # in meter\n",
"A=314 # area of each electrode in square cm\n",
"A=A*10**-4 # in square meter\n",
"omega=2*pi*f \n",
"C1= epsilon_r*epsilon_0*A/d # in F\n",
"# Formula tan (delta)= 1/(omega*C1*R1)\n",
"R1= 1/(omega*C1*tan(delta*pi/180)) # in ohm\n",
"C4= 1/(omega**2*C1*R1*R4) # in F\n",
"print \"Variable capacitor = %0.1f micro F\" %(C4*10**6)\n",
"R2= C3*R4*(cos(delta*pi/180))**2/C1 # in ohm\n",
"print \"Variable resistance = %0.f ohm\" %R2\n",
"\n",
"# Note: Calculation of R2 in the book is wrong"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Variable capacitor = 0.5 micro F\n",
"Variable resistance = 229 ohm\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.10 - Page No : 192"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f=25 #in kHz\n",
"f=f*10**3 # in Hz\n",
"R1=3.1*10**3 #in ohm\n",
"R2=25*10**3 #in ohm\n",
"R4=100*10**3 #in ohm\n",
"C1=5.2*10**-6 #in F\n",
"omega= 2*pi*f \n",
"# From C3/C1= R2/R4-R1/R3\n",
"# C3= C1*(R2/R4-R1/R3) (i)\n",
"# and omega= 1/sqrt(R1*R3*C1*C3)\n",
"# R3= 1/(omega**2*R1*C1*C3), putting this value in (i)\n",
"C3= C1*R2/(R4*(1+R1**2*C1**2*omega**2)) # in F\n",
"print \"Equivalent capacitance = %0.3f \u00b5\u00b5F\" %(C3*10**12)\n",
"R3= 1/(omega**2*R1*C1*C3) # in ohm\n",
"print \"Equivalent parallel resistance = %0.1f kohm\" %(R3*10**-3)\n",
"\n",
"\n",
"# Note Evaluating the value of C3 in the book is wrong."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equivalent capacitance = 0.203 \u00b5\u00b5F\n",
"Equivalent parallel resistance = 12.4 kohm\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.11 - Page No :193"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"R2= 5 # in ohm\n",
"R3= 2000 # in ohm\n",
"R4= 2950 # in ohm\n",
"C2= 0.5 # in miu F\n",
"C2=C2*10**-6 # in F\n",
"r2=0.4 # in ohm\n",
"f=450 # in Hz\n",
"omega= 2*pi*f \n",
"# Under Balace Condition Z1*Z4=Z2*Z3\n",
"# [r1+1/(j*omega*C1)]*R4= [r2+R2+1/(j*omega*C2)]*R3\n",
"# Equating the real parts we have, r1*R4= (r2+R2)*R3\n",
"r1= (r2+R2)*R3/R4 # in ohm\n",
"print \"Value of r1 = %0.3f ohm\" %r1\n",
"# Equating imaginary parts we have R4/(j*omega*C1)= R3/(j*omega*C2)\n",
"C1= R4/R3*C2 # in F\n",
"print \"Value of C1 = %0.4f micro F\" %(C1*10**6) \n",
"Tan_toh= omega*C1*r1 \n",
"print \"Dissipation Factor = %0.3e\" %Tan_toh"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of r1 = 3.661 ohm\n",
"Value of C1 = 0.7375 micro F\n",
"Dissipation Factor = 7.634e-03\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.12 - Page No : 195"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"L1= 52.6 # in mH\n",
"r1= 28.5 # in ohm\n",
"R2= 1.68 # in ohm\n",
"R3= 80 # resistance in ohm\n",
"R4= 80 # resistance in ohm\n",
"r2= r1*R3/R4-R2 # in ohm\n",
"print \"Resistance of coil = %0.2f ohm\" %r2\n",
"L2=L1*R3/R4 # in mH\n",
"print \"Inductance of coil = %0.1f mH\" %L2 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance of coil = 26.82 ohm\n",
"Inductance of coil = 52.6 mH\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.13 - Page No : 195"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"L= 47.8 # in mH\n",
"R= 1.36 # in ohm\n",
"R2= 100 # in ohm\n",
"R3= 32.7 #in ohm\n",
"R4= 100 #in ohm\n",
"R1= R2*R3/R4-R # in ohm\n",
"print \"Resistance of coil = %0.2f ohm\" %R1\n",
"L1= R2/R4*L # in mH\n",
"print \"Inductance of coil = %0.1f mH\" %L1 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance of coil = 31.34 ohm\n",
"Inductance of coil = 47.8 mH\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.14 - Page No : 198"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"R2= 1000 # in ohm\n",
"R3= 1000 #in ohm\n",
"R4= 1000 #in ohm\n",
"C4= 0.5 # in miu F\n",
"C4= C4*10**-6 # in F\n",
"R1= R2*R3/R4 # in ohm\n",
"print \"Resistance of inductor = %0.f ohm\" %R1\n",
"L1= C4*R2*R3 # in H\n",
"print \"Inductance of inductor = %0.1f H\" %L1 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance of inductor = 1000 ohm\n",
"Inductance of inductor = 0.5 H\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.15 - Page No : 200"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"r= 469 # in ohm\n",
"R2= 1000 # in ohm\n",
"R3= 218 #in ohm\n",
"R4= 1000 #in ohm\n",
"C= 10 # in miu F\n",
"C= C*10**-6 # in F\n",
"R1= R2*R3/R4 # in ohm\n",
"print \"Resistance of inductor = %0.f ohm\" %R1\n",
"L1= C*R2/R4*(r*(R3+R4)+R3*R4) # in H\n",
"print \"Inductance of inductor = %0.3f H\" %L1\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance of inductor = 218 ohm\n",
"Inductance of inductor = 7.892 H\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.16 - Page No : 200"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"r= 500 # in ohm\n",
"R2= 400 # in ohm\n",
"R3= 400 #in ohm\n",
"R4= 400 #in ohm\n",
"C= 2 # in miu F\n",
"C= C*10**-6 # in F\n",
"R= R2*R3/R4 # in ohm\n",
"print \"Resistance of AB = %0.f ohm\" %R\n",
"L= C*R2/R4*(r*(R3+R4)+R3*R4) # in H\n",
"print \"Inductance of AB = %0.2f H\" %L"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance of AB = 400 ohm\n",
"Inductance of AB = 1.12 H\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.17 - Page No : 200"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"r= 100 # in ohm\n",
"R2= 1000 # in ohm\n",
"R3= 500 #in ohm\n",
"R4= 1000 #in ohm\n",
"C= 3 # in micro F\n",
"C= C*10**-6 # in F\n",
"Rx= R2*R3/R4 # in ohm\n",
"print \"Value of Rx = %0.f ohm\" %Rx\n",
"Lx= C*R2/R4*(r*(R3+R4)+R3*R4) # in H\n",
"print \"Value of Lx = %0.2f H\" %Lx "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of Rx = 500 ohm\n",
"Value of Lx = 1.95 H\n"
]
}
],
"prompt_number": 32
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.18 - Page No : 203"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"R2= 1000 # in ohm\n",
"R3= 16800 #in ohm\n",
"R4= 833 #in ohm\n",
"C4= 0.38 # in miu F\n",
"C4= C4*10**-6 # in F\n",
"f= 50 # in Hz\n",
"omega=2*pi*f \n",
"L1= R2*R3*C4/(1+(omega*C4*R4)**2) # in H\n",
"print \"Unknown inductance = %0.2f H\" %L1 \n",
"R1= R2*R3*R4*omega**2*C4**2/(1+(omega*C4*R4)**2) # in ohm\n",
"print \"Unknown resistance = %0.2f ohm\" %R1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Unknown inductance = 6.32 H\n",
"Unknown resistance = 197.49 ohm\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.19 - Page No : 203"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"R1= 500 #in ohm\n",
"R2= 1000 # in ohm\n",
"R3= R2 #in ohm\n",
"L1= 0.18 # in H\n",
"f= 5000/(2*pi) # in Hz\n",
"omega= 2*pi*f \n",
"# L1= R2*R3*C4/(1+(omega*C4*R4)**2) (i) \n",
"# and R1= R2*R3*R4*omega**2*C4**2/(1+(omega*C4*R4)**2) or R1= omega**2*R4*C4*L1\n",
"R4C4= R1/(omega**2*L1) \n",
"# From eq (i)\n",
"C4= L1*(1+(omega*R4C4)**2)/(R2*R3) # in F\n",
"print \"The value of C = %0.4f micro F\" %(C4*10**6) \n",
"R4= R4C4/C4 # in ohm\n",
"print \"The value of R4 = %0.f ohm\" %R4"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of C = 0.2356 micro F\n",
"The value of R4 = 472 ohm\n"
]
}
],
"prompt_number": 35
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.20 - Page No : 204"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"R2= 1000 #in ohm\n",
"R3= 10000 # in ohm\n",
"R4= 2000 #in ohm\n",
"C4= 1*10**-6 # in F\n",
"omega= 3000 # radians/sec\n",
"L1= R2*R3*C4/(1+(omega*C4*R4)**2) # in H\n",
"print \"Equivalent inductance of the network = %0.2f H\" %L1\n",
"R1= R2*R3*R4*omega**2*C4**2/(1+(omega*C4*R4)**2) # in ohm\n",
"print \"Equivalent resistance of the network = %0.3f kohm\" %(R1*10**-3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equivalent inductance of the network = 0.27 H\n",
"Equivalent resistance of the network = 4.865 kohm\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.21 - Page No : 204"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"R2= 2410 #in ohm\n",
"R3= 750 # in ohm\n",
"R4= 64.5 #in ohm\n",
"C4= 0.35*10**-6 # in F\n",
"r4= 0.4 # series resistance of capacitor in ohm\n",
"f=500 #/ in Hz\n",
"omega= 2*pi*f # radians/sec\n",
"R4= R4+r4 # in ohm\n",
"R1= R2*R3*R4*omega**2*C4**2/(1+(omega*C4*R4)**2) # in ohm\n",
"print \"Resistance of the choke coil = %0.2f ohm\" %R1\n",
"L1= R2*R3*C4/(1+(omega*C4*R4)**2) # in H\n",
"print \"Inductance of the choke coil = %0.4f H\" %L1\n",
"\n",
"# Note: Calculation of finding the value of L1 in the book is wrong"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance of the choke coil = 141.11 ohm\n",
"Inductance of the choke coil = 0.6294 H\n"
]
}
],
"prompt_number": 38
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.22 - Page No :205"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import atan2 \n",
"#Given data\n",
"R2= 834 # in \u03a9\n",
"R3= 100 # in \u03a9\n",
"C2= 0.124 # in \u00b5F\n",
"C2= C2*10**-6 # in F\n",
"C4= 0.1 # in \u00b5F\n",
"C4= C4*10**-6 # in F\n",
"L1= R2*R3*C4 # in H\n",
"f= 2 # in kHz\n",
"f= f*10**3 # in kHz\n",
"print \"The value of L1 = %0.2f mH\" %(L1*10**3)\n",
"R1= R3*C4/C2 # in \u03a9\n",
"print \"The value of R1 = %0.2f \u03a9\" %R1\n",
"pi_2_f_L1= 2*pi*f*L1 # value of 2*pi*f*L1\n",
"i= 1j # complex number\n",
"i_XL= i*pi_2_f_L1 #imaginary part\n",
"Z= R1+i_XL # impedance in ohm\n",
"print \"The magnitude of effective impedence = %0.2f \u03a9\" %abs(Z)\n",
"theta= atan2(Z.imag,Z.real)*180/pi\n",
"print \"The angle of effective impedence = %0.2f\u00b0\" %theta"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of L1 = 8.34 mH\n",
"The value of R1 = 80.65 \u03a9\n",
"The magnitude of effective impedence = 132.24 \u03a9\n",
"The angle of effective impedence = 52.42\u00b0\n"
]
}
],
"prompt_number": 50
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.23 - Page No : 211"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"fr= 2 # in MHz\n",
"fr=fr*10**6 # in Hz\n",
"C=230+8 # in pF\n",
"C=C*10**-12 # in F\n",
"# Formula fr= 1/(2*pi*sqrt(L*C))\n",
"L= 1/((2*pi*fr)**2*C) # in H\n",
"print \"Value of L = %0.1f \u00b5H\" %(L*10**6)\n",
"# From the first set of data\n",
"fr= 1 # in MHz\n",
"fr=fr*10**6 # in Hz\\\n",
"C= 1/((2*pi*fr)**2*L) # in F\n",
"print \"Value of C = %0.f pF\" %(C*10**12)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of L = 26.6 \u00b5H\n",
"Value of C = 952 pF\n"
]
}
],
"prompt_number": 51
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.24 - Page No : 212"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"C1= 208 # in pF\n",
"C1=C1*10**-12 # in F\n",
"Q1= 80 \n",
"C2= 184 # in pF\n",
"C2=C2*10**-12 # in F\n",
"Q2= 50 \n",
"f=165 # in kHz\n",
"f=f*10**3 # in Hz\n",
"omega= 2*pi*f # in radians/sec\n",
"# Part (i)\n",
"Rm= 1/omega*(1/(C2*Q2)-1/(C1*Q1)) # in ohm\n",
"print \"Resistive component of unknown impedence = %0.2f ohm\" %Rm\n",
"# Part(ii)\n",
"Xm= 1/omega*(1/C2-1/C1) # in ohm\n",
"print \"Reactive component of unknown impedence = %0.f ohm\" %Xm"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistive component of unknown impedence = 46.88 ohm\n",
"Reactive component of unknown impedence = 605 ohm\n"
]
}
],
"prompt_number": 52
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.25 - Page No : 212"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"C1= 160*10**-12 # in F\n",
"C2= 36*10**-12 # in F\n",
"f1=250 # in kHz\n",
"f1=f1*10**3 # in Hz\n",
"f2=500 # in kHz\n",
"f2=f2*10**3 # in Hz\n",
"Cd= (C1-4*C2)/3 # in F\n",
"print \"Self Capacitance of the coil = %0.2f \u00b5\u00b5F\" %(Cd*10**12)\n",
"# Formula f1= 1/(2*pi*sqrt(L*(C1+Cd)))\n",
"L= 1/((2*pi*f1)**2*(C1+Cd)) # in H\n",
"print \"Self inductance of the coil = %0.f \u00b5H\" %(L*10**6) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Self Capacitance of the coil = 5.33 \u00b5\u00b5F\n",
"Self inductance of the coil = 2451 \u00b5H\n"
]
}
],
"prompt_number": 53
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.26 - Page No : 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"C1= 251*10**-12 # in F\n",
"C2= 50*10**-12 # in F\n",
"f1=3 # in MHz\n",
"f1=f1*10**6 # in Hz\n",
"f2=6 # in MHz\n",
"f2=f2*10**6 # in Hz\n",
"Cd= (C1-4*C2)/3 # in F\n",
"print \"Self Capacitance of the coil = %0.f pF\" %(Cd*10**12)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Self Capacitance of the coil = 17 pF\n"
]
}
],
"prompt_number": 54
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.27 - Page No : 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"C1= 1530 # in pF\n",
"C2= 162 # in pF\n",
"f1=1 # in MHz\n",
"f1=f1*10**6 # in Hz\n",
"f2=3 # in MHz\n",
"f2=f2*10**6 # in Hz\n",
"# f1= 1/(2*pi*sqrt(L*(C1+Cd)))\n",
"# f1= 1/(2*pi*sqrt(L*(C2+Cd))) and f2= 3*f1 so\n",
"Cd= (C1-9*C2)/8 # in pF\n",
"print \"Self capacitance of the coil = %0.f pF\" %Cd"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Self capacitance of the coil = 9 pF\n"
]
}
],
"prompt_number": 55
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.28 - Page No : 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f= 450 # in kHz\n",
"f=f*10**3 # in Hz\n",
"C=250 # in pF\n",
"C=C*10**-12 # in F\n",
"Rsh= 0.75 # in ohm\n",
"Q= 105 \n",
"omega= 2*pi*f # in radians/sec\n",
"# Formula f= 1/(2*pi*sqrt(L*C))\n",
"L= 1/((2*pi*f)**2*C) # in H\n",
"print \"Inductance of the coil = %0.f \u00b5H\" %(L*10**6)\n",
"R= omega*L/Q-Rsh # in ohm\n",
"print \"Resistance of the coil = %0.2f ohm\" %R"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Inductance of the coil = 500 \u00b5H\n",
"Resistance of the coil = 12.72 ohm\n"
]
}
],
"prompt_number": 56
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.29 - Page No : 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f= 500 # in kHz\n",
"f=f*10**3 # in Hz\n",
"C=120 # in pF\n",
"C=C*10**-12 # in F\n",
"R= 5 # in ohm\n",
"r=0.02 # resistance used across the oscillatory circuit in ohm\n",
"omega= 2*pi*f # in radians/sec\n",
"Q_True= 1/(omega*C*R) \n",
"Q_indicated= 1/(omega*C*(R+r)) \n",
"PerError= (Q_True-Q_indicated)*100/Q_True # in %\n",
"print \"Percentage Error = %0.1f %%\" %PerError"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Percentage Error = 0.4 %\n"
]
}
],
"prompt_number": 57
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.30 - Page No : 214"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f1= 800 # in kHz\n",
"f1=f1*10**3 # in Hz\n",
"f2= 2.5 # in MHz\n",
"f2=f2*10**6 # in Hz\n",
"C1=95 # in pF\n",
"C1=C1*10**-12 # in F\n",
"# L= 1/(omega1**2*(C1+Cd)) (i)\n",
"# L= 1/(omega2**2*Cd) (ii)\n",
"# From eq(i) and eq(ii)\n",
"Cd= f1**2*C1/(f2**2-f1**2) # in F\n",
"print \"Self capacitance of the radio coil = %0.2f pF\" %(Cd*10**12) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Self capacitance of the radio coil = 10.84 pF\n"
]
}
],
"prompt_number": 58
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example : 7.31 - Page No : 214"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" #Given data\n",
"f1= 1 # in MHz\n",
"f1=f1*10**6 # in Hz\n",
"f2= 2 # in MHz\n",
"f2=f2*10**6 # in Hz\n",
"C1=480 # in pF\n",
"C1=C1*10**-12 # in F\n",
"C2=90 # in pF\n",
"C2=C2*10**-12 # in F\n",
"R=10 # in ohm\n",
"omega1= 2*pi*f1 # in radians/sec\n",
"omega2= 2*pi*f2 # in radians/sec\n",
"\n",
"# Part (i)\n",
"Cd= (C1-4*C2)/3 # in F\n",
"print \"(i) : Self capacitance of the coil = %0.f pF\" %(Cd*10**12)\n",
"\n",
"# Part(ii)\n",
"Q_indicated1= 1/(omega1*(C1+Cd)*R) \n",
"print \"(ii) : Indicated or effective Q for first measurement = %0.3f\" %Q_indicated1\n",
"Q_True1= 1/(omega1*C1*R) \n",
"print \"True Q for first measurement = %0.3f \" %Q_True1\n",
"Q_indicated2= 1/(omega2*(C2+Cd)*R) \n",
"print \"Indicated or effective Q for second measurement = %0.3f\" %Q_indicated2\n",
"Q_True2= 1/(omega2*C2*R) \n",
"print \"True Q for second measurement = %0.2f\" %Q_True2 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) : Self capacitance of the coil = 40 pF\n",
"(ii) : Indicated or effective Q for first measurement = 30.607\n",
"True Q for first measurement = 33.157 \n",
"Indicated or effective Q for second measurement = 61.213\n",
"True Q for second measurement = 88.42\n"
]
}
],
"prompt_number": 60
}
],
"metadata": {}
}
]
}