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{
"metadata": {
"name": "",
"signature": "sha256:50315b4dee267422712255a4580dea3156e39933e372f17694b3cb35adb8e098"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"4: Capacitors"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 4.1, Page number 91"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"r=6750*10**3; #radius of earth(m)\n",
"#let x=4*pi*epsilon0\n",
"x=1/(9*10**9); \n",
"\n",
"#Calculation\n",
"C=x*r; #capacitance(F)\n",
"C=C*10**6; #capacitance(micro F)\n",
"\n",
"#Result\n",
"print \"capacitance is\",C,\"micro F\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"capacitance is 750.0 micro F\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 4.2, Page number 91"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"C1=20*10**-6; #capacitance(F)\n",
"V1=500; #potential(V)\n",
"C2=10*10**-6; #capacitance(F)\n",
"V2=200; #potential(V)\n",
"\n",
"#Calculation\n",
"q1=C1*V1; #charge on 1st capacitor(C)\n",
"q2=C2*V2; #charge on 2nd capacitor(C)\n",
"C=C1+C2; #resultant capacitance(C)\n",
"V=(q1+q2)/C; #combined potential(V)\n",
"\n",
"#Result\n",
"print \"combined potential is\",V,\"V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"combined potential is 400.0 V\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 4.3, Page number 92"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Cp=5; #resultant capacitance in parallel(micro F)\n",
"Cs=1.2; #resultant capacitance in series(micro F)\n",
"\n",
"#Calculation\n",
"C1C2=Cp*Cs; #product of capacitance(micro F)\n",
"C1_C2=math.sqrt((Cp**2)-(4*C1C2)); #difference of capacitance(micro F)\n",
"twoC1=Cp+C1_C2; \n",
"C1=twoC1/2; \n",
"twoC2=Cp-C1_C2;\n",
"C2=twoC2/2;\n",
"\n",
"#Result\n",
"print \"values of capacitors are\",C1,\"micro F and\",C2,\"micro F\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"values of capacitors are 3.0 micro F and 2.0 micro F\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 4.4, Page number 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"C=0.2*10**-6; #capacitance(F)\n",
"V=2; #potential(V)\n",
"\n",
"#Calculation\n",
"U=(1/2)*C*(V**2); #energy stored(J)\n",
"\n",
"#Result\n",
"print \"energy stored is\",U,\"J\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"energy stored is 4e-07 J\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 4.5, Page number 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"A=1; #area of plates(m**2)\n",
"k=7; #dielectric constant\n",
"d=0.01*10**-2; #distance between plates(m)\n",
"V=300; #potential(V)\n",
"epsilon0=8.85*10**-12; #dielectric permittivity of free space\n",
"\n",
"#Calculation\n",
"C=k*epsilon0*A/d; #capacitance(F)\n",
"E=(1/2)*C*(V**2); #energy stored in capacitor(J)\n",
"\n",
"#Result\n",
"print \"energy stored in capacitor is\",round(E*10**3,3),\"*10**-3 J\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"energy stored in capacitor is 27.877 *10**-3 J\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 4.6, Page number 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"A=2; #area(m**2)\n",
"d=1*10**-2; #distance(m)\n",
"V0=6000; #potential(V)\n",
"V=2000; #potential(V)\n",
"epsilon0=8.85*10**-12; #dielectric permittivity of free space\n",
"\n",
"#Calculation\n",
"C0=epsilon0*A/d; #capacitance when there is no dielectric(F)\n",
"Q=C0*V0; #charge on each plate(C)\n",
"C=Q/V; #capacitance when there is dielectric(F)\n",
"k=C/C0; #dielectric constant\n",
"E0=V0/d; #electric field intensity with air medium(V/m)\n",
"E=V/d; #electric field intensity with dielectric(V/m)\n",
"\n",
"#Result\n",
"print \"capacitance when there is no dielectric is\",C0*10**9,\"nF\"\n",
"print \"charge on each plate is\",Q,\"C\"\n",
"print \"capacitance when there is dielectric is\",C*10**9,\"nF\"\n",
"print \"dielectric constant is\",k\n",
"print \"electric field intensity with air medium is\",E0/10**5,\"*10**5 V/m\"\n",
"print \"electric field intensity with dielectric is\",E/10**5,\"*10**5 V/m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"capacitance when there is no dielectric is 1.77 nF\n",
"charge on each plate is 1.062e-05 C\n",
"capacitance when there is dielectric is 5.31 nF\n",
"dielectric constant is 3.0\n",
"electric field intensity with air medium is 6.0 *10**5 V/m\n",
"electric field intensity with dielectric is 2.0 *10**5 V/m\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 4.7, Page number 95"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"k=5.4; #dielectric constant\n",
"E=10**6; #electric field intensity(V/m)\n",
"A=50*10**-4; #area(m**2)\n",
"epsilon0=8.85*10**-12; #dielectric permittivity of free space\n",
"d=5*10**-3; #distance(m)\n",
"\n",
"#Calculation\n",
"u=(1/2)*k*epsilon0*(E**2); #energy density(J/m**3)\n",
"\n",
"#Result\n",
"print \"energy density is\",u,\"J/m**3\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"energy density is 23.895 J/m**3\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|
