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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#6: Dielectric Materials"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 6.1, Page number 6.34"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"insulation resistance is 0.85 *10**18 ohm\n",
"answer varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rho=5*10**16; #resistivity(ohm m)\n",
"l=5*10**-2; #thickness(m)\n",
"b=8*10**-2; #length(m)\n",
"w=3*10**-2; #width(m)\n",
"\n",
"#Calculation\n",
"A=b*w; #area(m**2)\n",
"Rv=rho*l/A; \n",
"X=l+b; #length(m)\n",
"Y=w; #perpendicular(m)\n",
"Rs=Rv*X/Y; \n",
"Ri=Rs*Rv/(Rs+Rv); #insulation resistance(ohm)\n",
"\n",
"#Result\n",
"print \"insulation resistance is\",round(Ri/10**18,2),\"*10**18 ohm\"\n",
"print \"answer varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 6.2, Page number 6.34"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"DC dielectric loss is 1 *10**-3 watt\n",
"AC dielectric loss is 22.22 *10**-3 watt\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rho=10**10; #resistivity(ohm m)\n",
"d=10**-3; #thickness(m)\n",
"A=10**4*10**-6; #area(m**2)\n",
"V=10**3; #voltage(V)\n",
"f=50; #power frequency(Hz)\n",
"epsilonr=8;\n",
"epsilon0=8.84*10**-12;\n",
"tan_delta=0.1;\n",
"\n",
"#Calculation\n",
"Rv=rho*d/A; \n",
"dl_DC=V**2/Rv; #DC dielectric loss(watt)\n",
"C=A*epsilon0*epsilonr/d;\n",
"dl_AC=V**2*2*math.pi*f*C*tan_delta; #AC dielectric loss(watt)\n",
"\n",
"#Result\n",
"print \"DC dielectric loss is\",int(dl_DC*10**3),\"*10**-3 watt\"\n",
"print \"AC dielectric loss is\",round(dl_AC*10**3,2),\"*10**-3 watt\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 6.3, Page number 6.35"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"polarisability of He is 0.185 *10**-40 farad m**2\n",
"relative permittivity is 1.000056\n",
"answer varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"epsilon0=8.84*10**-12;\n",
"R=0.55*10**-10; #radius(m)\n",
"N=2.7*10**25; #number of atoms\n",
"\n",
"#Calculation\n",
"alpha_e=4*math.pi*epsilon0*R**3; #polarisability of He(farad m**2)\n",
"epsilonr=1+(N*alpha_e/epsilon0); #relative permittivity\n",
"\n",
"#Result\n",
"print \"polarisability of He is\",round(alpha_e*10**40,3),\"*10**-40 farad m**2\"\n",
"print \"relative permittivity is\",round(epsilonr,6)\n",
"print \"answer varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 6.4, Page number 6.35"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"field strength is 3.535 *10**7 V/m\n",
"total dipole moment is 33.4 *10**-12 Cm\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"A=360*10**-4; #area(m**2)\n",
"V=15; #voltage(V)\n",
"C=6*10**-6; #capacitance(farad)\n",
"epsilonr=8;\n",
"epsilon0=8.84*10**-12;\n",
"\n",
"#Calculation\n",
"E=V*C/(epsilon0*epsilonr*A); #field strength(V/m)\n",
"dm=epsilon0*(epsilonr-1)*V*A; #total dipole moment(Cm)\n",
"\n",
"#Result\n",
"print \"field strength is\",round(E/10**7,3),\"*10**7 V/m\"\n",
"print \"total dipole moment is\",round(dm*10**12,1),\"*10**-12 Cm\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 6.5, Page number 6.36"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"capacitance is 226.3 *10**-12 farad\n",
"parallel loss resistance is 10 mega ohm\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=0.08*10**-3; #thickness(m)\n",
"A=8*10**-4; #area(m**2)\n",
"epsilonr=2.56;\n",
"epsilon0=8.84*10**-12;\n",
"tan_delta=0.7*10**-4;\n",
"new=10**6; #frequency(Hz)\n",
"\n",
"#Calculation\n",
"C=A*epsilon0*epsilonr/d; #capacitance(farad)\n",
"epsilonrdash=tan_delta*epsilonr;\n",
"omega=2*math.pi*new;\n",
"R=d/(epsilon0*epsilonrdash*omega*A); #parallel loss resistance(ohm)\n",
"\n",
"#Result\n",
"print \"capacitance is\",round(C*10**12,1),\"*10**-12 farad\"\n",
"print \"parallel loss resistance is\",int(R/10**6),\"mega ohm\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 6.6, Page number 6.36"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the complex polarizability is (3.50379335033-0.0600074383321j) *10**-40 F-m**2\n",
"answer cant be rouned off to 2 decimals as given in the textbook. Since it is a complex number and complex cant be converted to float\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"epsilonr=4.36; #dielectric constant\n",
"t=2.8*10**-2; #loss tangent(t)\n",
"N=4*10**28; #number of electrons\n",
"epsilon0=8.84*10**-12; \n",
"\n",
"#Calculation\n",
"epsilon_r = epsilonr*t;\n",
"epsilonstar = (complex(epsilonr,-epsilon_r));\n",
"alphastar = (epsilonstar-1)/(epsilonstar+2);\n",
"alpha_star = 3*epsilon0*alphastar/N; #complex polarizability(Fm**2)\n",
"\n",
"#Result\n",
"print \"the complex polarizability is\",alpha_star*10**40,\"*10**-40 F-m**2\"\n",
"print \"answer cant be rouned off to 2 decimals as given in the textbook. Since it is a complex number and complex cant be converted to float\""
]
}
],
"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
}
|
