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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
|---|---|---|
| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
| commit | 4a1f703f1c1808d390ebf80e80659fe161f69fab (patch) | |
| tree | 31b43ae8895599f2d13cf19395d84164463615d9 /ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter4_4.ipynb | |
| parent | 9d260e6fae7328d816a514130b691fbd0e9ef81d (diff) | |
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diff --git a/ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter4_4.ipynb b/ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter4_4.ipynb new file mode 100644 index 00000000..b5443c89 --- /dev/null +++ b/ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter4_4.ipynb @@ -0,0 +1,732 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 4:Behaviour of Dielectric Materials in ac and dc Fields"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.1,Page No:4.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dielectric constant of argon = 1.0005466\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "alpha = 1.8*10**-40; #polarisability of argon in Fm**2\n",
+ "e0 = 8.85*10**-12; #dielectric constant F/m\n",
+ "N1 = 6.02*10**23; #avagadro number in mol**-1\n",
+ "x = 22.4*10**3; #volume in m**3\n",
+ " \n",
+ "#formula\n",
+ "#er-1=N*p/e0*E=(N/e0)*alpha\n",
+ "#calculation\n",
+ "N = N1/float(x); #number of argon atoms in per unit volume in cm**3\n",
+ "N2 = N*10**6; #number of argon atoms in per unit volume in m**3\n",
+ "er = 1+((N2/float(e0)))*(alpha); #dielectric constant F/m\n",
+ "\n",
+ "\n",
+ "#result\n",
+ "print'dielectric constant of argon = %3.7f'%er;"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.2,Page No:4.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "displacement = 1.25e-17 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "alpha = 1.8*10**-40; #polarisability of argon in F*m^2\n",
+ "E = 2*10**5; # in V/m\n",
+ "z = 18;\n",
+ "e = 1.6*10**-19;\n",
+ " \n",
+ " \n",
+ "#formula\n",
+ "#p=18*e*x\n",
+ "#calculation\n",
+ "p = alpha*E;\n",
+ "x = p/float(18*e); #displacement in m\n",
+ "\n",
+ " \n",
+ "#result\n",
+ "print'displacement = %3.2e'%x,'m';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.3,Page No:4.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "local field of benzene=4.40e+03 V/m\n",
+ "local field of water=-1.570e+06 V/m\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "E0 = 300*10**2; #local field in V/m\n",
+ "P1 = 3.398*10**-7; #dipole moment Coulomb/m\n",
+ "P2 = 2.124*10**-5; #dipole moment Coulomb/m\n",
+ "e0 = 8.85*10**-12; #permittivity in F/m\n",
+ " \n",
+ " \n",
+ "#formula\n",
+ "#E10Ci=E0-(2*Pi/3*e0)\n",
+ "#calculation\n",
+ "E10C1 = E0-((2*P1)/float(3*e0)); #local field of benzene in V/m\n",
+ "E10C2 = E0-((2*P2)/float(3*e0)); #local field of water in V/m\n",
+ " \n",
+ "#result\n",
+ "print'local field of benzene=%3.2e'%E10C1,'V/m';\n",
+ "print'local field of water=%3.3e'%E10C2,'V/m';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.4,Page No:4.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "polarisability of benzene = 1.16e-37 F*m**2\n",
+ "polarisability of water = 4.04e-40 F*m**2\n",
+ "Note: mistake in textbok,alpha1 value is printed as 1.16*10**-38 instead of 1.16*10**-37\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "p1 = 5.12*10**-34; #p of benzene kg/m**3\n",
+ "p2 = 6.34*10**-34; #p of water kg/m**3\n",
+ "e10C1 = 4.4*10**3; #local field of benzene in V/m\n",
+ "e10C2 = 1570*10**3; #local field of water in V/m\n",
+ " \n",
+ " \n",
+ "#formula\n",
+ "#p=alphai*e10Ci\n",
+ "#calculation\n",
+ "alpha1 = p1/float(e10C1); #polarisability of benzene in F*m**2\n",
+ "alpha2 = p2/float(e10C2); #polarisability of water in F*m**2\n",
+ " \n",
+ "\n",
+ "#result\n",
+ "print'polarisability of benzene = %3.2e'%alpha1,'F*m**2';\n",
+ "print'polarisability of water = %3.2e'%alpha2,'F*m**2';\n",
+ "print'Note: mistake in textbok,alpha1 value is printed as 1.16*10**-38 instead of 1.16*10**-37';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.5,Page No:4.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "polarisation of benzene = 6.80e-07 c/m**2\n",
+ "polarisation of water = 4.25e-05. c/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "e0 = 8.85*10**-12; #abslute permitivity in (m**-3)*(kg**-1)*(s**4)*(A**2)\n",
+ "E = 600*10**2; #strength in V/cm\n",
+ "er1 = 2.28; #dielectric constant of benzene in coulomb/m\n",
+ "er2 = 81; #dielectric constant of water in coulomb/m\n",
+ "\n",
+ "\n",
+ "#fomula\n",
+ "#p=e0*E*(er-1)\n",
+ "#calculation\n",
+ "pB = e0*E*(er1-1); #polarisation of benzene in c/m**2\n",
+ "pW = e0*E*(er2-1); #polarisation of water in c/m**2\n",
+ " \n",
+ "\n",
+ "#result\n",
+ "print'polarisation of benzene = %3.2e'%pB,'c/m**2';\n",
+ "print'polarisation of water = %3.2e.'%pW,'c/m**2';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.6,Page No:4.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "percentage contribution from ionic polaristion = 59.82 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "er0 = 5.6; #static dielectric cnstant of NaCl \n",
+ "n = 1.5; #optical index of refraction\n",
+ " \n",
+ "\n",
+ "#calculation\n",
+ "er = er0-n**2;\n",
+ "d = ((er/float(er0))*100); #percentage contribution from ionic polaristion in %\n",
+ " \n",
+ "#result \n",
+ "print'percentage contribution from ionic polaristion = %3.2f'%d,'%';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.7,Page No:4.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "separation=1.69e-17 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "alpha = 0.18*10**-40; #polarisability of He in F *m**2\n",
+ "E = 3*10**5; #constant in V/m\n",
+ "N = 2.6*10**25; #number of atoms in per m**3\n",
+ "e = 1.6*10**-19;\n",
+ " \n",
+ " \n",
+ "#formula\n",
+ "#P=N*p\n",
+ "#charge of He=2*electron charge\n",
+ "#p=2(e*d)\n",
+ "#calculation\n",
+ "P = N*alpha*E; #in coul/m**2\n",
+ "p = P/float(N); #polarisation of He in coul.m\n",
+ "d = p/float(2*e); #separation between charges in m\n",
+ " \n",
+ " \n",
+ "#result \n",
+ "print'separation=%3.2e'%d,'m';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## Example 4.8,Page No:4.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "oriental polarisation=9.66e-08 coul/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "N = 10**27; #number of HCl molecules in molecules/m**3\n",
+ "E = 10**5; #electric field in V/m\n",
+ "P = 1.04*3.33*10**-30; #permanent dipole moment in coul.m\n",
+ "T = 300; #temperature in kelvin\n",
+ "K = 1.38*10**-23;\n",
+ " \n",
+ " \n",
+ "#calculation\n",
+ "P0 = (N*(P**2)*E)/float(3*K*T); #oriental polarisation in coul/m^2\n",
+ "\n",
+ " \n",
+ "#result\n",
+ "print'oriental polarisation=%3.2e'%P0,'coul/m**2';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## Example 4.9,Page No:4.11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "relative dielectric constant =1.0\n",
+ " Note: calculation mistake in text book in calculating relative dielectric constant\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "N = 6.023*10**26; #avagadro number (lb-mol)**-1\n",
+ "alpha = 3.28*10**-40; #polarisability in F*m**2\n",
+ "M = 32; #molecular weight in kilograms\n",
+ "p = 2.08*10**3; #density of sulphur in g/cm**3\n",
+ "e0 = 8.85*10**12; #permitivity in F/m\n",
+ "\n",
+ "#calculation\n",
+ "er = ((2*N*p*alpha)+(3*M*e0))/float((3*M*e0)-(N*p*alpha)); \n",
+ "\n",
+ "#result\n",
+ "\n",
+ "print'relative dielectric constant =%3.1f'%er;\n",
+ "print' Note: calculation mistake in text book in calculating relative dielectric constant';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.10,Page No:4.12"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ratio of electronic and ionic probabilities =1.6\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "er = 4.94;\n",
+ "n = 1.64;\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "#(alphae)/(alphai) =x\n",
+ "x = ((er-1)/float(er+2))*(((n**2)+2)/float((n**2)-1)); #ratio of electronic and ionic probabilities\n",
+ "\n",
+ "\n",
+ "#result\n",
+ "print'ratio of electronic and ionic probabilities =%3.1f'%x;"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.11,Page No:4.17"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dielectric constant=16.43\n",
+ "electrical suseptibility=1.3711e-10 c**2*N**-1*M**-2\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declartion\n",
+ "E = 1.46*10**-10; #permitivity in c**2*N**-1*m**-2\n",
+ "E0 = 8.885*10**-12; #permitivity in c**2*N**-1*m**-2\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "Er = E/float(E0);\n",
+ "sighe = E0*(Er-1); #electrical susceptbility in c**2*N**-1*M**-2\n",
+ " \n",
+ " \n",
+ "#result\n",
+ "print'dielectric constant=%3.2f'%Er;\n",
+ "print'electrical suseptibility=%3.4e'%sighe,'c**2*N**-1*M**-2';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.12,Page No:4.17"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "polarisation=8.4e-07 cm**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "r = 0.1; #radius in m\n",
+ "pw = 1; #density of water in g/ml\n",
+ "Mw = 18; # molecular mass of water \n",
+ "E = 6.0*10**-30; #dipole moment of water in cm\n",
+ "N = 6.0*10**26; #avagadro constant in (lb-mol)−1\n",
+ " \n",
+ " \n",
+ "#calculation\n",
+ "n = N*(4*(math.pi)*(r**3)*pw)/(Mw*3); #number of water molecules in a water drop \n",
+ "p = n*E; #polarisation in cm**2\n",
+ "\n",
+ "\n",
+ "#result\n",
+ "print'polarisation=%3.1e'%p,'cm**2';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.13,Page No:4.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dielectric susceptibility=0.000074\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "Er = 1.000074; #dielectric constant for a gas at 0°C\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "sighe = Er-1; #dielectric susceptibility\n",
+ " \n",
+ " \n",
+ "#result\n",
+ "print'dielectric susceptibility=%3.6f'%sighe;\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.14,Page No:4.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "free charge=2.65e-05 Coul/m**2\n",
+ "polarisation=5.31e-05 Coul/m\n",
+ "displacement=7.96e-05\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "E = 10**6; #dielectric in volts/s\n",
+ "er = 3; #dielectric in mm\n",
+ "e0 = 8.85*10**-12;\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "E0 = er*E; #electric field in V/m\n",
+ "sigma = e0*E0; #free charge in Coul/m^2\n",
+ "P = e0*(er-1)*E0; #polarisation in coul/m\n",
+ "D = e0*er*E0; #displacement in in dielectric\n",
+ " \n",
+ " \n",
+ "#result\n",
+ "print'free charge=%3.2e'%sigma,'Coul/m**2';\n",
+ "print'polarisation=%3.2e'%P,'Coul/m';\n",
+ "print'displacement=%3.2e'%D; "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.15,Page No:4.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "capacitance = 3.42e-11 Farad\n",
+ "charge =3.42e-10 coulomb\n",
+ "displacement =5.31e-07 c/m**2\n",
+ "polarisation =4.42e-07 c/m**2\n",
+ "Note:error in calculation of P,E value is taken as 5000 instead of 10**4\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "d = 1.0*10**-3; #separation between plates in m\n",
+ "A = 6.45*10**-4; # surface area in m^2\n",
+ "e0 = 8.85*10**-12; #permitivity of electron in (m**-3)*(kg**-1)*(s**4)*(A**2)\n",
+ "er = 6.0; #relative permitivity in (m**-3)*(kg**-1)*(s**4)*(A**2)\n",
+ "V = 10; #voltage in V\n",
+ "E = 10; \n",
+ " \n",
+ " \n",
+ "#calculation\n",
+ "C = (e0*er*A)/float(d); #capacitance in Farad\n",
+ "q = C*V; #charge in coulomb\n",
+ "D = (e0*er*E)/float(10**-3); #displacement vector in c/m**2\n",
+ "P = D-(e0*E/float(10**-3)); #polarisation vector in c/m**2\n",
+ "\n",
+ "\n",
+ "#result\n",
+ "print'capacitance = %3.2e'%C,'Farad';\n",
+ "print'charge =%3.2e'%q,'coulomb';\n",
+ "print'displacement =%3.2e'%D,'c/m**2';\n",
+ "print'polarisation =%3.2e'%P,'c/m**2';\n",
+ "print'Note:error in calculation of P,E value is taken as 5000 instead of 10**4\\n';\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## Example 4.16,Page No:4.30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "frequency = 8.84 KHz\n",
+ "phase difference = 45 °\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "t = 18*10**-6; #relaxation time in s\n",
+ "er1 = 1; #permitivity in F/m\n",
+ "er = 1; #permitivity in F/m\n",
+ "t = 18*10**-6; #relaxation time in s\n",
+ " \n",
+ "#calculation\n",
+ "f = 1/float(2*math.pi*t); #frequency in Hz\n",
+ "theta_c = math.atan(er1/float(er));\n",
+ "#theta_c_deg = (theta_c*180)/float(math.pi);\n",
+ "#phi = 90-theta_c_deg; #phase difference in degrees\n",
+ " \n",
+ " \n",
+ "#result\n",
+ "print'frequency = %3.2f'%(f*10**-3),'KHz';\n",
+ "print'phase difference =%3.0f'%((theta_c*180)/float(math.pi)),'°';\n",
+ " "
+ ]
+ }
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