diff options
Diffstat (limited to 'Electrical_Circuit_Theory_And_Technology/chapter_09-checkpoint_2.ipynb')
| -rwxr-xr-x | Electrical_Circuit_Theory_And_Technology/chapter_09-checkpoint_2.ipynb | 759 |
1 files changed, 759 insertions, 0 deletions
diff --git a/Electrical_Circuit_Theory_And_Technology/chapter_09-checkpoint_2.ipynb b/Electrical_Circuit_Theory_And_Technology/chapter_09-checkpoint_2.ipynb new file mode 100755 index 00000000..02f3e6f4 --- /dev/null +++ b/Electrical_Circuit_Theory_And_Technology/chapter_09-checkpoint_2.ipynb @@ -0,0 +1,759 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h1>Chapter 9: Electromagnetic induction</h1>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 1, page no. 102</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Determine the current flowing in the conductor when \n",
+ "#(a) its ends are open-circuited, \n",
+ "#(b) its ends are connected to a load of 20 ohm resistance.\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "l = 0.3;# in m\n",
+ "v = 4;# in m/s\n",
+ "B = 1.25;# in Tesla\n",
+ "R = 20;# in ohms\n",
+ "u0 = 4*math.pi*1E-7;\n",
+ "\n",
+ "#calculation:\n",
+ "E = B*l*v\n",
+ "I2 = E/R\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\nResult\\n\\n\"\n",
+ "print \"\\n (a)If the ends of the conductor are open circuited \"\n",
+ "print \"no current will flow even though \",E,\" V has been induced.\\n\"\n",
+ "print \"\\n (b)From Ohms law, I = \",I2,\" Ampere\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ "Result\n",
+ "\n",
+ "\n",
+ "\n",
+ " (a)If the ends of the conductor are open circuited no current will flow even though 1.5 V has been induced.\n",
+ "\n",
+ "\n",
+ " (b)From Ohms law, I = 0.075 Ampere"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 2, page no. 103</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#At what velocity must a conductor 75 mm long cut a magnetic field of flux density 0.6 T\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "l = 0.075;# in m\n",
+ "E = 9;# in Volts\n",
+ "B = 0.6;# in Tesla\n",
+ "R = 20;# in ohms\n",
+ "u0 = 4*math.pi*1E-7;\n",
+ "\n",
+ "#calculation:\n",
+ "v = E/(B*l)\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\nResult\\n\\n\"\n",
+ "print \"\\n velocity v = \",v,\" m/s\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ "Result\n",
+ "\n",
+ "\n",
+ "\n",
+ " velocity v = 200.0 m/s"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 3, page no. 103</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#find the magnitude of the induced e.m.f. in each case.\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#initializing the variables:\n",
+ "l = 0.02;# in m\n",
+ "b = 0.02;# in m\n",
+ "v = 15;# in m/s\n",
+ "R = 20;# in ohms\n",
+ "Phi = 5E-6;# in Wb\n",
+ "u0 = 4*math.pi*1E-7;\n",
+ "a1 = 90;# in degrees\n",
+ "a2 = 60;# in degrees\n",
+ "a3 = 30;# in degrees\n",
+ "\n",
+ "#calculation:\n",
+ "A = l*b\n",
+ "B = Phi/A\n",
+ "E90 = B*l*v*math.sin(a1*math.pi/180)\n",
+ "E60 = B*l*v*math.sin(a2*math.pi/180)\n",
+ "E30 = B*l*v*math.sin(a3*math.pi/180)\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\nResult\\n\\n\"\n",
+ "print \"\\n Induced e.m.f. at angles 90\u00b0, 60\u00b0, 30\u00b0 are \",(E90/1E-3),\" V, \",round((E60/1E-3),2),\" V, \"\n",
+ "print \"(E30/1E-3),\" V respectively\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ "Result\n",
+ "\n",
+ "\n",
+ "\n",
+ " Induced e.m.f. at angles 90\u00c2\u00b0, 60\u00c2\u00b0, 30\u00c2\u00b0 are 3.75 V, 3.25 V, 1.875 V respectively"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4, page no. 103</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#determine the e.m.f. induced between its wing tips\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "s = 36;# in m\n",
+ "v = 400;# in km/h\n",
+ "u0 = 4*math.pi*1E-7;\n",
+ "B = 40E-6;# in Tesla\n",
+ "\n",
+ "#calculation:\n",
+ "v0 = v*5/18\n",
+ "E = B*s*v0\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\nResult\\n\\n\"\n",
+ "print \"\\n Induced e.m.f. = \",E,\" V\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ "Result\n",
+ "\n",
+ "\n",
+ "\n",
+ " Induced e.m.f. = 0.16 V"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 6, page no. 105</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Determine the e.m.f. induced in a coil\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "N = 200;# no. of turns\n",
+ "dt = 0.050;# change of time in sec\n",
+ "u0 = 4*math.pi*1E-7;\n",
+ "dPhi = 0.025;# change of flux in Wb\n",
+ "\n",
+ "#calculation:\n",
+ "E = -1*N*dPhi/dt\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\nResult\\n\\n\"\n",
+ "print \"\\n Induced e.m.f. = \",E,\" V\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ "Result\n",
+ "\n",
+ "\n",
+ "\n",
+ " Induced e.m.f. = -100.0 V"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 7, page no. 105</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Find the average e.m.f. induced.\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "N = 150;# no. of turns\n",
+ "dt = 0.040;# change of time in sec\n",
+ "u0 = 4*math.pi*1E-7;\n",
+ "dPhi = 800E-6;# change of flux in Wb\n",
+ "\n",
+ "#calculation:\n",
+ "#Since the flux reverses, the flux changes from C400 \u03bcWb to \u0003400 \u03bcWb, a total change of flux of 800 \u03bcWb\n",
+ "E = -1*N*dPhi/dt\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\nResult\\n\\n\"\n",
+ "print \"\\n Induced e.m.f. = \",E,\" V\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ "Result\n",
+ "\n",
+ "\n",
+ "\n",
+ " Induced e.m.f. = -3.0 V"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 8, page no. 105</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Calculate the e.m.f. induced in a coil\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "L = 12;# in Henry\n",
+ "u0 = 4*math.pi*1E-7;\n",
+ "dIdt = 4;# change of current with change in time in A/s\n",
+ "\n",
+ "#calculation:\n",
+ "E = -1*L*dIdt\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\nResult\\n\\n\"\n",
+ "print \"\\n Induced e.m.f. = \",E,\" V\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ "Result\n",
+ "\n",
+ "\n",
+ "\n",
+ " Induced e.m.f. = -48 V"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 9, page no. 106</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#find inductance of the coil.\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "E = 1500;# in Volts\n",
+ "dt = 0.008;# Change of time in sec\n",
+ "dI = 4;# change of current in A/s\n",
+ "\n",
+ "#calculation:\n",
+ "L = abs(E)*dt/dI\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n Inductance L= \",L,\" H\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " Inductance L= 3.0 H"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 10, page no. 107</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#How much energy is stored in the magnetic field of the inductor?\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "L = 8;# in Henry\n",
+ "I = 3;# in Amperes\n",
+ "\n",
+ "#calculation:\n",
+ "W = L*I*I/2\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n Energy stored, W = \",W,\" J\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " Energy stored, W = 36.0 J"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 11, page no. 107</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Calculate the coil inductance\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "I = 4;# in Amperes\n",
+ "N = 800;#turns\n",
+ "Phi = 0.005;# in Wb\n",
+ "\n",
+ "#calculation:\n",
+ "L = N*Phi/I\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n Inductance L = \",L,\" H\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " Inductance L = 1.0 H"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 12, page no. 107</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Calculate (a) the inductance of the coil, \n",
+ "#(b) the energy stored in the magnetic field, and \n",
+ "#(c) the average e.m.f. induced if the current falls to zero in 150 ms.\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "I1 = 3;# in Amperes\n",
+ "I2 = 0;# in Amperes\n",
+ "dt = 0.150;# in secs\n",
+ "N = 1500;#turns\n",
+ "Phi = 0.025;# in Wb\n",
+ "\n",
+ "#calculation:\n",
+ "L = N*Phi/I1\n",
+ "W = L*I1*I1/2\n",
+ "dI = I1 - I2\n",
+ "E = -1*L*dI/dt\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n (a)Inductance L = \",L,\" H\\n\"\n",
+ "print \"\\n (b)energy stored W = \",W,\" J\\n\"\n",
+ "print \"\\n (c)e.m.f. induced = \",E,\" V\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " (a)Inductance L = 12.5 H\n",
+ "\n",
+ "\n",
+ " (b)energy stored W = 56.25 J\n",
+ "\n",
+ "\n",
+ " (c)e.m.f. induced = -250.0 V"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 13, page no. 108</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Calculate the flux linking the coil and the e.m.f. induced in the coil when the current collapses to zero in 20 ms\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "I1 = 2;# in Amperes\n",
+ "I2 = 0;# in Amperes\n",
+ "dt = 0.020;# in secs\n",
+ "N = 750;#turns\n",
+ "L = 3;# in Henry\n",
+ "\n",
+ "#calculation:\n",
+ "Phi = L*I1/N\n",
+ "dI = I1 - I2\n",
+ "E = -1*L*dI/dt\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n (a)Flux = \",Phi,\" Wb\\n\"\n",
+ "print \"\\n (b)e.m.f. induced = \",E,\" V\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " (a)Flux = 0.008 Wb\n",
+ "\n",
+ "\n",
+ " (b)e.m.f. induced = -300.0 V"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 14, page no. 108</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Calculate the mutual inductance between two coils\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "dI1dt = 200;# change of current with change in time in A/s\n",
+ "N = 2;# no. of coils\n",
+ "E2 = 1.5;# in Volts\n",
+ "\n",
+ "#calculation:\n",
+ "M = abs(E2)/dI1dt\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n mutual inductance, M = \", M,\" H\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " mutual inductance, M = 0.0075 H"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 15, page no. 109</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Calculate the steady rate of change of current in one coil to induce an e.m.f. of 0.72 V in the other.\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "M = 0.018;# in Henry\n",
+ "N = 2;# no. of coils\n",
+ "E2 = 0.72;# in Volts\n",
+ "\n",
+ "#calculation:\n",
+ "dI1dt = abs(E2)/M\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n rate of change of current dI1/dt = \", dI1dt,\" A/s\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " rate of change of current dI1/dt = 40.0 A/s"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 16, page no. 109</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate (a) the average induced e.m.f. in the second coil, \n",
+ "#(b) the change of flux linked with the second coil if it is wound with 500 turns.\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "#initializing the variables:\n",
+ "M = 0.2;# in Henry\n",
+ "I1 = 10;# in Amperes\n",
+ "I2 = 4;# in Amperes\n",
+ "dt = 0.010;# in secs\n",
+ "N = 500;# turns\n",
+ "\n",
+ "#calculation:\n",
+ "dI1dt = (I1 -I2)/dt \n",
+ "E2 = -1*dI1dt*M\n",
+ "dPhi = abs(E2)*dt/N\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n (a)Induced e.m.f. E2 = \", E2,\" V\\n\"\n",
+ "print \"\\n (b)change of flux = \", dPhi,\" Wb\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " (a)Induced e.m.f. E2 = -120.0 V\n",
+ "\n",
+ "\n",
+ " (b)change of flux = 0.0024 Wb"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |