From a4206084fd8c2bd696ea4ae4012aa83534979456 Mon Sep 17 00:00:00 2001 From: Jovina Dsouza Date: Tue, 22 Jul 2014 00:00:04 +0530 Subject: adding book --- .../chapter_35-checkpoint_1.ipynb | 637 +++++++++++++++++++++ 1 file changed, 637 insertions(+) create mode 100755 Electrical_Circuit_Theory_And_Technology/chapter_35-checkpoint_1.ipynb (limited to 'Electrical_Circuit_Theory_And_Technology/chapter_35-checkpoint_1.ipynb') diff --git a/Electrical_Circuit_Theory_And_Technology/chapter_35-checkpoint_1.ipynb b/Electrical_Circuit_Theory_And_Technology/chapter_35-checkpoint_1.ipynb new file mode 100755 index 00000000..7462b3a9 --- /dev/null +++ b/Electrical_Circuit_Theory_And_Technology/chapter_35-checkpoint_1.ipynb @@ -0,0 +1,637 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Chapter 35: Maximum power transfer theorems and impedance matching

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 1, page no. 620

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine (a) the value of R for maximum power to be transferred from the source to the load,\n", + "#and (b) the value of the maximum power delivered to R\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "rv = 120;# in volts\n", + "thetav = 0;# in degrees\n", + "Z = 15 + 1j*20;# in ohm\n", + "\n", + " #calculation: \n", + " #voltage\n", + "V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180)\n", + " #maximum power transfer occurs when R = mod(Z)\n", + "R = abs(Z)\n", + " #the total circuit impedance\n", + "ZT = Z + R\n", + " #Current I flowing in the load is given by\n", + "I = V/ZT\n", + "Imag = abs(I)\n", + " #maximum power delivered\n", + "P = R*I**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)maximum power transfer occurs when R is \",R,\" ohm\"\n", + "print \"\\n (b) maximum power delivered is \",abs(P),\" W\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)maximum power transfer occurs when R is 25.0 ohm\n", + "\n", + " (b) maximum power delivered is 180.0 W\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 2, page no. 620

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#determine\n", + "#(a) the value of Z that results in maximum power transfer, and\n", + "#(b) the value of the maximum power.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "rv = 120;# in volts\n", + "thetav = 0;# in degrees\n", + "Z = 15 + 1j*20;# in ohm\n", + "\n", + " #calculation: \n", + " #voltage\n", + "V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180)\n", + " #maximum power transfer occurs when X = -1*imag(Z) and R = real(Z)\n", + "z = Z.real - 1j*Z.imag\n", + " #Total circuit impedance at maximum power transfer condition,\n", + "ZT = Z + z\n", + " #Current I flowing in the load is given by\n", + "I = V/ZT\n", + "Imag = abs(I)\n", + " #maximum power delivered\n", + "P = Z.real*I**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)maximum power transfer occurs when Z is \",z.real,\" + (\", z.imag,\")i ohm\"\n", + "print \"\\n (b) maximum power delivered is \",abs(P),\" W\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)maximum power transfer occurs when Z is 15.0 + ( -20.0 )i ohm\n", + "\n", + " (b) maximum power delivered is 240.0 W" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 3, page no. 620

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#determine\n", + "#(a) the value of the load resistance R required for maximum power transfer, and\n", + "#(b) the value of the maximum power transferred.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "rv = 200;# in volts\n", + "thetav = 0;# in degrees\n", + "R1 = 100;# in ohm\n", + "C = 1E-6;# in farad\n", + "f = 1000;# in Hz\n", + "\n", + " #calculation: \n", + " #voltage\n", + "V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180)\n", + " #Capacitive reactance, Xc\n", + "Xc = 1/(2*math.pi*f*C)\n", + " #Hence source impedance,\n", + "z = R1*(1j*Xc)/(R1 + 1j*Xc)\n", + " #maximum power transfer is achieved when R = mod(z)\n", + "R = abs(z)\n", + " #Total circuit impedance at maximum power transfer condition,\n", + "ZT = z + R\n", + " #Current I flowing in the load is given by\n", + "I = V/ZT\n", + "Imag = abs(I)\n", + " #maximum power transferred,\n", + "P = R*Imag**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)maximum power transfer occurs when R is \",round(R,2),\" ohm\"\n", + "print \"\\n (b) maximum power delivered is \",round(P,2),\" W\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)maximum power transfer occurs when R is 84.67 ohm\n", + "\n", + " (b) maximum power delivered is 127.9 W" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 4, page no. 621

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine (a) the value of R for which the power transferred to the load is a maximum, and \n", + "#(b) the value of the maximum power.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "rv = 60;# in volts\n", + "thetav = 0;# in degrees\n", + "R1 = 4;# in ohm\n", + "XL = 10;# in ohm\n", + "Xc = 7;# in ohm\n", + "R2 = XL*1j;# in ohm\n", + "R3 = -1j*Xc;# in ohm\n", + "\n", + " #calculation: \n", + " #voltage\n", + "V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180)\n", + " #maximum power transfer is achieved when\n", + "R = (R1**2 + (XL - Xc)**2)**0.5\n", + " #Hence source impedance,\n", + "ZT = R1 + R2 + R3 + R\n", + " #Current I flowing in the load is given by\n", + "I = V/ZT\n", + "Imag = abs(I)\n", + " #maximum power transferred,\n", + "P = R*Imag**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)maximum power transfer occurs when R is \",R,\" ohm\"\n", + "print \"\\n (b) maximum power delivered is \",P,\" W\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)maximum power transfer occurs when R is 5.0 ohm\n", + "\n", + " (b) maximum power delivered is 200.0 W" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 5, page no. 622

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the value of the load resistance R\n", + "#calculate the value of this power.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "V = 20;# in volts\n", + "R1 = 5;# in ohm\n", + "R2 = 15;# in ohm\n", + "\n", + "#calculation: \n", + " #R is removed from the network as shown in Figure 35.6\n", + " #P.d. across AB, E\n", + "E = (R2/(R1 + R2))*V\n", + " #Impedance \u2018looking-in\u2019 at terminals AB with the source removed is given by\n", + "r = R1*R2/(R1 + R2)\n", + " #The equivalent Th\u00b4evenin circuit supplying terminals AB is shown in Figure 35.7. \n", + " #From condition (2), for maximum power transfer\n", + "R = r\n", + " #Current I flowing in the load is given by\n", + "I = E/(R + r)\n", + " #maximum power transferred,\n", + "P = R*I**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)maximum power transfer occurs when R is \",R,\" ohm\"\n", + "print \"\\n (b) maximum power delivered is \",P,\" W\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)maximum power transfer occurs when R is 3.75 ohm\n", + "\n", + " (b) maximum power delivered is 15.0 W" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 6, page no. 622

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#determine (a) the values of R and X that will result in maximum power being transferred across terminals AB, and \n", + "#(b) the value of the maximum power.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "rv = 100;# in volts\n", + "thetav = 30;# in degrees\n", + "R1 = 5;# in ohm\n", + "R2 = 5;# in ohm\n", + "R3 = 10j;# in ohm\n", + "\n", + "#calculation: \n", + " #voltage\n", + "V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180)\n", + " #Resistance R and reactance X are removed from the network as shown in Figure 35.9\n", + " #P.d. across AB,\n", + "E = ((R2 + R3)/(R1 + R2 + R3))*V\n", + " #With the source removed the impedance, z, \u2018looking in\u2019 at terminals AB is given by:\n", + "z = (R2 + R3)*R1/(R1 + R2 + R3)\n", + " #The equivalent Th\u00b4evenin circuit is shown in Figure 35.10. From condition 3, \n", + " #maximum power transfer is achieved when X = -1*imag(z) and R = real(z)\n", + "X = -1*z.imag\n", + "R = z.real\n", + "Z = R + 1j*X\n", + " #Current I flowing in the load is given by\n", + "I = E/(z + Z)\n", + "Imag = abs(I)\n", + " #maximum power transferred,\n", + "P = R*Imag**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)maximum power transfer occurs when R is \",R,\" ohm and X is \", X,\" ohm\"\n", + "print \"\\n (b) maximum power delivered is \",round(P,2),\" W\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)maximum power transfer occurs when R is 3.75 ohm and X is -1.25 ohm\n", + "\n", + " (b) maximum power delivered is 416.67 W" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 7, page no. 624

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the optimum value of load resistance for maximum power transfer\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "Ro = 448;# in ohm\n", + "tr = 8;# turn ratio N1/N2\n", + "\n", + " #calculation: \n", + " #The equivalent input resistance r of the transformer must be Ro for maximum power transfer.\n", + "r = Ro\n", + "RL = r*(1/tr)**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n the optimum value of load resistance is \",RL,\" ohm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " the optimum value of load resistance is 7.0 ohm" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 8, page no. 624

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the turns ratio of an ideal transformer necessary to match the generator to a load of (40 + j19) ohm \n", + "#for maximum transfer of power.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "Zo = 450 + 1j*60;# in ohm\n", + "ZL = 40 + 1j*19;# in ohm\n", + "\n", + " #calculation: \n", + " #transformer turns ratio tr = (N1/N2)\n", + "Zomag = abs(Zo)\n", + "ZLmag = abs(ZL)\n", + "tr = (Zomag/ZLmag)**0.5\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n the transformer turns ratio is \",round(tr,2),\"\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " the transformer turns ratio is 3.2 " + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 9, page no. 625

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#determine (a) the primary current flowing, and \n", + "#(b) the power dissipated in the load resistance.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "V1 = 240;# in volts\n", + "V2 = 1920;# in volts\n", + "R1 = 5;# in ohms\n", + "R2 = 1600;# in ohms\n", + "\n", + "#calculation: \n", + " #The network is shown in Figure 35.12.\n", + " #turn ratio N1/N2 = V1/V2\n", + "tr = V1/V2\n", + " #Equivalent input resistance of the transformer,\n", + "RL = R2\n", + "r = RL*tr**2\n", + " #Total input resistance,\n", + "Rin = R1 + r\n", + " #primary current, I1\n", + "I1 = V1/Rin\n", + " #For an ideal transformer V1/V2 = I2/I1\n", + "I2 = I1*(V1/V2)\n", + " #Power dissipated in the load resistance\n", + "P = RL*I2**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a) primary current flowing is \",I1,\" A\"\n", + "print \"\\n (b) Power dissipated in the load resistance is \",P,\"W\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a) primary current flowing is 8.0 A\n", + "\n", + " (b) Power dissipated in the load resistance is 1600.0 W" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 10, page no. 625

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine for maximum power transfer (a) the value of the load resistance,\n", + "# and (b) the power dissipated in the load.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "rv = 30;# in volts\n", + "thetav = 0;# in degrees\n", + "r = 20000;# in ohms\n", + "tr = 20;# turn ratio\n", + "\n", + "#calculation:\n", + " #voltage\n", + "V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180) \n", + " #The network diagram is shown in Figure 35.13.\n", + " #For maximum power transfer, r1 must be equal to\n", + "r1 = r\n", + " #load resistance RL\n", + "RL = r1/tr**2\n", + " #The total input resistance when the source is connected to the matching transformer is\n", + "RT = r + r1\n", + " #Primary current\n", + "I1 = V/RT\n", + " #N1/N2 = I2/I1\n", + "I2 = I1*tr\n", + " #Power dissipated in load resistance RL is given by\n", + "P = RL*I2**2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)the value of the load resistance is \",RL,\" ohm\"\n", + "print \"\\n (b) Power dissipated in the load resistance is \",abs(P*1000),\"mW\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)the value of the load resistance is 50.0 ohm\n", + "\n", + " (b) Power dissipated in the load resistance is 11.25 mW" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit