{ "metadata": { "name": "", "signature": "sha256:aec700ae8e541452237ee9c0f10eb2b8642d7039520473250339382162750967" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "9: Varying and alternating currents" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.1, Page number 242" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "L=0.1; #inductance(H)\n", "R=10; #resistance(ohm)\n", "t1=0; #time(sec)\n", "t2=0.002; #time(sec)\n", "t3=0.04; #time(sec)\n", "E=5; #voltage(V)\n", "\n", "#Calculation\n", "tow=L/R; #time(sec)\n", "a=E/R;\n", "i1=a*(1-math.exp(-t1/tow)); #current for t=0 sec(A)\n", "i2=a*(1-math.exp(-t2/tow)); #current for t=0.002 sec(A)\n", "i3=a*(1-math.exp(-t3/tow)); #current for t=0.04 sec(A)\n", "i4=a*(1-math.exp(-tow/tow)); #current for t=tow sec(A)\n", "\n", "#Result\n", "print \"current for t=0 sec is\",i1,\"A\"\n", "print \"current for t=0.002 sec is\",round(i2,2),\"A\"\n", "print \"current for t=0.04 sec is\",round(i3,2),\"A\"\n", "print \"current for t=tow sec is\",round(i4,3),\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "current for t=0 sec is 0.0 A\n", "current for t=0.002 sec is 0.09 A\n", "current for t=0.04 sec is 0.49 A\n", "current for t=tow sec is 0.316 A\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.2, Page number 243" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "L=0.5; #inductance(H)\n", "R=5; #resistance(ohm)\n", "E=2; #voltage(V)\n", "t=0.2; #time(sec)\n", "\n", "#Calculation\n", "tow=L/R; #time(sec)\n", "a=E/R;\n", "i=a*(1-math.exp(-t/tow)); #current(A)\n", "dibydt=(E-(R*i))/L; #rate of growth of current(A/s)\n", "E=(1/2)*L*(i**2); #energy stored by inductor(J)\n", "\n", "#Result\n", "print \"rate of growth of current is\",round(dibydt,2),\"A/s\"\n", "print \"energy stored by inductor is\",round(E,2),\"J\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "rate of growth of current is 0.54 A/s\n", "energy stored by inductor is 0.03 J\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.3, Page number 244" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "L=10; #inductance(H)\n", "R=10; #resistance(ohm)\n", "E=10; #voltage(V)\n", "t1=0.3; #time(sec)\n", "t2=0.5; #time(sec)\n", "t3=1; #time(sec)\n", "\n", "#Calculation\n", "tow=L/R; #time(sec)\n", "i0=E/R;\n", "i1=i0*math.exp(-t1/tow); #current for t=0.3 sec(A)\n", "i2=i0*math.exp(-t2/tow); #current for t=0.5 sec(A)\n", "i3=i0*math.exp(-t3/tow); #current for t=1 sec(A)\n", "\n", "#Result\n", "print \"current for t=0.3 sec is\",round(i1,2),\"A\"\n", "print \"current for t=0.5 sec is\",round(i2,2),\"A\"\n", "print \"current for t=1 sec is\",round(i3,2),\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "current for t=0.3 sec is 0.74 A\n", "current for t=0.5 sec is 0.61 A\n", "current for t=1 sec is 0.37 A\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.4, Page number 250" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "E=5; #voltage(V)\n", "C=2*10**-6; #capacitor(F)\n", "R=1*10**6; #resistance(ohm)\n", "t=1; #time(sec)\n", "v=40/100; #decay value(%)\n", "\n", "#Calculation\n", "q=E*C*(1-math.exp(-t/(R*C))); #charge on plates(C)\n", "Vc=q/C; #voltage drop across capacitor(V)\n", "i0=E/R;\n", "i=i0*math.exp(-t/(R*C)); #current in circuit(A)\n", "V=i*R; #voltage drop across resistor(V)\n", "E=(1/2)*C*(Vc**2); #energy stored by capacitor(J)\n", "tow=R*C; #time constant(sec)\n", "t=2*math.log(1/v); #time taken(sec)\n", "\n", "#Result\n", "print \"voltage drop across capacitor is\",round(Vc,2),\"V\"\n", "print \"current in circuit is\",int(i*10**6),\"micro A\"\n", "print \"voltage drop across resistor is\",int(V),\"V\"\n", "print \"energy stored by capacitor is\",round(E*10**6,1),\"*10**-6 J\"\n", "print \"time constant is\",tow,\"sec\"\n", "print \"time taken is\",round(t,4),\"sec\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "voltage drop across capacitor is 1.97 V\n", "current in circuit is 3 micro A\n", "voltage drop across resistor is 3 V\n", "energy stored by capacitor is 3.9 *10**-6 J\n", "time constant is 2.0 sec\n", "time taken is 1.8326 sec\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.5, Page number 265" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "L=1*10**-3; #inductance(H)\n", "C=0.1*10**-6; #capacitor(F)\n", "R=1; #resistance(ohm)\n", "\n", "#Calculation\n", "a=1/(L*C);\n", "b=(R**2)/(4*(L**2)); \n", "omega=math.sqrt(a-b); #angular frequency(per sec)\n", "Q=omega*L/R; #Q-factor\n", "\n", "#Result\n", "print \"angular frequency is\",round(omega),\"per sec\"\n", "print \"answer varies due to rounding off errors\"\n", "print \"Q-factor is\",round(Q)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "angular frequency is 99999.0 per sec\n", "answer varies due to rounding off errors\n", "Q-factor is 100.0\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.6, Page number 280" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "#v=7sin(314+pi/6)\n", "v=7;\n", "R=100; #resistance(ohm)\n", "\n", "#Calculation\n", "Im=v/R; #maximum current(A)\n", "Irms=Im/math.sqrt(2); #rms value of current(A)\n", "Vrms=v/math.sqrt(2);\n", "P=Vrms*Irms; #average power(W)\n", "\n", "#Result\n", "print \"maximum current is\",Im,\"A\"\n", "print \"rms value of current is\",round(Irms,2),\"A\"\n", "print \"average power is\",round(P,3),\"W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "maximum current is 0.07 A\n", "rms value of current is 0.05 A\n", "average power is 0.245 W\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.7, Page number 283" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "#V=7sin(314t+pi/6)\n", "v=7;\n", "omega=314; \n", "L=0.05; #inductance(H)\n", "\n", "#Calculation\n", "XL=omega*L;\n", "betaL=1/XL; #susceptance(per ohm)\n", "i=v*betaL; #current through inductor\n", "Im=i;\n", "Irms=Im/math.sqrt(2); #rms current(A)\n", "P=0; #power loss\n", "\n", "#Result\n", "print \"susceptance is\",round(betaL,4),\"per ohm\"\n", "print \"current through inductor is\",round(i,2),\"sin(314t-math.pi/3)\"\n", "print \"rms current is\",round(Irms,2),\"A\"\n", "print \"power loss is\",P" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "susceptance is 0.0637 per ohm\n", "current through inductor is 0.45 sin(314t-math.pi/3)\n", "rms current is 0.32 A\n", "power loss is 0\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.8, Page number 286" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "#V=7sin(314t+pi/6)\n", "v=7;\n", "omega=314; \n", "C=0.05*10**-6; #capacitance(F)\n", "\n", "#Calculation\n", "XC=1/(omega*C); #value of XC \n", "i=v/XC; #current through capacitor\n", "Im=i;\n", "Irms=Im/math.sqrt(2); #rms current(A)\n", "P=0; #power loss\n", "\n", "#Result\n", "print \"value of XC is\",round(XC/10**3,1),\"K ohm\"\n", "print \"current through capacitor is\",i*10**3,\"*10**-3 sin(314t+2*math.pi/3)\"\n", "print \"rms current is\",int(Irms*10**6),\"micro A\"\n", "print \"power loss is\",P" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "value of XC is 63.7 K ohm\n", "current through capacitor is 0.1099 *10**-3 sin(314t+2*math.pi/3)\n", "rms current is 77 micro A\n", "power loss is 0\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.9, Page number 294" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "V1=110; #voltage(V)\n", "P=40; #power(W)\n", "V2=230; #voltage(V)\n", "\n", "#Calculation\n", "RB=V1**2/P; #resistance of bulb(ohm)\n", "i=V1/RB; #electric current through bulb(A)\n", "Z=V2/i; #series resistance(ohm)\n", "R=Z-RB; #pure resistance(ohm)\n", "XL=math.sqrt((Z**2)-(RB**2)); \n", "L=XL/314; #inductance(H)\n", "\n", "#Result\n", "print \"pure resistance is\",R,\"ohm\"\n", "print \"inductance is\",round(L,3),\"H\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "pure resistance is 330.0 ohm\n", "inductance is 1.769 H\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.10, Page number 311" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "C=10**-6; #capacitance(F)\n", "L=10*10**-3; #inductance(H)\n", "R=1*10**3; #resistance(ohm)\n", "\n", "#Calculation\n", "fr=1/(2*math.pi*math.sqrt(L*C)); #resonant frequency(Hz)\n", "Z=L/(C*R); #impedence(ohm)\n", "\n", "#Result\n", "print \"resonant frequency is\",round(fr/10**3,3),\"KHz\"\n", "print \"impedence is\",Z,\"ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resonant frequency is 1.592 KHz\n", "impedence is 10.0 ohm\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.11, Page number 312" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "C=5*10**-6; #capacitance(F)\n", "R=10; #resistance(ohm)\n", "new=50; #frequency(Hz)\n", "\n", "#Calculation\n", "omega=2*math.pi*new;\n", "L=1/(C*(omega**2)); #self inductance(H)\n", "\n", "#Result\n", "print \"self inductance is\",round(L,3),\"H\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "self inductance is 2.026 H\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.12, Page number 312" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "C=0.1*10**-6; #capacitance(F)\n", "L=1*10**-3; #inductance(H)\n", "R=10; #resistance(ohm)\n", "\n", "#Calculation\n", "omega0=1/math.sqrt(L*C); #resonant frequency(rad/sec)\n", "d=R/L; #difference between two half power points\n", "cosphi=R/R; #power factor at resonance\n", "\n", "#Result\n", "print \"resonant frequency is\",omega0/10**5,\"*10**5 rad/sec\"\n", "print \"power factor at resonance is\",cosphi" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resonant frequency is 1.0 *10**5 rad/sec\n", "power factor at resonance is 1.0\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.13, Page number 313" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "C=0.1*10**-6; #capacitance(F)\n", "L=10*10**-3; #inductance(H)\n", "R=10; #resistance(ohm)\n", "\n", "#Calculation\n", "Z=L/(C*R); #impedence at resonance(ohm)\n", "\n", "#Result\n", "print \"impedence at resonance is\",Z/10**4,\"*10**4 ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "impedence at resonance is 1.0 *10**4 ohm\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.14, Page number 313" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "C=5*10**-6; #capacitance(F)\n", "L=10*10**-3; #inductance(H)\n", "R=10*10**3; #resistance(ohm)\n", "\n", "#Calculation\n", "omegar=1/math.sqrt(L*C); #resonant frequency(Hz)\n", "omegar=round(omegar/10**3,1);\n", "delta_omega=1/(R*C); #bandwidth(Hz)\n", "Q=omegar*10**3/delta_omega; #Q-factor\n", "\n", "#Result\n", "print \"resonant frequency is\",omegar,\"*10**3 Hz\"\n", "print \"bandwidth is\",delta_omega,\"Hz\"\n", "print \"Q-factor is\",Q" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resonant frequency is 4.5 *10**3 Hz\n", "bandwidth is 20.0 Hz\n", "Q-factor is 225.0\n" ] } ], "prompt_number": 36 } ], "metadata": {} } ] }