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| author | hardythe1 | 2014-07-25 12:35:04 +0530 |
|---|---|---|
| committer | hardythe1 | 2014-07-25 12:35:04 +0530 |
| commit | 6846da7f30aadc7b3812538d1b1c9ef2e465a922 (patch) | |
| tree | 0ac5e382d6515013c6a1f23d3529dc46e03d0015 /Electrical_Circuit_Theory_And_Technology/chapter_36-checkpoint_3.ipynb | |
| parent | dccd504f6bd2f5e97c54d1f0b0d2a99f83497ce5 (diff) | |
| download | Python-Textbook-Companions-6846da7f30aadc7b3812538d1b1c9ef2e465a922.tar.gz Python-Textbook-Companions-6846da7f30aadc7b3812538d1b1c9ef2e465a922.tar.bz2 Python-Textbook-Companions-6846da7f30aadc7b3812538d1b1c9ef2e465a922.zip | |
removing unwanted:
Diffstat (limited to 'Electrical_Circuit_Theory_And_Technology/chapter_36-checkpoint_3.ipynb')
| -rwxr-xr-x | Electrical_Circuit_Theory_And_Technology/chapter_36-checkpoint_3.ipynb | 1011 |
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diff --git a/Electrical_Circuit_Theory_And_Technology/chapter_36-checkpoint_3.ipynb b/Electrical_Circuit_Theory_And_Technology/chapter_36-checkpoint_3.ipynb deleted file mode 100755 index 3cc6ab7f..00000000 --- a/Electrical_Circuit_Theory_And_Technology/chapter_36-checkpoint_3.ipynb +++ /dev/null @@ -1,1011 +0,0 @@ -{
- "metadata": {
- "name": "",
- "signature": "sha256:fe5e092c877ff6677e6a5e3ccdd3dedece58eaf02a85044a49674acc32664be2"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h1>Chapter 36: Complex Waveforms</h1>"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 1, page no. 643</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "V = 240; # in Volts\n",
- "f = 50; # in Hz\n",
- "x = 0.2;\n",
- "phi3 = 3*math.pi/4; # in Rad\n",
- "\n",
- " #calculation:\n",
- "Vamp = V*2**0.5\n",
- "w = 2*math.pi*f\n",
- "T = 1/f\n",
- "V3 = Vamp*x\n",
- "f3 = 3*f\n",
- "w3 = 3*w\n",
- "\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n voltage, V =\",round(Vamp,1),\"sin(\",round(w,1),\"t) + \",round(V3,1),\"sin(\", round(w3,1),\"t - \", round(phi3,1),\") volts\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- " voltage, V = 339.4 sin( 314.2 t) + 67.9 sin( 942.5 t - 2.4 ) volts"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 3, page no. 648</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "A1 = 0.100;# in amperes\n",
- "A3 = 0.020;# in amperes\n",
- "A5 = 0.010;# in amperes\n",
- "\n",
- " #calculation:\n",
- " #the rms value of current is given by\n",
- "Irms = ((A1**2 + A3**2 + A5**2)/2)**0.5\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n the rms value of current is \",round(Irms*1000,2),\" mA\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- " the rms value of current is 72.46 mA"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 4, page no. 649</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "A1 = 10;# in volts\n",
- "A3 = 3;# in volts\n",
- "A5 = 2;# in volts\n",
- "\n",
- "#calculation:\n",
- " #the rms value of voltage is given by\n",
- "Vrms = ((A1**2 + A3**2 + A5**2)/2)**0.5\n",
- " #the mean value of voltage is given by\n",
- " #x = wt\n",
- "Vav = (1/math.pi)*((10 + 1 + 2/5)-(-10 - 1 - 2/5))\n",
- " #form factor is given by\n",
- "ff = Vrms/Vav\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n (a)the rms value of voltage is \",round(Vrms,2),\" V\"\n",
- "print \"\\n (b)the mean value of voltage is \",round(Vav,2),\" V\"\n",
- "print \"\\n (c)form factor is \",round(ff,3),\" \""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- " (a)the rms value of voltage is 7.52 V\n",
- "\n",
- " (b)the mean value of voltage is 7.26 V\n",
- "\n",
- " (c)form factor is 1.036 "
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 5, page no. 649</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "V = 240;# in volts\n",
- "x = 0.3;# for third harmonic\n",
- "y = 0.1;# for fifth harmonic\n",
- "f = 31.83;# in Hz\n",
- "\n",
- " #calculation:\n",
- " #V3 = x*V1\n",
- " #V5 = y*V1\n",
- " #the rms value of the fundamental,\n",
- "V1 = ((V**2)/(1 + x**2 + y**2))**0.5\n",
- " #Rms value of the third harmonic\n",
- "V3 = x*V1\n",
- " #the rms value of the fifth harmonic,\n",
- "V5 = y*V1\n",
- " #Maximum value of the fundamental,\n",
- "V1m = V1*2**0.5\n",
- " #Maximum value of the third harmonic,\n",
- "V3m = V3*2**0.5\n",
- " #Maximum value of the fifth harmonic,\n",
- "V5m = V5*2**0.5\n",
- "w = 2*math.pi*f\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"v = \",round(V1m,2),\"sin\",round(w,2),\"t + \",round(V3m,2),\"sin\",round((3*w),2),\"t + \",round(V5m,2),\"sin\",round((5*w),2),\"t Volts\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "v = 323.62 sin 199.99 t + 97.08 sin 599.98 t + 32.36 sin 999.97 t Volts\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 6, page no. 652</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "A1 = 12;# in amperes\n",
- "A3 = 5;# in amperes\n",
- "A5 = 2;# in amperes\n",
- "R = 20;# in ohms\n",
- "\n",
- "#calculation:\n",
- " #rms current\n",
- "Irms = ((A1**2 + A3**2 + A5**2)/2)**0.5\n",
- " #average power\n",
- "P = R*Irms**2\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n average power \",P,\" W\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- " average power 1730.0 W"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 7, page no. 652</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "Ia1 = 2;# in amperes\n",
- "Ia3 = 0.3;# in amperes\n",
- "Ia5 = 0.1;# in amperes\n",
- "Va1 = 60;# in volts\n",
- "Va3 = 15;# in volts\n",
- "Va5 = 10;# in volts\n",
- "Phii1 = -1*math.pi/6;# in radians\n",
- "Phii3 = -1*math.pi/12;# in radians\n",
- "Phii5 = -8*math.pi/9;# in radians\n",
- "Phiv1 = 0;# in radians\n",
- "Phiv3 = math.pi/4;# in radians\n",
- "Phiv5 = -1*math.pi/2;# in radians\n",
- "\n",
- "\n",
- " #calculation:\n",
- " #rms values;\n",
- "I1 = Ia1/(2**0.5);# in amperes\n",
- "I3 = Ia3/(2**0.5);# in amperes\n",
- "I5 = Ia5/(2**0.5);# in amperes\n",
- "V1 = Va1/(2**0.5);# in volts\n",
- "V3 = Va3/(2**0.5);# in volts\n",
- "V5 = Va5/(2**0.5);# in volts\n",
- " #total power supplied,\n",
- "P = V1*I1*math.cos(Phiv1 - Phii1) + V3*I3*math.cos(Phiv3 - Phii3) + V5*I5*math.cos(Phiv5 - Phii5)\n",
- " #rms current\n",
- "Irms = ((I1**2 + I3**2 + I5**2))**0.5\n",
- " #rms voltage\n",
- "Vrms = ((V1**2 + V3**2 + V5**2))**0.5\n",
- " #overall power factor\n",
- "pf = P/(Vrms*Irms)\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n(a)the total active power supplied to the circuit \",round(P,2),\" W\"\n",
- "print \"\\n(b)overall power factor \",round(pf,2)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- "(a)the total active power supplied to the circuit 53.26 W\n",
- "\n",
- "(b)overall power factor 0.84"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 8, page no. 655</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "R1 = 40;# in ohm\n",
- "L = 7.96E-3;# in Henry\n",
- "C = 25E-6; # in Farad\n",
- "f = 1000; # in Hx\n",
- "\n",
- "#calculation:\n",
- "wL = 2*math.pi*1000*L\n",
- "wC = 2*math.pi*1000*C\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"(a)i = \",round(100/R1,2),\"sin(wt) +\",round(30/R1,2),\"sin(3wt - pi/3) +\",round(10/R1,2),\"sin(5wt - pi/6) A\"\n",
- "print \"(b)i = \",round(100/wL,2),\"sin(wt - pi/2) +\",round(30/(3*wL),2),\"sin(3wt - pi/6) +\",round(10/(5*wL),2),\"sin(5wt - 2pi/3) A\"\n",
- "print \"(c)i = \",round(100*wC,2),\"sin(wt + pi/2) +\",round(30*3*wC,2),\"sin(3wt + 5pi/6) +\",round(10*5*wC,2),\"sin(5wt + pi/3) A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "(a)i = 2.5 sin(wt) + 0.75 sin(3wt - pi/3) + 0.25 sin(5wt - pi/6) A\n",
- "(b)i = 2.0 sin(wt - pi/2) + 0.2 sin(3wt - pi/6) + 0.04 sin(5wt - 2pi/3) A\n",
- "(c)i = 15.71 sin(wt + pi/2) + 14.14 sin(3wt + 5pi/6) + 7.85 sin(5wt + pi/3) A\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 9, page no. 656</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "V1m = 240;# in volts\n",
- "V3m = 40;# in volts\n",
- "V5m = 30;# in volts\n",
- "w1 = 314;# fundamental\n",
- "R = 12;# in ohm\n",
- "L = 0.00955;# in Henry\n",
- "\n",
- " #calculation:\n",
- " #fundamental or first harmonic\n",
- " #inductive reactance,\n",
- "XL1 = w1*L\n",
- " #impedance at the fundamental frequency,\n",
- "Z1 = R + 1j*XL1\n",
- " #Maximum current at fundamental frequency\n",
- "I1m = V1m/Z1\n",
- "I1mag = abs(I1m)\n",
- "phii1 = cmath.phase(complex(I1m.real,I1m.imag))\n",
- " #Third harmonic\n",
- "XL3 = 3*XL1\n",
- " #impedance at the third harmonic frequency,\n",
- "Z3 = R + 1j*XL3\n",
- " #Maximum current at third harmonic frequency\n",
- "I3m = V3m/Z3\n",
- "I3mag = abs(I3m)\n",
- "phii3 = cmath.phase(complex(I3m.real,I3m.imag))\n",
- " #fifth harmonic\n",
- "XL5 = 5*XL1\n",
- " #impedance at the third harmonic frequency,\n",
- "Z5 = R + 1j*XL5\n",
- " #Maximum current at third harmonic frequency\n",
- "I5m = V5m/Z5\n",
- "I5mag = abs(I5m)\n",
- "phii5 = cmath.phase(complex(I5m.real,I5m.imag))\n",
- " #rms voltage\n",
- "Vrms = ((V1m**2 + V3m**2 + V5m**2)/2)**0.5\n",
- " #rms current\n",
- "Irms = ((I1mag**2 + I3mag**2 + I5mag**2)/2)**0.5\n",
- " #power dissipated\n",
- "P = R*Irms**2\n",
- " #overall power factor\n",
- "pf = P/(Vrms*Irms)\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n(a)i = \",round(I1mag,2),\"sin(\",round(w1,2),\"t + (\",round(phii1,2),\")) + \",round(I3mag,2),\"sin(\",round((w1*3),2),\"t + (\",round(phii3,2),\")) + \",round(I5mag,2),\"sin(\",round((w1*5),2),\"t + (\",round(phii5,2),\")) A\"\n",
- "print \"\\n(b)the rms value of current is \",round(Irms,2),\" A\"\n",
- "print \"\\n(c)the rms value of voltage is \",round(Vrms,2),\" V\"\n",
- "print \"\\n(d)the total power dissipated \",round(P,2),\" W\"\n",
- "print \"\\n(e)overall power factor \",round(pf,2)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- "(a)i = 19.4 sin( 314.0 t + ( -0.24 )) + 2.67 sin( 942.0 t + ( -0.64 )) + 1.56 sin( 1570.0 t + ( -0.9 )) A\n",
- "\n",
- "(b)the rms value of current is 13.89 A\n",
- "\n",
- "(c)the rms value of voltage is 173.35 V\n",
- "\n",
- "(d)the total power dissipated 2316.26 W\n",
- "\n",
- "(e)overall power factor 0.96"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 10, page no. 658</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "Vom = 50;# in volts\n",
- "V1m = 200;# in volts\n",
- "V2m = 40;# in volts\n",
- "V4m = 5;# in volts\n",
- "f = 50;# in Hz\n",
- "R = 50;# in ohm\n",
- "C = 100E-6;# in farad\n",
- "phiv1 = 0;# in rad\n",
- "phiv2 = -1*math.pi/2;# in rad\n",
- "phiv4 = math.pi/4;# in rad\n",
- "\n",
- " #calculation:\n",
- " #voltage\n",
- "V1 = V1m*math.cos(phiv1) + 1j*V1m*math.sin(phiv1)\n",
- "V2 = V2m*math.cos(phiv2) + 1j*V2m*math.sin(phiv2)\n",
- "V4 = V4m*math.cos(phiv4) + 1j*V4m*math.sin(phiv4)\n",
- " #Inductance has no effect on a steady current. Hence the d.c. component of the current, i0, is given by\n",
- "Iom = 0\n",
- " #fundamental or first harmonic\n",
- "w1 = 2*math.pi*f\n",
- " #inductive reactance,\n",
- "Xc1 = 1/(w1*C)\n",
- " #impedance at the fundamental frequency,\n",
- "Z1 = R + 1j*Xc1\n",
- " #Maximum current at fundamental frequency\n",
- "I1m = V1/Z1\n",
- "I1mag = abs(I1m)\n",
- "phii1 = cmath.phase(complex(I1m.real,I1m.imag))\n",
- " #second harmonic\n",
- "Xc2 = Xc1/2\n",
- " #impedance at the third harmonic frequency,\n",
- "Z2 = R + 1j*Xc2\n",
- " #Maximum current at third harmonic frequency\n",
- "I2m = V2/Z2\n",
- "I2mag = abs(I2m)\n",
- "phii2 = cmath.phase(complex(I2m.real,I2m.imag))\n",
- " #fourth harmonic\n",
- "Xc4 = Xc1/4\n",
- " #impedance at the third harmonic frequency,\n",
- "Z4 = R + 1j*Xc4\n",
- " #Maximum current at third harmonic frequency\n",
- "I4m = V4/Z4\n",
- "I4mag = abs(I4m)\n",
- "phii4 = cmath.phase(complex(I4m.real,I4m.imag))\n",
- " #rms current\n",
- "Irms = (Iom**2 + (I1mag**2 + I2mag**2 + I4mag**2)/2)**0.5\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"(a)i = \",round(Iom,2),\" + \",round(I1mag,2),\"sin(\",round(w1,2),\"t + (\",round(phii1,2),\")) + \",round(I2mag,2),\"sin(\",round((w1*2),2),\"t + (\",round(phii2,2),\")) + \",round(I4mag,2),\"sin(\",round((w1*4),2),\"t + (\",round(phii4,2),\")) A\"\n",
- "print \"(b)the rms value of current is \",round(Irms,2),\" A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "(a)i = 0.0 + 3.37 sin( 314.16 t + ( -0.57 )) + 0.76 sin( 628.32 t + ( -1.88 )) + 0.1 sin( 1256.64 t + ( 0.63 )) A\n",
- "(b)the rms value of current is 2.45 A\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 11, page no. 659</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "Vom = 25;# in volts\n",
- "V1m = 100;# in volts\n",
- "V3m = 40;# in volts\n",
- "V5m = 20;# in volts\n",
- "w1 = 10000;# fundamental\n",
- "R = 5;# in ohm\n",
- "L = 500E-6;# in Henry\n",
- "phiv1 = 0;# in rad\n",
- "phiv3 = math.pi/6;# in rad\n",
- "phiv5 = math.pi/12;# in rad\n",
- "\n",
- " #calculation:\n",
- " #voltage\n",
- "V1 = V1m*math.cos(phiv1) + 1j*V1m*math.sin(phiv1)\n",
- "V3 = V3m*math.cos(phiv3) + 1j*V3m*math.sin(phiv3)\n",
- "V5 = V5m*math.cos(phiv5) + 1j*V5m*math.sin(phiv5)\n",
- " #Inductance has no effect on a steady current. Hence the d.c. component of the current, i0, is given by\n",
- "Iom = Vom/R\n",
- " #fundamental or first harmonic\n",
- " #inductive reactance,\n",
- "XL1 = w1*L\n",
- " #impedance at the fundamental frequency,\n",
- "Z1 = R + 1j*XL1\n",
- " #Maximum current at fundamental frequency\n",
- "I1m = V1/Z1\n",
- "I1mag = abs(I1m)\n",
- "phii1 = cmath.phase(complex(I1m.real,I1m.imag))\n",
- "#Third harmonic\n",
- "XL3 = 3*XL1\n",
- " #impedance at the third harmonic frequency,\n",
- "Z3 = R + 1j*XL3\n",
- " #Maximum current at third harmonic frequency\n",
- "I3m = V3/Z3\n",
- "I3mag = abs(I3m)\n",
- "phii3 = cmath.phase(complex(I3m.real,I3m.imag))\n",
- " #fifth harmonic\n",
- "XL5 = 5*XL1\n",
- " #impedance at the third harmonic frequency,\n",
- "Z5 = R + 1j*XL5\n",
- " #Maximum current at third harmonic frequency\n",
- "I5m = V5/Z5\n",
- "I5mag = abs(I5m)\n",
- "phii5 = cmath.phase(complex(I5m.real,I5m.imag))\n",
- " #rms current\n",
- "Irms = (Iom**2 + (I1mag**2 + I3mag**2 + I5mag**2)/2)**0.5\n",
- " #power dissipated\n",
- "P = R*Irms**2\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n(a)i = \",round(Iom,2),\" + \",round(I1mag,2),\"sin(\",round(w1,2),\"t + (\",round(phii1,2),\")) + \",round(I3mag,2),\"sin(\",round((w1*3),2),\"t + (\",round(phii3,2),\")) + \",round(I5mag,2),\"sin(\",round((w1*5),2),\"t + (\",round(phii5,2),\")) A\"\n",
- "print \"\\n(b)the rms value of current is \",round(Irms,2),\" A\"\n",
- "print \"\\n(c)the total power dissipated \",round(P,3),\" W\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- "(a)i = 5.0 + 14.14 sin( 10000.0 t + ( -0.79 )) + 2.53 sin( 30000.0 t + ( -0.73 )) + 0.78 sin( 50000.0 t + ( -1.11 )) A\n",
- "\n",
- "(b)the rms value of current is 11.34 A\n",
- "\n",
- "(c)the total power dissipated 642.538 W\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 12, page no. 661</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "Vom = 30;# in volts\n",
- "V1m = 40;# in volts\n",
- "V2m = 25;# in volts\n",
- "V4m = 15;# in volts\n",
- "Iom = 0;# in amperes\n",
- "I1m = 0.743;# in Amperes\n",
- "I2m = 0.781;# in Amperes\n",
- "I4m = 0.636;# in Amperes\n",
- "phii1 = 1.190;# in rad\n",
- "phii2 = 0.896;# in rad\n",
- "phii4 = 0.559;# in rad\n",
- "w = 1000;# in rad\n",
- "\n",
- " #calculation:\n",
- " #the average power P is given by\n",
- "P = Vom*Iom+(0.707*V1m)*(0.707*I1m)*math.cos(phii1)+(0.707*V2m)*(0.707*I2m)*math.cos(phii2) + (0.707*V4m)*(0.707*I4m)*math.cos(phii4)\n",
- " #rms current\n",
- "Irms = (Iom**2 + (I1m**2 + I2m**2 + I4m**2)/2)**0.5\n",
- " #resistance R\n",
- "R = P/(Irms**2)\n",
- " #impedance\n",
- "Z1 = V1m/I1m\n",
- " #Xc1\n",
- "Xc1 = (Z1**2 - R**2)**0.5\n",
- " #capacitance\n",
- "C = 1/(w*Xc1)\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n(a)the average power P is \",round(P,2),\" W\"\n",
- "print \"\\n(c)the resistance R \",round(R,2),\" ohm and capacitance \",round(C*1E6,2),\"uF\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- "(a)the average power P is 15.66 W\n",
- "\n",
- "(c)the resistance R 19.99 ohm and capacitance 20.01 uF\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 13, page no. 662</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "V1m = 300;# in volts\n",
- "V3m = 120;# in volts\n",
- "phiv1 = 0;# in rad\n",
- "phiv2 = 0.698;# in rad\n",
- "w1 = 314;# in rad\n",
- "C = 2.123E-6;# in farads\n",
- "R1 = 560;# in ohms\n",
- "R2 = 2000;# in Ohm\n",
- "\n",
- "#calculation:\n",
- " #voltage\n",
- "V1 = V1m*math.cos(phiv1) + 1j*V1m*math.sin(phiv1)\n",
- "V3 = V3m*math.cos(phiv2) + 1j*V3m*math.sin(phiv2)\n",
- " #capacitive reactance,\n",
- "Xc1 = 1/(w1*C)\n",
- " #impedance at the fundamental frequency,\n",
- "Z1 = R1 - 1j*Xc1*R2/(R2 - 1j*Xc1)\n",
- " #Maximum current at fundamental frequency\n",
- "I1m = V1/Z1\n",
- "I1mag = abs(I1m)\n",
- "phii1 = cmath.phase(complex(I1m.real,I1m.imag))\n",
- " #Third harmonic\n",
- "Xc3 = Xc1/3\n",
- " #impedance at the third harmonic frequency,\n",
- "Z3 = R1 - 1j*Xc3*R2/(R2 - 1j*Xc3)\n",
- "I1m = V1m/Z1\n",
- "I1mag = abs(I1m)\n",
- "phii1 = cmath.phase(complex(I1m.real,I1m.imag))\n",
- " #Maximum current at third harmonic frequency\n",
- "I3m = V3/Z3\n",
- "I3mag = abs(I3m)\n",
- "phii3 = cmath.phase(complex(I3m.real,I3m.imag))\n",
- " #Percentage harmonic content of the supply current is given by\n",
- "percent = I3mag*100/I1mag\n",
- " #total active power\n",
- "P = (0.707*V1m)*(0.707*I1mag)*math.cos(phiv1 - phii1) + (0.707*V3m)*(0.707*I3m)*math.cos(phiv2 - phii3)\n",
- "\n",
- "I1 = I1m*R2/(R2 - 1j*Xc1)\n",
- "I3 = I3m*R2/(R2 - 1j*Xc3)\n",
- "\n",
- "I1nmag = abs(I1)\n",
- "phini1 = cmath.phase(complex(I1.real,I1.imag))\n",
- "I3nmag = abs(I3)\n",
- "phini3 = cmath.phase(complex(I3.real,I3.imag))\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n(a)supply current, i=\", round(I1mag,3),\"sin(\", w1,\"t +\",round(phii1,3),\") + \",round(I3mag,3),\"sin(\", 3*w1,\"t +\",round(phii3,3),\") A\"\n",
- "print \"\\n(b)Percentage harmonic content of the supply current is \",round(percent,2),\" percent\"\n",
- "print \"\\n(c)total active power is \",round(abs(P),2),\" W\"\n",
- "print \"\\n(d)Voltage, v1 =\", round(I1mag*R1,3),\"sin(\", w1,\"t +\",round(phii1,3),\") + \",round(I3mag*R1,3),\"sin(\", 3*w1,\"t +\",round(phii3,3),\") A\"\n",
- "print \"\\n(e)current, ic =\", round(I1nmag,3),\"sin(\", w1,\"t +\",round(phini1,3),\") + \",round(I3nmag,3),\"sin(\", 3*w1,\"t +\",round(phini3,3),\") A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- "(a)supply current, i= 0.187 sin( 314 t + 0.643 ) + 0.145 sin( 942 t + 1.305 ) A\n",
- "\n",
- "(b)Percentage harmonic content of the supply current is 77.57 percent\n",
- "\n",
- "(c)total active power is 25.34 W\n",
- "\n",
- "(d)Voltage, v1 = 104.996 sin( 314 t + 0.643 ) + 81.45 sin( 942 t + 1.305 ) A\n",
- "\n",
- "(e)current, ic = 0.15 sin( 314 t + 1.287 ) + 0.141 sin( 942 t + 1.55 ) A"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 14, page no. 664</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "V1m = 400;# in volts\n",
- "V3m = 10;# in volts\n",
- "C = 0.2E-6;# in farads\n",
- "R = 2;# in ohms\n",
- "L = 0.5;# in Henry\n",
- "\n",
- " #calculation:\n",
- " #Resonance with the third harmonic means that\n",
- "w = (1/(9*L*C))**0.5\n",
- " #fundamental frequency, f\n",
- "f = w/(2*math.pi)\n",
- " #At the fundamental frequency,\n",
- " #impedance Z1\n",
- "Z1 = R + 1j*(w*L - 1/(w*C))\n",
- "Z1mag = abs(Z1)\n",
- "phiZ1 = cmath.phase(complex(Z1.real,Z1.imag))\n",
- " #Maximum value of current at the fundamental frequency,\n",
- "I1m = V1m/Z1mag\n",
- " #At the third harmonic frequency,\n",
- "Z3 = R + 1j*(3*w*L - 1/(3*w*C))\n",
- "Z3mag = abs(Z3)\n",
- "phiZ3 = cmath.phase(complex(Z3.real,Z3.imag))\n",
- " #Maximum value of current at the third harmonic frequency,\n",
- "I3m = V3m/Z3\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"(a)fundamental frequency for resonance with the third harmonic is \",round(f,2),\" Hz\"\n",
- "print \"(b)Maximum value of current at fundamental freq. is\",round(abs(I1m),3),\"A \"\n",
- "print \"and at the third harmonic frequency \", abs(I3m),\" A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "(a)fundamental frequency for resonance with the third harmonic is 167.76 Hz\n",
- "(b)Maximum value of current at fundamental freq. is 0.095 A \n",
- "and at the third harmonic frequency 5.0 A\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "<h3>Example 15, page no. 665</h3>"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "from __future__ import division\n",
- "import math\n",
- "import cmath\n",
- "#initializing the variables:\n",
- "V1m = 800;# in volts\n",
- "f = 50;# in Hz\n",
- "x = 0.015;\n",
- "C = 0.122E-6;# in farads\n",
- "R = 5;# in ohms\n",
- "L = 0.369;# in Henry\n",
- "\n",
- " #calculation:\n",
- " #voltage at nth harmonic\n",
- "Vnm = x*V1m\n",
- "w = 2*math.pi*f\n",
- " #For resonance at the nth harmonic nwL = 1/nwC\n",
- "n = 1/(w*(L*C)**0.5)\n",
- " #At resonance, impedance\n",
- "Zn = R\n",
- " #the maximum value of current at the nth harmonic\n",
- "Inm = Vnm/Zn\n",
- " #capacitive reactance, at nth harmonic\n",
- "Xcn = 1/(n*w*C)\n",
- " #the p.d. across the capacitor at the nth harmonic\n",
- "Vcn = Inm*Xcn\n",
- " #At the fundamental frequency, inductive reactance,\n",
- "XL1 = w*L\n",
- " #capacitive reactance\n",
- "Xc1 = 1/(w*C)\n",
- " #Impedance at the fundamental frequency,\n",
- "Z1 = R + 1j*(XL1 - Xc1)\n",
- "Z1mag = abs(Z1)\n",
- "phiZ1 = cmath.phase(complex(Z1.real,Z1.imag))\n",
- " #Maximum value of current at the fundamental frequency,\n",
- "I1m = V1m/Z1mag\n",
- "\n",
- "\n",
- "#Results\n",
- "print \"\\n\\n Result \\n\\n\"\n",
- "print \"\\n(a)n = \",round(n,2),\"\"\n",
- "print \"\\n(b)the maximum value of current at the nth harmonic \",round(Inm,2),\" A\"\n",
- "print \"\\n(c)the p.d. across the capacitor at the nth harmonic is \",round(Vcn,2),\"\"\n",
- "print \"\\n(d)the maximum value of the fundamental current. \",round(I1m,2),\" A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "\n",
- " Result \n",
- "\n",
- "\n",
- "\n",
- "(a)n = 15.0 \n",
- "\n",
- "(b)the maximum value of current at the nth harmonic 2.4 A\n",
- "\n",
- "(c)the p.d. across the capacitor at the nth harmonic is 4173.92 \n",
- "\n",
- "(d)the maximum value of the fundamental current. 0.03 A"
- ]
- }
- ],
- "prompt_number": 14
- }
- ],
- "metadata": {}
- }
- ]
-}
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