From c8733e4b6b4bffcddf7eb45ff1c72ccc837aa3af Mon Sep 17 00:00:00 2001 From: Jovina Dsouza Date: Tue, 22 Jul 2014 00:00:04 +0530 Subject: adding book --- .../chapter_28-checkpoint_1.ipynb | 736 +++++++++++++++++++++ 1 file changed, 736 insertions(+) create mode 100755 Electrical_Circuit_Theory_And_Technology/chapter_28-checkpoint_1.ipynb (limited to 'Electrical_Circuit_Theory_And_Technology/chapter_28-checkpoint_1.ipynb') diff --git a/Electrical_Circuit_Theory_And_Technology/chapter_28-checkpoint_1.ipynb b/Electrical_Circuit_Theory_And_Technology/chapter_28-checkpoint_1.ipynb new file mode 100755 index 00000000..35880e50 --- /dev/null +++ b/Electrical_Circuit_Theory_And_Technology/chapter_28-checkpoint_1.ipynb @@ -0,0 +1,736 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Chapter 28: Series resonance and Q-factor

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

Example 1, page no. 492

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine at what frequency resonance occurs, and (b) the current flowing at resonance.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "R = 10;# in ohms\n", + "C = 40e-6;# IN fARADS\n", + "L = 0.075;# IN Henry\n", + "V = 200;# in Volts\n", + "\n", + "#calculation:\n", + " #Resonant frequency,\n", + "fr = 1/(2*math.pi*((L*C)**0.5))\n", + " #Current at resonance, I\n", + "I = V/R\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)Resonant frequency = \",round(fr,2),\" Hz\\n\"\n", + "print \"\\n (b)Current at resonance, I is \",I,\" A\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)Resonant frequency = 91.89 Hz\n", + "\n", + "\n", + " (b)Current at resonance, I is 20.0 A\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 2, page no. 493

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the value of capacitor C for series resonance.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "R = 8;# in ohms\n", + "L = 0.010;# IN Henry\n", + "f = 1000;# in Hz\n", + "\n", + "#calculation:\n", + " #At resonance\n", + " #capacitance C\n", + "C = 1/(L*(2*math.pi*f)**2)\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n capacitance, C is \",round(C*1E6,2),\"uF\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " capacitance, C is 2.53 uF\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 3, page no. 493

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the values of (a) the stray capacitance CS, and (b) the coil inductance L.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "C1 = 1000e-12;# IN fARADS\n", + "C2 = 500e-12;# IN fARADS\n", + "fr1 = 92500;# in Hz\n", + "fr2 = 127800;# in Hz\n", + "\n", + "#calculation:\n", + " #For a series R\u2013L\u2013C circuit the resonant frequency fr is given by:\n", + " #fr = 1/(2pi*(L*C)**2)\n", + "Cs = ((C1 - C2)/((fr2/fr1)**2 - 1)) - C2\n", + "L = 1/((C1 + Cs)*(2*math.pi*fr1)**2)\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)stray capacitance, Cs is \",round(Cs*1E12,2),\"pF\\n\"\n", + "print \"\\n (b)inductance, L is \",round(L*1000,2),\"mH\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)stray capacitance, Cs is 50.13 pF\n", + "\n", + "\n", + " (b)inductance, L is 2.82 mH\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 4, page no. 497

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine for this condition (a) the value of inductance L, (b) the p.d. across each component and (c) the Q-factor.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "R = 10;# in ohms\n", + "C = 5e-6;# IN fARADS\n", + "rv = 20;#in volts\n", + "thetav = 0;# in degrees\n", + "f = 318.3;# in Hz\n", + "\n", + "#calculation:\n", + "wr = 2*math.pi*f\n", + " #The maximum voltage across the resistance occurs at resonance when the current is a maximum. \n", + " #At resonance,L = 1/c*wr**2\n", + "L = 1/(C*wr**2)\n", + " #voltage\n", + "V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180)\n", + " #Current at resonance Ir\n", + "Ir = V/R\n", + " #p.d. across resistance, VR\n", + "VR = Ir*R\n", + " #inductive reactance, XL\n", + "XL = wr*L\n", + " #p.d. across inductance, VL\n", + "VL = Ir*(1j*XL)\n", + " #capacitive reactance, Xc\n", + "Xc = 1/(wr*C)\n", + " #p.d. across capacitor, Vc\n", + "Vc = Ir*(-1j*Xc)\n", + " #Q-factor at resonance, Qr\n", + "Qr = VL.imag/V\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)inductance, L is \",round(L*1000,2),\"mH\\n\"\n", + "print \"\\n (b)p.d. across resistance, VR is \",VR,\" V, p.d. across inductance, VL \",round( VL.imag,2),\"j V \"\n", + "print \"and p.d. across capacitor, VC \",round(Vc.imag,2),\" V\\n\"\n", + "print \"\\n (c)Q-factor at resonance, Qr is \",round(abs(Qr),2),\" \\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)inductance, L is 50.0 mH\n", + "\n", + "\n", + " (b)p.d. across resistance, VR is (20+0j) V, p.d. across inductance, VL 200.01 j V \n", + "and p.d. across capacitor, VC -200.01 V\n", + "\n", + "\n", + " (c)Q-factor at resonance, Qr is 10.0 \n", + "\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 5, page no. 502

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#determine (a) the resonant frequency, (b) the value of the p.d. across the capacitor at the resonant frequency, \n", + "#(c) the frequency at which the p.d. across the capacitor is a maximum, and \n", + "#(d) the value of the maximum voltage across the capacitor.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "R = 80;# in ohms\n", + "C = 0.4e-6;# IN fARADS\n", + "L = 0.020;# IN Henry\n", + "Vm = 12;#in volts\n", + "\n", + "#calculation:\n", + " #Resonant frequency,\n", + "fr = 1/(2*math.pi*((L*C)**0.5))\n", + "wr = 2*math.pi*fr\n", + " #Q = wr*L/R\n", + "Q = wr*L/R\n", + "Vc = Q*Vm\n", + " #the frequency f at which VC is a maximum value,\n", + "f = fr*(1 - (1/(2*Q*Q)))**0.5\n", + " #the maximum value of the p.d. across the capacitor is given by:\n", + "Vcm = Vc/((1 - (1/(2*Q*Q)))**0.5)\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)The resonant frequency is \",round(fr,2),\" Hz\\n\"\n", + "print \"\\n (b)the value of the p.d. across the capacitor at the resonant frequency \",round(Vc,2),\" V\\n\"\n", + "print \"\\n (c)the frequency f at which Vc is a maximum value, is \",round(f,2),\" Hz\\n\"\n", + "print \"\\n (d)the maximum value of the p.d. across the capacitor is \",round(Vcm,2),\" V\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)The resonant frequency is 1779.41 Hz\n", + "\n", + "\n", + " (b)the value of the p.d. across the capacitor at the resonant frequency 33.54 V\n", + "\n", + "\n", + " (c)the frequency f at which Vc is a maximum value, is 1721.52 Hz\n", + "\n", + "\n", + " (d)the maximum value of the p.d. across the capacitor is 34.67 V\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 6, page no. 503

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the overall Q-factor of the circuit.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "QL = 60;# Q-factor\n", + "Qc = 390;# Q-factor\n", + "\n", + "#calculation:\n", + "QT = QL*Qc/(QL + Qc)\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n the overall Q-factor is \",QT" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " the overall Q-factor is 52.0" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 7, page no. 505

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the bandwidth of the filter.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "R = 5;# in ohms\n", + "L = 0.010;# IN Henry\n", + "fr = 10000;# in Hz\n", + "\n", + "#calculation:\n", + "wr = 2*math.pi*fr\n", + " #Q-factor at resonance is given by\n", + "Qr = wr*L/R\n", + " #Since Qr = fr/(f2 - f1),\n", + "bw = fr/Qr\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n bandwidth of the filter is \",round(bw,2),\" Hz\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " bandwidth of the filter is 79.58 Hz\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 8, page no. 507

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#determine the values of (a) the inductance, and (b) the capacitance. Find also (c) the bandwidth,\n", + "#(d) the lower and upper half-power frequencies and (e) the value of the circuit impedance at the half-power frequencies\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "Zr = 50;# in ohms\n", + "fr = 1200;# in Hz\n", + "Qr = 30;# Q-factor\n", + "\n", + "#calculation:\n", + " #At resonance the circuit impedance, Z\n", + "R = Zr\n", + "wr = 2*math.pi*fr\n", + " #Q-factor at resonance is given by Qr = wr*L/R, then L is\n", + "L = Qr*R/wr\n", + " #At resonance r*L = 1/(wr*C)\n", + " #capacitance, C\n", + "C = 1/(L*wr*wr)\n", + " #bandwidth,.(f2 \u2212 f1)\n", + "bw = fr/Qr\n", + " #upper half-power frequency, f2\n", + "f2 = (bw + ((bw**2) + 4*(fr**2))**0.5)/2\n", + " #lower half-power frequency, f1\n", + "f1 = f2 - bw\n", + " #At the half-power frequencies, current I\n", + " #I = 0.707*Ir\n", + " #Hence impedance\n", + "Z = (2**0.5)*R\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)inductance, L is \",round(L*1000,2),\"mH\\n\"\n", + "print \"\\n (b)capacitance, C is \",round(C*1E9,2),\"nF\\n\"\n", + "print \"\\n (c)bandwidth is \",round(bw,2),\" Hz\\n\"\n", + "print \"\\n (d)the upper half-power frequency, f2 is \",round(f2,2),\" Hz \"\n", + "print \" and the lower half-power frequency, f1 is \",round(f1,2),\" Hz\\n\"\n", + "print \"\\n (e)impedance at the half-power frequencies is \",round(Z,2),\" ohm\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)inductance, L is 198.94 mH\n", + "\n", + "\n", + " (b)capacitance, C is 88.42 nF\n", + "\n", + "\n", + " (c)bandwidth is 40.0 Hz\n", + "\n", + "\n", + " (d)the upper half-power frequency, f2 is 1220.17 Hz \n", + " and the lower half-power frequency, f1 is 1180.17 Hz\n", + "\n", + "\n", + " (e)impedance at the half-power frequencies is 70.71 ohm\n", + "\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 9, page no. 508

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the value of (a) the circuit resistance,\n", + "#(b) the circuit inductance, (c) the circuit capacitance, and\n", + "#(d) the voltage across the capacitor\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "V = 0.2;# in Volts\n", + "I = 0.004;# in Amperes\n", + "fr = 3000;# in Hz\n", + "Qr = 100;# Q-factor\n", + "\n", + "#calculation:\n", + "wr = 2*math.pi*fr\n", + " #At resonance, impedance\n", + "Z = V/I\n", + " #At resonance the circuit impedance, Z\n", + "R = Z\n", + " #Q-factor at resonance is given by Qr = wr*L/R, then L is\n", + "L = Qr*R/wr\n", + " #At resonance r*L = 1/(wr*C)\n", + " #capacitance, C\n", + "C = 1/(L*wr*wr)\n", + " #Q-factor at resonance in a series circuit represents the voltage magnification Qr = Vc/V, then Vc is\n", + "Vc = Qr*V\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)the circuit resistance is \",round(R,2),\" ohm\\n\"\n", + "print \"\\n (b)inductance, L is \",round(L*1000,2),\"mH\\n\"\n", + "print \"\\n (c)capacitance, C is \",round(C*1E9,2),\"nF\\n\"\n", + "print \"\\n (d)the voltage across the capacitor is \",round(Vc,2),\" V\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)the circuit resistance is 50.0 ohm\n", + "\n", + "\n", + " (b)inductance, L is 265.26 mH\n", + "\n", + "\n", + " (c)capacitance, C is 10.61 nF\n", + "\n", + "\n", + " (d)the voltage across the capacitor is 20.0 V\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 10, page no. 509

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine (a) the resonant frequency, (b) the Q-factor at resonance, (c) the bandwidth,\n", + "#and (d) the lower and upper -3dB frequencies.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "R = 8.84;# in ohms\n", + "L = 0.3518;# IN Henry\n", + "C = 20e-6;# IN fARADS\n", + "\n", + "#calculation:\n", + " #Resonant frequency,\n", + "fr = 1/(2*math.pi*((L*C)**0.5))\n", + "wr = 2*math.pi*fr\n", + " #Q-factor at resonance, Q = wr*L/R\n", + "Qr = wr*L/R\n", + " #bandwidth,.(f2 \u2212 f1)\n", + "bw = fr/Qr\n", + " #the lower \u22123 dB frequency\n", + "f1 = fr - bw/2\n", + " #the upper \u22123 dB frequency\n", + "f2 = fr + bw/2\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)Resonant frequency, fr is \",round(fr,2),\" Hz\\n\"\n", + "print \"\\n (b)Q-factor at resonance is \",round(Qr,2),\"\\n\"\n", + "print \"\\n (c)Bandwidth is \",round(bw,2),\" Hz\\n\"\n", + "print \"\\n (d)the lower -3dB frequency, f1 is \",round(f1,2),\" Hz \"\n", + "print \" and the upper -3dB frequency, f2 is \",round(f2,2),\" Hz\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)Resonant frequency, fr is 60.0 Hz\n", + "\n", + "\n", + " (b)Q-factor at resonance is 15.0 \n", + "\n", + "\n", + " (c)Bandwidth is 4.0 Hz\n", + "\n", + "\n", + " (d)the lower -3dB frequency, f1 is 58.0 Hz \n", + " and the upper -3dB frequency, f2 is 62.0 Hz\n", + "\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Example 11, page no. 511

" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Determine the current flowing in the circuit when the input voltage is 7.56/_0\u00b0 V and the frequency is \n", + "#(a) the resonant frequency, (b) a frequency 3% above the resonant frequency\n", + "#(c) the impedance of the circuit when the frequency is 3% above the resonant frequency.\n", + "from __future__ import division\n", + "import math\n", + "import cmath\n", + "#initializing the variables:\n", + "R = 15;# in ohms\n", + "L = 0.008;# IN Henry\n", + "C = 0.3e-6;# IN fARADS\n", + "rv = 7.56;#in volts\n", + "thetav = 0;# in degrees\n", + "x = 0.03;\n", + "\n", + "#calculation:\n", + " #Resonant frequency,\n", + "fr = 1/(2*math.pi*((L*C)**0.5))\n", + "wr = 2*math.pi*fr\n", + " #At resonance,\n", + "Zr = R\n", + " #voltage\n", + "V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180)\n", + " #Current at resonance\n", + "Ir = V/Zr\n", + " #Q-factor at resonance, Q = wr*L/R\n", + "Qr = wr*L/R\n", + " #If the frequency is 3% above fr, then\n", + "de = x\n", + "I = Ir/(1 + (2*de*Qr*1j))\n", + "Z = V/I\n", + "\n", + "\n", + "#Results\n", + "print \"\\n\\n Result \\n\\n\"\n", + "print \"\\n (a)Current at resonance, Ir is \",round(abs(Ir),2),\" A\\n\"\n", + "print \"\\n (b)current flowing in the circuit when frequency 3 percent\"\n", + "print \" above the resonant frequency is \",round(I.real,2),\" + (\",round( I.imag,2),\")i A\\n\"\n", + "print \"\\n (c)impedance of the circuit when the frequency is 3 percent\"\n", + "print \" above the resonant frequency is \",round(Z.real,2),\" + (\",round(Z.imag,2),\")i A\\n\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Result \n", + "\n", + "\n", + "\n", + " (a)Current at resonance, Ir is 0.5 A\n", + "\n", + "\n", + " (b)current flowing in the circuit when frequency 3 percent\n", + " above the resonant frequency is 0.35 + ( -0.23 )i A\n", + "\n", + "\n", + " (c)impedance of the circuit when the frequency is 3 percent\n", + " above the resonant frequency is 15.0 + ( 9.8 )i A\n", + "\n" + ] + } + ], + "prompt_number": 4 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit