From 6846da7f30aadc7b3812538d1b1c9ef2e465a922 Mon Sep 17 00:00:00 2001
From: hardythe1
Date: Fri, 25 Jul 2014 12:35:04 +0530
Subject: removing unwanted:
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-{
- "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