{ "metadata": { "name": "", "signature": "sha256:3733f4bc277677bc2f9c52d22638fa67f4c2b3f988678afdd8082febee12d607" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 11 Bridges" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.1 Page no 323" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R2=15*10**3 #ohm\n", "R3=40*10**3 #ohm\n", "R1=10.0*10**3 #ohm\n", "\n", "#Calculation\n", "Rx=(R2*R3)/R1\n", "\n", "#Result \n", "print\"Value of unknown resistance is \",Rx*10**-3,\"Kohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Value of unknown resistance is 60.0 Kohm\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.2 Page no 325" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "E=6 #Volts\n", "R1=1.0*10**3 #ohm\n", "R2=2.5*10**3 #ohm\n", "R3=3.5*10**3 #ohm\n", "R4=10*10**3 #ohm\n", "Rg=300.0 #ohm\n", "\n", "#Calculation\n", "Eth=E*((R4/(R2+R4))-(R3/(R1+R3)))\n", "Rth=((R1*R3)/(R1+R3))+((R2*R4)/(R2+R4))\n", "Ig=Eth/(Rth+Rg)\n", "\n", "#Result\n", "print\"Current through galvanometer is \", round(Ig*10**6,0),\"micro A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Current through galvanometer is 43.0 micro A\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.3 Page no 327" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "E=10 #Volts\n", "r=35\n", "R=700 #ohm\n", "Rth=700 #ohm\n", "Rg=125 #ohm\n", "\n", "#Calculation\n", "Eth=E*r/(4.0*R)\n", "Ig=Eth/(Rth+Rg)\n", "print\"current through the galvanometer is \", round(Ig*10**6,1),\"micro A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "current through the galvanometer is 151.5 micro A\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.4 Page no 331" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R1=5 #ohm\n", "Rb=1 #ohm\n", "Ra=1000.0 #ohm\n", "\n", "#Calculation\n", "R2=R1/0.5\n", "Rx=(Rb*R2)/Ra\n", "\n", "#Result\n", "print\"Value of Rx is \",Rx,\"ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Value of Rx is 0.01 ohm\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.5 Page no 333" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R1=5.0*10**3 #ohm\n", "R2=5.0*10**3 #ohm\n", "R3=5.0*10**3 #ohm\n", "E=6 #Volts\n", "RV=4.5*10**3 #ohm\n", "r=500\n", "\n", "#Calculation\n", "Rv=(R2*R3)/R1\n", "es=E*((R3/(R1+R3))-(RV/(R2+RV)))\n", "\n", "#Result\n", "print\"(i) The bridge is balanced when the temperature is 80 degree.\"\n", "print\"The amplitude of the error signal at 60 degree \", round(es,3),\"V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) The bridge is balanced when the temperature is 80 degree.\n", "The amplitude of the error signal at 60 degree 0.158 V\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.6 (a) Page no 337" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R1=10*10**3 #ohm\n", "R2=50*10**3 #ohm\n", "R3=100*10**3 #ohm\n", "C3=100*10**-6 #farad\n", "\n", "#Calculation\n", "Rx=(R2*R3)/R1\n", "Cx=(R1*C3)/R2\n", "\n", "#Result\n", "print\"The unknown capacitance is \", Cx*10**6,\"micro F\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The unknown capacitance is 20.0 micro F\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.6 (b) Page no 338" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R1=2000.0 #ohm\n", "R2=2850.0 #ohm\n", "R4=52 #ohm\n", "C4=0.4*10**-6 #Farad\n", "f=400 #Hz\n", "\n", "#Calculation\n", "import math\n", "Rx=(R1*R4)/R2\n", "Cx=(R2*C4)/R1\n", "A=2*math.pi*f*Cx*Rx\n", "\n", "#Result\n", "print\"Loss angle of capacitor is \", round(A,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Loss angle of capacitor is 0.052\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.7 Page no 339" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "L3=10*10**-3 #H\n", "R1=10.0*10**3 #ohm\n", "R2=40*10**3 #ohm\n", "R3=100*10**3 #ohm\n", "\n", "#Calculation\n", "Rx=(R2*R3)/R1\n", "Lx=(R2*L3)/R1\n", "\n", "#Result\n", "print\"Equivalent unknown resistance is \", Lx*10**3,\"mH\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Equivalent unknown resistance is 40.0 mH\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.8 (a) Page no 341" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "C1=0.01*10**-6 #Farad\n", "R1=470.0*10**3 #ohm\n", "R2=5.1*10**3 #ohm\n", "R3=100*10**3 #ohm\n", "\n", "#Calculation\n", "Rx=(R2*R3)/R1\n", "Lx=R2*R3*C1\n", "\n", "#Result\n", "print\"The value of unknown impedence \", Lx,\"H\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of unknown impedence 5.1 H\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.8 (b) Page no 341" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R1=32.7 #ohm\n", "L1=50*10**-3 #H\n", "R2=1.36 #ohm\n", "R3=100.0 #ohm\n", "R4=100 #ohm\n", "\n", "#Calculation\n", "r=((R4*R1)/R3)-R2\n", "L2=L1*(R4/R3)\n", "\n", "#Result\n", "print\"Resistance of the coil is \",r,\"ohm \\nInductance of the coil is \" ,L2*10**3,\"mH\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resistance of the coil is 31.34 ohm \n", "Inductance of the coil is 50.0 mH\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.9 (a) Page no 343" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "w=3000 #rad/s\n", "R2=10*10**3 #ohm\n", "R1=2*10**3 #ohm\n", "C1=1*10**-6 #farad\n", "R3=1*10**3 #ohm\n", "\n", "#Calculation\n", "Rx=(w**2*R1*R2*R3*C1**2)/(1+w**2*R1**2*C1**2)\n", "Lx=(R2*R3*C1)/(1+w**2*R1**2*C1**2)\n", "\n", "#Result\n", "print\" series equivalent impedence is \", round(Lx*10**3,0),\"mH\",\"\\n Series equivqlent resistance is \",round(Rx*10**-3,2),\"Kohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " series equivalent impedence is 270.0 mH \n", " Series equivqlent resistance is 4.86 Kohm\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.9 (b) Page no 343" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R2=1000 #ohm\n", "R3=16500 #ohm\n", "R4=800 #ohm\n", "C4=2*10**-6 #F\n", "f=50 #Hz\n", "\n", "#Calculation\n", "import math\n", "w=2*math.pi*f\n", "Lx=(R2*R3*C4)/(1+(w**2*C4**2*R4**2))\n", "Rx=(w**2*C4**2*R4*R2*R3)/(1+w**2*C4**2*R4**2)\n", "\n", "#Result\n", "print\"Resistance of the coil is \", round(Rx*10**-3,1),\"Kohm\"\n", "print\"Inductance of the coil is \",round(Lx,1),\"H\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resistance of the coil is 4.2 Kohm\n", "Inductance of the coil is 26.3 H\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.9 (c) Page no 345" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "C4=1*10**-6 #F\n", "R2=1000 #ohm\n", "w=314 #rad/s\n", "R3=1000\n", "R4=1000\n", "\n", "#Calculation\n", "L1=(R3*R4*C4)/(1+(w**2*C4**2*R4**2))\n", "Rx=(w**2*C4**2*R4*R2*R3)/(1+w**2*C4**2*R4**2)\n", "\n", "#Result\n", "print\"unknown resistance is\" ,round(L1,2),\"H\"\n", "print\"unknown inductance is\", round(Rx,2),\"ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "unknown resistance is 0.91 H\n", "unknown inductance is 89.75 ohm\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.10 (a) Page no 346 " ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "C1=0.5*10**-6 #farad\n", "C3=0.5*10**-6 #farad\n", "R2=2*10**3 #ohm\n", "R1=1*10**3 #ohm\n", "f=1000 #Hz\n", "\n", "#Calculation\n", "import math\n", "Rx=(C1*R2)/C3\n", "Cx=(R1*C3)/R2\n", "D=2*math.pi*f*Cx*Rx\n", "\n", "#Result\n", "print\" The unknown capacitance is \",Cx*10**6,\"micro farad\", \"\\n Dissipation factor is \",round(D,4)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The unknown capacitance is 0.25 micro farad \n", " Dissipation factor is 3.1416\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.10 (b) Page no 347" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R3=100.0 #ohm\n", "R4=300 #ohm\n", "C4=0.5*10**-6 #F\n", "C2=100.0 #pf\n", "f=50 #Hz\n", "\n", "#Calculation\n", "import math\n", "W=2*math.pi*f\n", "C1=(R4/R3)*C2\n", "R1=(C4/C2)*R3\n", "Pf=W*R4*C4\n", "\n", "#Result\n", "print\"Capacitance is \", C1,\"pF\"\n", "print\"Equivalent series resistance is \",R1*10**6,\"Mohm\"\n", "print\"PF of insulation is \",round(Pf,4)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Capacitance is 300.0 pF\n", "Equivalent series resistance is 0.5 Mohm\n", "PF of insulation is 0.0471\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.10 (c) Page no 348" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R4=100 #ohm\n", "C4=0.1 #micro F\n", "C2=500 #pf\n", "R3=300.0 #ohm\n", "f=50 #Hz\n", "\n", "#Calculation\n", "import math\n", "W=2*math.pi*f\n", "C1=(R4/R3)*C2\n", "A=W*C4*R4*10**-5\n", "\n", "#Result\n", "print\"The Capacitance is \",round(C1,1),\"pF\" \n", "print\"Dielectric loss of angle is \",round(A*180/3.14,1),\"degree\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Capacitance is 166.7 pF\n", "Dielectric loss of angle is 1.8 degree\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.10 (d) Page no 348" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "d=4.5*10**-3\n", "f=50 #Hz\n", "C2=105*10**-12\n", "C4=0.5*10**-6 #F\n", "R3=260.0 #ohm\n", "R4=1000/3.14\n", "K0=8.854*10**-12\n", "\n", "#Calculation\n", "import math\n", "W=2*math.pi*f\n", "C1=(R4/R3)*C2\n", "A=W*C4*R4\n", "a=math.pi*(6*10**-2)**2\n", "K=(C1*d)/(K0*a)\n", "\n", "#Result\n", "print\"The capacitance is \",round(C1*10**12,1),\"pF\"\n", "print\"Value of PF is \",round(A,3)\n", "print\"Relative permittivity is \",round(K,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The capacitance is 128.6 pF\n", "Value of PF is 0.05\n", "Relative permittivity is 5.78\n" ] } ], "prompt_number": 63 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.10 (e) Page no 349" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R3=100 #ohm\n", "R4=300 #ohm\n", "C2=100.0 #pF\n", "C4=0.5 #micro F\n", "\n", "#Calculation\n", "import math\n", "C1=(R4/R3)*C2\n", "r1=R3*(C4/C2)\n", "W=2*math.pi*f\n", "C1=(R4/R3)*C2\n", "A=W*C4*R4*10**-6\n", "\n", "#Result\n", "print\"The value of capacitor is \",C1,\"pF\"\n", "print\"PF of the capacitor is \",round(A,4)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of capacitor is 300.0 pF\n", "PF of the capacitor is 0.0471\n" ] } ], "prompt_number": 71 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.10 (f) Page no 350" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R1=300 #ohm\n", "R2=100.0 #ohm\n", "C1=0.6*10**-6 # F\n", "C3=100.0*10**-12 #F\n", "\n", "#Calculation\n", "Rx=R2*(C1/C3)\n", "C=(R1/R2)*C3\n", "\n", "#Result\n", "print\"The value of series resistance is \", Rx*10**-5,\"Mohm\"\n", "print\"The value of capacitance is \",C*10**12,\"pF\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of series resistance is 6.0 Mohm\n", "The value of capacitance is 300.0 pF\n" ] } ], "prompt_number": 80 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.10 (g) Page no 350" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "C1=0.1*10**-6 #F\n", "C2=0.25*10**-6 #F\n", "R2=5000.0 #ohm\n", "C3=0.25*10**-6 #F\n", "f=2000 #Hz\n", "\n", "#Calculation\n", "import math\n", "Rx=R2*(C1/C2)\n", "C=(R1/R2)*C3\n", "W=2*math.pi*f\n", "A=W*C*Rx*10**-6\n", "#Result\n", "print\"The value of capacitance is \", round(C*10**7,1),\"micro F\"\n", "print\"Dissipation factor is \", round(A*10**7,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of capacitance is 0.1 micro F\n", "Dissipation factor is 3.77\n" ] } ], "prompt_number": 102 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.11 Page no 352" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R1=4.7*10**3 #ohm\n", "R2=20*10**3 #ohm\n", "R3=10*10**3 #ohm\n", "R4=100*10**3 #ohm\n", "C1=5*10**-9 #farad\n", "C3=10*10**-9 #farad\n", "\n", "#Calculation\n", "import math\n", "f=1/(2.0*math.pi*(math.sqrt(C1*R1*R3*C3)))\n", "print\"Frequency of the circuit is \", round(f*10**-3,3),\"KHz\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Frequency of the circuit is 3.283 KHz\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.12 Page no 353" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R1=3.1*10**3 #ohm\n", "C1=5.2*10**-6 #farad\n", "R2=25.0*10**3 #ohm\n", "f=2.5*10**3 #ohm\n", "R4=100.0*10**3 #ohm\n", "\n", "#Calculation\n", "import math\n", "w=2*math.pi*f\n", "R3=R4/R2*(R1+(1/w**2*R1*C1**2))\n", "C3=R2/R4*(C1/(1+w**2*R1**2*C1**2))\n", "\n", "#CResult\n", "print\" Equivalent parallel resistance is \",R3*10**-3,\"Kohm \",\"\\n Equivalent parallel capaciatnce is \", round(C3*10**12,1),\"pf\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Equivalent parallel resistance is 12.4 Kohm \n", " Equivalent parallel capaciatnce is 20.3 pf\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.13 Page no 353" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "C1=0.5*10**-6 #farad\n", "R1=800.0 #ohm\n", "C2=1.0*10**-6 #farad\n", "R2=400 #ohm\n", "R4=1000 #ohm\n", "\n", "#Calculation\n", "import math\n", "f=1/(2.0*math.pi*math.sqrt(R1*C1*R2*C2))\n", "R3=R4/((R2/R1)+(C1/C2))\n", "\n", "#Result\n", "print\"(i) The value of frequency for which the bridge is balanced \", round(f*10**-3,3),\"KHz\"\n", "print\"(ii) The value of R required to produce balance \",R3,\"ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) The value of frequency for which the bridge is balanced 0.398 KHz\n", "(ii) The value of R required to produce balance 1000.0 ohm\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.14 Page no 359" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "R2=200 #ohm\n", "R3=1000 #ohm\n", "R4=1000.0\n", "C=10*10**-6 #Farad\n", "r=496\n", "\n", "#Calculation\n", "R1=(R2*R3)/R4\n", "L1=(C*R3/R4)*(r*R4+R2*R4+r*R2)\n", "\n", "#Result\n", "print\"The value of inductance is \", L1,\"H\"\n", "print\"The value of resistance is \",R1,\"ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of inductance is 7.952 H\n", "The value of resistance is 200.0 ohm\n" ] } ], "prompt_number": 108 } ], "metadata": {} } ] }