{ "metadata": { "name": "", "signature": "sha256:4e527403e3e23cec992884b304469d3eb94c6edd5b7caf76ef7e787ddafbe409" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter - 3 : PMMC Instruments" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.1 - Page No : 57" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "N= 100 \n", "A=4*3 # in cm**2\n", "A=A*10**-4 # in m**2\n", "i=20 # in mA\n", "i=i*10**-3 # in A\n", "B=0.05 # in T\n", "T=N*i*B*A #in Nm\n", "print \"Torque developed by the coil = %0.1e Nm\" %T" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque developed by the coil = 1.2e-04 Nm\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.2 - Page No : 57" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "N= 125 \n", "A=4*2.5 # in cm**2\n", "A=A*10**-4 # in m**2\n", "i=25 # in mA\n", "i=i*10**-3 # in A\n", "B=0.06 # in T\n", "Td=N*i*B*A #in Nm\n", "Tc_BY_theta= 25*10**-7 # in Nm/\u00b0\n", "# Formula Tc=Td\n", "theta= Td/Tc_BY_theta # in \u00b0\n", "print \"Deflection = %0.f degree\" %theta" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Deflection = 75 degree\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.3 - Page No :57" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "#Given data\n", "N= 100 \n", "B=6*10**-2 # in Wb/m**2\n", "A=3*4 # in cm**2\n", "A=A*10**-4 # in m**2\n", "V=300 # in volt\n", "R=12000 # in ohm\n", "i= V/R # in amp\n", "Td=N*i*B*A #in Nm\n", "Tc_BY_theta= 25*10**-7 # in Nm/\u00b0\n", "# Formula Tc=Td\n", "theta= Td/Tc_BY_theta # in \u00b0\n", "print \"Deflection = %0.f degree\" %theta" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Deflection = 72 degree\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.4 - Page No : 62" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy import pi\n", "#Given data\n", "d= 42 # in mm\n", "d=d*10**-3 # in meter\n", "r= 0.6 # in meter\n", "# Formula d= 2*theta*r\n", "theta= d/(2*r) # radian\n", "theta= 180*theta/pi # in \u00b0\n", "print \"Angle through which coil turn = %0.f\u00b0\" %theta " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angle through which coil turn = 2\u00b0\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.5 - Page No : 62" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "B=1.8*10**-3 # in Wb/m**2\n", "K= 1.4*10**-7 # in Nm/radian\n", "theta= 90 # in \u00b0\n", "theta=theta*pi/180 \n", "Tc= K*theta # in N-m\n", "i=5 # in mA\n", "i=i*10**-3 # in amp\n", "A=1.5*1.2 # in cm**2\n", "A=A*10**-4 # in m**2\n", "# Formula Tc= Td= B*i*A*N \n", "N= Tc/(B*i*A) \n", "N=round(N) \n", "print \"Number of turns = %0.f\" %N " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Number of turns = 136\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.6 - Page No : 63" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "B=0.1 # in T\n", "C= 100*10**-7 # in Nm/radian\n", "theta= 120 # in \u00b0\n", "theta=theta*pi/180 \n", "Tc= C*theta # in N-m\n", "N=200 # number of turns\n", "A=2.5*2 # in cm**2\n", "A=A*10**-4 # in m**2\n", "# Formula Tc= Td= B*i*A*N \n", "i= Tc/(B*A*N) # in amp\n", "print \"Current in the coil = %0.4f mA\" %(i*10**3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Current in the coil = 2.0944 mA\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.7 - Page No : 63" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "d=150 # in mm\n", "i=2.5 # in micro amp\n", "R=200 # in ohm\n", "V= R*i # in micro volt\n", "r=2.5 # in meter\n", "# Part(i)\n", "Si= d/i # in mm/micro amp\n", "print \"Current sensitivity = %0.f mm/\u00b5A\" %Si\n", "\n", "# Part(ii)\n", "Sv= d/V # in mm/micro volt\n", "print \"Voltage sensitivity = %0.1f mm/\u00b5V\" %Sv\n", "\n", "# Part(iii)\n", "So= 1/(1/60*10**-6) # in ohm/mm\n", "So=So*10**-6 # in Mohm\n", "print \"Megohm sensitivity = %0.f Mohm/mm\" %So\n", "\n", "# Part(iv)\n", "i=5 # in micro amp\n", "d=60*i # in mm\n", "d=d*10**-3 # in meter\n", "theta=d/(2*r) #in radian \n", "print \"The value of deflection = %0.2f radians\" %theta" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Current sensitivity = 60 mm/\u00b5A\n", "Voltage sensitivity = 0.3 mm/\u00b5V\n", "Megohm sensitivity = 60 Mohm/mm\n", "The value of deflection = 0.06 radians\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.8 - Page No : 65" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "Im= 50*10**-6 # in amp\n", "Rm= 1000 # in ohm\n", "I=1 # in amp\n", "Rs= Rm/(I/Im-1) # in ohm\n", "print \"Resistance of ammeter shunt required = %0.7f ohm\" %Rs" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resistance of ammeter shunt required = 0.0500025 ohm\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.9 - Page No : 65" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from fractions import Fraction\n", "#Given data\n", "Rm= 1.0 # in ohm\n", "Rse= 4999 # in ohm\n", "V=250 # full scale deflection voltage in volt\n", "# Formula V= Im*(Rm+Rse)\n", "Im= V/(Rm+Rse) # in amp\n", "\n", "# Part(a)\n", "Rs= 1/4999 # in ohm\n", "Is= Im*Rm/Rs #in amp\n", "I= Im+Is # in amp\n", "print \"Current range = %0.f A\" %I\n", "\n", "# Part(b)\n", "I=50 # in amp\n", "N=I/Im \n", "Rs= Rm/(N-1) # in ohm\n", "print \"Required shunt resistance =\",Fraction(Rs).limit_denominator(1000),\"ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Current range = 250 A\n", "Required shunt resistance = 1/999 ohm\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.10 - Page No : 66" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "Im= 50 # in micro amp\n", "Im=Im*10**-6 # in amp\n", "Rm= 49 # in ohm\n", "Rs= 1 # in ohm\n", "Is= Im*Rm/Rs #in amp\n", "I= Im+Is # in amp\n", "# (i)\n", "I1= I # in amp\n", "I2= I*0.5 # in amp\n", "I3= I*0.1 # in amp\n", "print \"Main circuit current at FSD = %0.1f mA\" %(I1*10**3)\n", "print \"Main circuit current at 0.5 FSD = %0.2f mA\" %(I2*10**3)\n", "print \"Main circuit current at 0.1 FSD = %0.2f mA\" %(I3*10**3)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Main circuit current at FSD = 2.5 mA\n", "Main circuit current at 0.5 FSD = 1.25 mA\n", "Main circuit current at 0.1 FSD = 0.25 mA\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.11 - Page No : 67" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "Rm= 40 # in ohm\n", "Im= 1 # in mA\n", "# For switch at position 1 (lowest range of 10 mA)\n", "I=10 # in mA\n", "N1= I/Im \n", "R1= Rm/(N1-1) # in ohm\n", "# For switch at position 2 (range of 20 mA)\n", "I=20 # in mA\n", "N2= I/Im \n", "R2= (R1+Rm)/N2 # in ohm\n", "# For switch at position 3 (range of 30 mA)\n", "I=30 # in mA\n", "N3= I/Im \n", "R3= (R1+Rm)/N3 # in ohm\n", "# For switch at position 4 (range of 40 mA)\n", "I=40 # in mA\n", "N4= I/Im \n", "R4= (R1+Rm)/N4 # in ohm\n", "# For switch at position 5 (range of 50 mA)\n", "I=50 # in mA\n", "N5= I/Im \n", "R5= (R1+Rm)/N5 # in ohm\n", "r1= R1-R2 # in ohm\n", "r2= R2-R3 # in ohm\n", "r3= R3-R4 # in ohm\n", "r4= R4-R5 # in ohm\n", "r5= R5 # in ohm\n", "print \"Resistance of the various sections of the Ayrton's shunt :\"\n", "print \"r1 = %0.3f ohm\" %r1\n", "print \"r2 = %0.4f ohm\" %r2\n", "print \"r3 = %0.4f ohm\" %r3\n", "print \"r4 = %0.3f ohm\" %r4\n", "print \"r5 = %0.3f ohm\" %r5\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resistance of the various sections of the Ayrton's shunt :\n", "r1 = 2.222 ohm\n", "r2 = 0.7407 ohm\n", "r3 = 0.3704 ohm\n", "r4 = 0.222 ohm\n", "r5 = 0.889 ohm\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.12 - Page No : 68" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "Rm= 1000 # in ohm\n", "Im= 1 # in mA\n", "Im=Im*10**-3 # in amp\n", "r3=0.05 # in ohm\n", "r2=0.45 # in ohm\n", "r1=4.5 # in ohm\n", "# For switch at contact 1\n", "Rm1= Rm # in ohm\n", "Rs1= r1+r2+r3 # in ohm\n", "I1= Im*(Rm1/Rs1+1) # in A\n", "I1=I1*10**3 # in mA\n", "I1=round((I1/10))*10 \n", "\n", "print \"Ammeter range at contact 1 = %0.f mA\" %I1\n", "# For switch at contact 2\n", "Rm2= Rm+r1 # in ohm\n", "Rs2= r2+r3 # in ohm\n", "I2= Im*(Rm2/Rs2+1) # in A\n", "I2=round(I2) \n", "print \"Ammeter range at contact 2 = %0.f A\" %I2\n", "\n", "# For switch at contact 3\n", "Rm3= Rm+r1+r2 # in ohm\n", "Rs3= r3 # in ohm\n", "I3= Im*(Rm3/Rs3+1) # in A\n", "I3=round(I3) \n", "print \"Ammeter range at contact 3 = %0.f A\" %I3" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ammeter range at contact 1 = 200 mA\n", "Ammeter range at contact 2 = 2 A\n", "Ammeter range at contact 3 = 20 A\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.13 - Page No : 70" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from fractions import Fraction \n", "#Given data\n", "Rm= 10 # in ohm\n", "Im= 50 # in mA\n", "Im=Im*10**-3 # in amp\n", "V=750 # in volt\n", "R= V/Im-Rm # in ohm\n", "print \"External resistance = %0.f ohm\" %R\n", "# Part(ii)\n", "I=100 # in A\n", "N=I/Im \n", "Rs= Rm/(N-1) # in ohm\n", "print \"Shunt resistance required =\",Fraction(Rs).limit_denominator(10000),\"ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "External resistance = 14990 ohm\n", "Shunt resistance required = 10/1999 ohm\n" ] } ], "prompt_number": 39 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.14 - Page No : 70" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "Tc= 120*10**-6 # in N-m\n", "B= 0.5 # in wb/m**2\n", "N=100 \n", "A= 4*3 # in cm**2\n", "A=A*10**-4# in m**2\n", "Rm=0 \n", "V= 100*1 \n", "# Formula Tc= Td = B*I*N*A\n", "I= Tc/(B*N*A) # in amp\n", "R= V/I-Rm # in ohm\n", "print \"External required resistance = %0.f ohm\" %R" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "External required resistance = 50000 ohm\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.15 - Page No : 71" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "Im= 0.2*10**-3 # in amp\n", "Rm= 10 # in ohm\n", "V=100 # in volt\n", "R= V/Im-Rm # in ohm\n", "print \"External required resistance = %0.2f kohm\" %(R*10**-3)\n", "Im1= 0.75*Im #in amp\n", "V1= Im1*(R+Rm) # in volt\n", "print \"Applied voltage at instrument current 0.75 FSD = %0.f volts\" %V1 \n", "\n", "Im2= 0.5*Im #in amp\n", "V2= Im2*(R+Rm) # in volt\n", "print \"Applied voltage at instrument current 0.5 FSD = %0.f volts\" %V2 \n", "\n", "Im3= 0.25*Im #in amp\n", "V3= Im3*(R+Rm) # in volt\n", "print \"Applied voltage at instrument current 0.25 FSD = %0.f volts\" %V3 \n", "\n", "Im4= 0.1*Im #in amp\n", "V4= Im4*(R+Rm) # in volt\n", "print \"Applied voltage at instrument current 0.1 FSD = %0.f volts\" %V4 \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "External required resistance = 499.99 kohm\n", "Applied voltage at instrument current 0.75 FSD = 75 volts\n", "Applied voltage at instrument current 0.5 FSD = 50 volts\n", "Applied voltage at instrument current 0.25 FSD = 25 volts\n", "Applied voltage at instrument current 0.1 FSD = 10 volts\n" ] } ], "prompt_number": 44 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.16 - Page No : 72" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "CS= 0.1*10**-3 # current sensitivity in amp\n", "VS= 1/CS # voltage sensitivity in ohm/volt\n", "VS= VS*10**-3 # in kohm/volt\n", "Rm=500 # in ohm\n", "Rm=Rm*10**-3 # in kohm\n", "\n", "# (i) 0-10 V range\n", "V=10 # full scale delection voltage in volt\n", "R_T= VS*V # in kohm\n", "R1= R_T-Rm # in kohm\n", "print \"Additional required resistance at 0-10 V range = %0.1f kohm\" %R1\n", "\n", "# (ii) 0-50 V range\n", "V=50 # full scale delection voltage in volt\n", "R_T= VS*V # in kohm\n", "R2= R_T-R1-Rm # in kohm\n", "print \"Additional required resistance at 0-50 V range = %0.f kohm\" %R2\n", "\n", "# (i) 0-100 V range\n", "V=100 # full scale delection voltage in volt\n", "R_T= VS*V # in kohm\n", "R3= R_T-R1-R2-Rm # in kohm\n", "print \"Additional required resistance at 0-100 V range = %0.f kohm\" %R3\n", "\n", "# (i) 0-500 V range\n", "V=500 # full scale delection voltage in volt\n", "R_T= VS*V # in kohm\n", "R4= R_T-R1-R2-R3-Rm # in kohm\n", "print \"Additional required resistance at 0-500 V range = %0.f kohm\" %R4\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Additional required resistance at 0-10 V range = 99.5 kohm\n", "Additional required resistance at 0-50 V range = 400 kohm\n", "Additional required resistance at 0-100 V range = 500 kohm\n", "Additional required resistance at 0-500 V range = 4000 kohm\n" ] } ], "prompt_number": 47 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.17 - Page No : 74" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "E= 1.5 # in V\n", "R1addRm= 10 # addition of R1 and Rm in kohm\n", "Rx= 0 \n", "R=R1addRm+Rx # in kohm\n", "R=R*10**3 # in ohm\n", "I= E/R #meter FSD current in amp\n", "\n", "# At 0.8 FSD\n", "Im= 0.8*I # in amp\n", "R= E/Im # in ohm\n", "R=R*10**-3 # in kohm\n", "Rx= R-R1addRm #in kohm\n", "print \"Unknown resistance at 0.8 FSD = %0.1f k\u03a9\" %Rx\n", "\n", "# At 0.5 FSD\n", "Im= 0.5*I # in amp\n", "R= E/Im # in ohm\n", "R=R*10**-3 # in kohm\n", "Rx= R-R1addRm #in kohm\n", "print \"Unknown resistance at 0.5 FSD = %0.f k\u03a9\" %Rx\n", "\n", "# At 0.25 FSD\n", "Im= 0.25*I # in amp\n", "R= E/Im # in ohm\n", "R=R*10**-3 # in kohm\n", "Rx= R-R1addRm #in kohm\n", "print \"Unknown resistance at 0.25 FSD = %0.f k\u03a9\" %Rx\n", "\n", "# At 0.1 FSD\n", "Im= 0.1*I # in amp\n", "R= E/Im # in ohm\n", "R=R*10**-3 # in kohm\n", "Rx= R-R1addRm #in kohm\n", "print \"Unknown resistance at 0.1 FSD = %0.f k\u03a9\" %Rx\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Unknown resistance at 0.8 FSD = 2.5 k\u03a9\n", "Unknown resistance at 0.5 FSD = 10 k\u03a9\n", "Unknown resistance at 0.25 FSD = 30 k\u03a9\n", "Unknown resistance at 0.1 FSD = 90 k\u03a9\n" ] } ], "prompt_number": 50 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example : 3.18 - Page No : 74" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Given data\n", "Rm= 50 # in ohm\n", "R1= 10 # in kohm\n", "R1=R1*10**3 # in ohm\n", "R2= 50 # in ohm\n", "Im_FSD= 100*10**-6 #meter FSD current in amp\n", "\n", "# At 0.5 FSD , with 1.5 V\n", "E=1.5 # in volt\n", "Im= 0.5*Im_FSD # in amp\n", "Vm= Im*Rm # in volt\n", "I0= Vm/R2 #in amp\n", "I=I0+Im # in amp\n", "Rx= E/I-R1 # in ohm\n", "Rx=Rx*10**-3 #in kohm\n", "print \"Unknown resistance at 0.5 FSD with 1.5 V = %0.f kohm\" %Rx\n", "# With E= 1.25 V and Rx=0\n", "E=1.25 # in volt\n", "Rx=0 \n", "I=E/(R1+Rx) # in amp\n", "I0=I-Im_FSD # in amp\n", "Vm= Im_FSD*Rm # in volt\n", "R2= Vm/I0 # in ohm\n", "print \"Zero adjuster resistance = %0.f ohm\" %R2\n", "\n", "# At 0.5 FSD , with 1.25 V\n", "E=1.25 # in volt\n", "Im= 0.5*Im_FSD # in amp\n", "Vm= Im*Rm # in volt\n", "I0= Vm/R2 #in amp\n", "I=I0+Im # in amp\n", "Rx= E/I-R1 # in ohm\n", "Rx=Rx*10**-3 #in kohm\n", "print \"Unknown resistance at 0.5 FSD with 1.25 V = %0.f kohm\" %Rx" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Unknown resistance at 0.5 FSD with 1.5 V = 5 kohm\n", "Zero adjuster resistance = 200 ohm\n", "Unknown resistance at 0.5 FSD with 1.25 V = 10 kohm\n" ] } ], "prompt_number": 51 } ], "metadata": {} } ] }