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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:212ce889d9f64f00c714723a9e3110b735cade9ea1d505fecd98a7e24257c63b"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter3 - Electromechanical Instruments"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2.1 - page : 3-5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Torque\n",
+ "#given data :\n",
+ "N=10 # turns\n",
+ "L=1.5*10**-2 # in m\n",
+ "I=1 # in mA\n",
+ "I*=10**-3 #A\n",
+ "B=0.5 # T\n",
+ "d=1*10**-2 # in m\n",
+ "Td=B*I*L*d*N # Nm\n",
+ "print \"Torque, Td = \", Td,\"Nm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Torque, Td = 7.5e-07 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2. - page : 3-5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# number of turns\n",
+ "#given data :\n",
+ "import math\n",
+ "theta=math.pi/2\n",
+ "I=5*10**-3 # in A\n",
+ "B=1.8*10**-3 # in Wb/m2\n",
+ "C=0.14*10**-6 # in Nm/rad\n",
+ "L=15*10**-3 # in m\n",
+ "d=12*10**-3 # in m\n",
+ "N=(C*theta)/(B*I*L*d)\n",
+ "print \"Number of turns, N = \", round(N),\"turns\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Number of turns, N = 136.0 turns\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2.3 - page : 3-6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# resistance\n",
+ "#given data :\n",
+ "Tc=240*10**-6 #in Nm\n",
+ "N=100 # Turns\n",
+ "L=40*10**-3 # in m\n",
+ "d=30*10**-3 # in m\n",
+ "B=1 #in Wb/m2\n",
+ "TdBYI=N*B*L*d\n",
+ "I=Tc/TdBYI\n",
+ "#voltage per division=I*(R/100)\n",
+ "R=100/I # ohm\n",
+ "R*=10**-3 # kohm\n",
+ "print \"Resistance, R = \", R,\"kohm\"\n",
+ "#UNIT IS GIVEN WRONG FOR THE ANSWER IN THE BOOK."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resistance, R = 50.0 kohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2.4 - page : 3-7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# flux density and diameter\n",
+ "import math\n",
+ "#given data :\n",
+ "p=1.7*10**-8 #in ohm-m\n",
+ "V=100*10**-3 #in V\n",
+ "R=50 # in ohm\n",
+ "theta=120 #in degree\n",
+ "L=30 # in mm\n",
+ "d=25 # in mm\n",
+ "N=100\n",
+ "C=0.375*10**-6 # in Nm/degree\n",
+ "I=V/R # A\n",
+ "Td_By_B=I*L*10**-3*d*10**-3*N\n",
+ "Tc=C*theta # N-m\n",
+ "B=Tc/Td_By_B # in Wb/m2\n",
+ "print \"The flux density, B = \", B,\"Wb/m2\"\n",
+ "Rc=0.3*R\n",
+ "Lmt=2*(L+d)\n",
+ "a=(N*p*Lmt*10**-3*10**6)/Rc\n",
+ "D=(4/(math.pi*a))**(1.0/2)\n",
+ "print \"Diameter, D = \", round(D,1),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The flux density, B = 0.3 Wb/m2\n",
+ "Diameter, D = 10.1 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.4.1 - page : 3-11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# shunt resistor\n",
+ "#given data :\n",
+ "Im=3*10**-3 # in A\n",
+ "Rm=100 # in ohm\n",
+ "I=150*10**-3 #in A\n",
+ "Rsh=(Im*Rm)/(I-Im)\n",
+ "print \"Shunt resistor, Rsh = \", round(Rsh,2),\"ohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shunt resistor, Rsh = 2.04 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.4.2 - page : 3-11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# shunt resistormultiplying factor and resistance\n",
+ "#given data :\n",
+ "Rsh=300 #in ohm\n",
+ "Rm=1500 #in ohm\n",
+ "m=1+(Rm/Rsh)\n",
+ "print \"Multiplying factor, m = \",m\n",
+ "m1=40.0\n",
+ "Rsh1=Rm/(m1-1)\n",
+ "print \"The shunt resistor, Rsh1 = \", round(Rsh1,2),\"ohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Multiplying factor, m = 6\n",
+ "The shunt resistor, Rsh1 = 38.46 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.5.1 - page : 3-13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given data :\n",
+ "Rm=100.0 # in ohm\n",
+ "Im=1.0\n",
+ "#for range 0-20 mA\n",
+ "I1=20.0\n",
+ "m=I1/Im\n",
+ "Rsh1=Rm/(m-1)\n",
+ "print \"The shunt resistor, Rsh1 = \", round(Rsh1,2),\"ohm\"\n",
+ "#for the range of 0-100 mA\n",
+ "I2=100.0\n",
+ "m=I2/Im\n",
+ "Rsh2=Rm/(m-1)\n",
+ "print \"The shunt resistor, Rsh2 = \", round(Rsh2,2),\"ohm\"\n",
+ "#for the range 0-200 mA\n",
+ "I3=200.0\n",
+ "m=I3/Im\n",
+ "Rsh3=Rm/(m-1)\n",
+ "print \"The shunt resistor, Rsh3 = \", round(Rsh3,2),\"ohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The shunt resistor, Rsh1 = 5.26 ohm\n",
+ "The shunt resistor, Rsh2 = 1.01 ohm\n",
+ "The shunt resistor, Rsh3 = 0.5 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6.1 - page : 3-15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import numpy\n",
+ "from numpy.linalg import inv\n",
+ "#design\n",
+ "Rm=50.0 #in ohm\n",
+ "Im=2.0 #in mA\n",
+ "Im*=10**-3 # A\n",
+ "I1=2.0 #in A\n",
+ "I2=10.0 #in A\n",
+ "I3=15.0 #in A\n",
+ "#Let Rs=R1+R2+R3\n",
+ "A=numpy.array([[I1,I1,I1],[-Im,I2,I2],[Im,Im,-I3]])\n",
+ "B=numpy.array([[Im*Rm],[Im*Rm],[-Im*Rm]])\n",
+ "Ainv=inv(A)\n",
+ "X=numpy.dot(Ainv,B)\n",
+ "R1=X[0]\n",
+ "R2=X[1]\n",
+ "R3=X[2]\n",
+ "print \"Value of shunt resistors are : \"\n",
+ "print \"R1 is %f ohm, R2 is %.1e ohm & R3 is %.2e ohm\" %(round(R1,5), R2, R3)\n",
+ "# Answer is wrong in the textbook."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Value of shunt resistors are : \n",
+ "R1 is 0.039990 ohm, R2 is 3.3e-03 ohm & R3 is 6.67e-03 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9.1 - page : 3-19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Multiplier\n",
+ "#Given data :\n",
+ "Vin=20.0 #in volts\n",
+ "I_fsd=50.0*10 **-6 # in Farad\n",
+ "Rm=200.0 # in ohm\n",
+ "Rs=(Vin/I_fsd)-Rm # in ohm\n",
+ "Rs=Rs/10**3 # kohm\n",
+ "print \"The multiplier, Rs = \", Rs, \" kohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The multiplier, Rs = 399.8 kohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9.2 - page : 3-19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Full scale deflection current\n",
+ "#given data :\n",
+ "Vin=10.0 # in V\n",
+ "Rs=200.0 #in kohm\n",
+ "Rm=400.0 # in ohm\n",
+ "I_fsd=Vin/((Rs*10 **3)+Rm) # A\n",
+ "I_fsd*=10**6 # micro A\n",
+ "print \"Full scale deflection current, I_fsd = \", round(I_fsd,1), \" micro A\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Full scale deflection current, I_fsd = 49.9 micro A\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.10.1 - page : 3-22"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Multiplier\n",
+ "#given data :\n",
+ "V1=200.0 #in V\n",
+ "V2=100.0 #in V\n",
+ "V3=10.0 # in V\n",
+ "Rm=100.0 #in ohm\n",
+ "I_fsd=50*10 **-3 \n",
+ "#for the range 0-10V \n",
+ "Rt3=V3/I_fsd \n",
+ "Rs3=Rt3-Rm # ohm\n",
+ "print \"The multiplier, Rs3 = \", Rs3, \" ohm.\"\n",
+ "#for the range 0-100V\n",
+ "Rt2=V2/I_fsd \n",
+ "Rs2=Rt2-(Rm+Rs3) # ohm \n",
+ "print \"The multiplier, Rs2 = \", Rs2, \" ohm.\"\n",
+ "Rt1=V1/I_fsd \n",
+ "Rs1=Rt1-(Rm+Rs3+Rs2) \n",
+ "print \"The multiplier, Rs1 = \", Rs1, \" ohm.\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The multiplier, Rs3 = 100.0 ohm.\n",
+ "The multiplier, Rs2 = 1800.0 ohm.\n",
+ "The multiplier, Rs1 = 2000.0 ohm.\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.11.1 - page : 3-23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Multiplier\n",
+ "#given data :\n",
+ "Rm=200.0 #in ohm\n",
+ "I_fsd=150.0*10 **-6 # in A\n",
+ "S=1/I_fsd \n",
+ "V=50 #in V\n",
+ "Rs=(S*V)-Rm # ohm \n",
+ "Rs*=10**-3 # kohm\n",
+ "print \"Multiplier, Rs = \", round(Rs,2), \" kohm.\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Multiplier, Rs = 333.13 kohm.\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.11.2 - page : 3-24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Accurate voltmeter reading\n",
+ "r1=50.0 # in kohms\n",
+ "r2=50.0 #in kohms\n",
+ "v=100.0 #in V\n",
+ "vr2=(r1/(r1+r2))*v # voltage in V\n",
+ "#case 1\n",
+ "s1=12000.0 #sensivity in ohm/V\n",
+ "rm1=r1*s1*10**-3 # in kohm\n",
+ "req=((rm1*r1)/(rm1+r1)) #equivalent resistance in ohm\n",
+ "v1=((req/(r1+req)))*v # voltmeter reading when sensivity is 12000 ohm/V\n",
+ "#case 2\n",
+ "s2=15000 #sensivity in ohm/V V\n",
+ "rm2=r1*s2*10**-3 # in kohm\n",
+ "req1=((rm2*r1)/(rm2+r1)) #equivalent resistance in ohm\n",
+ "v2=((req1/(r1+req1)))*v # voltmeter reading when sensivity is 15000 ohm/V\n",
+ "print \"Voltmeter reading when sensivity is 12000 ohm/V is \", round(v1,2), \" V\"\n",
+ "print \"Voltmeter reading when sensivity is 15000 ohm/V is \", round(v2,2), \" V. This voltmeter will measure the correct value.\"\n",
+ "# Answer in the textbook is not accurate"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Voltmeter reading when sensivity is 12000 ohm/V is 48.0 V\n",
+ "Voltmeter reading when sensivity is 15000 ohm/V is 48.39 V. This voltmeter will measure the correct value.\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15.1 - page : 3-28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#voltage\n",
+ "r1=25.0 # kohms\n",
+ "r2=5.0 #in kohms\n",
+ "v=30.0 #in V\n",
+ "# part(i)\n",
+ "vr2=(r2/(r1+r2))*v # voltage in V across 5 kohms resistance\n",
+ "Vactual=vr2 # V\n",
+ "print \"Voltage across 5 kohm Resistance is \", vr2, \" V.\"\n",
+ "#part (ii)\n",
+ "vr2=(r1/(r1+r2))*v # voltage in V across 5 kohm resistance\n",
+ "#case 1\n",
+ "s1=1.0 #sensivity in kohm/V\n",
+ "v1=10.0 # in V\n",
+ "rm1=v1*s1 #in kohm\n",
+ "req=((rm1*r2)/(rm1+r2)) # equivalent resistance in ohm\n",
+ "vrb1=((req/(r1+req)))*v # voltmeter reading when sensivity is 1 kohm/V\n",
+ "print \"Voltmeter reading when sensivity is 1 kohm/V is \",round(vrb1,2), \" V.\"\n",
+ "# part(iii)\n",
+ "#case 2\n",
+ "s2=20 #sensivity in kohm/V\n",
+ "v1=10 # in V\n",
+ "rm2=v1*s2 #in kohm\n",
+ "req1=((rm2*r2)/(rm2+r2)) #equivalent resistance in ohm\n",
+ "vrb2=((req1/(r1+req1)))*v # voltmeter reading when sensivity is 1 kohm/V\n",
+ "print \"Voltmeter reading when sensivity is 1 kohm/V is \",round(vrb2,2), \" V.\"\n",
+ "#part(iii) #error\n",
+ "er1=(Vactual-vrb1)/Vactual*100 #voltmeter 1 error in %\n",
+ "er2=(Vactual-vrb2)/Vactual*100 #voltmeter 2 error in %\n",
+ "print \"Voltmeter 1 error is \",round(er1,2),\" %\"\n",
+ "print \"Voltmeter 2 error is \",round(er2,1),\" %\"\n",
+ "#Answer is wrong in the textbook"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Voltage across 5 kohm Resistance is 5.0 V.\n",
+ "Voltmeter reading when sensivity is 1 kohm/V is 3.53 V.\n",
+ "Voltmeter reading when sensivity is 1 kohm/V is 4.9 V.\n",
+ "Voltmeter 1 error is 29.41 %\n",
+ "Voltmeter 2 error is 2.0 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15.2 - page : 3-29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Shunt resistance\n",
+ "#Given data :\n",
+ "Im=1.0 # in mA\n",
+ "Rm=100.0 # in ohm\n",
+ "I=100.0 # in mA\n",
+ "Rsh=(Im*10**-3*Rm)/((I-Im)*10**-3) \n",
+ "print \"Shunt resistance, Rsh = \",round(Rsh,3),\" ohm.\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shunt resistance, Rsh = 1.01 ohm.\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15.3 - page : 3-29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Shunt resistance\n",
+ "#Given data :\n",
+ "Im=1.0 # in mA\n",
+ "P=100.0 # in kW\n",
+ "I=100.0 # in mA\n",
+ "Rm=(P)/(Im)**2 # ohm\n",
+ "Rsh=((Im*10**-3*Rm*10**3)/((I-Im)*10**-3))*10**-3 # ohm\n",
+ "print \"Shunt resistance, Rsh = \",round(Rsh,3), \" kohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shunt resistance, Rsh = 1.01 kohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15.4 - page : 3-29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Shunt resistance\n",
+ "#given data :\n",
+ "Rsh=200.0 # in ohm\n",
+ "Rm=100.0 # in ohm\n",
+ "m=50.0 \n",
+ "Rsh=Rm/(m-1) # ohm\n",
+ "print \"The shunt resistance, Rsh = \", round(Rsh,2), \" ohm.\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The shunt resistance, Rsh = 2.04 ohm.\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15.5 - page : 3-30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# shunt resistance\n",
+ "#Given data :\n",
+ "Im=1.0 # in mA\n",
+ "Rm=100.0 # in ohm\n",
+ "I=100.0 # in mA\n",
+ "Rsh=(Im*10**-3*Rm)/((I-Im)*10**-3) # ohm\n",
+ "print \"Shunt resistance, Rsh = \", round(Rsh,3), \" kohm.\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shunt resistance, Rsh = 1.01 kohm.\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 07:40:52 +0000