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-{
- "metadata": {
- "name": "",
- "signature": "sha256:95b9e0f83468dda84f2de4d99c5a704a6fadf8064c232b063678fd245192ca75"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter2 - Measurement Errors"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.1 - page : 2-8"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#precision of the 5th measurement\n",
- "#given data :\n",
- "X1=98.0 \n",
- "X2=101.0\n",
- "X3=102.0 \n",
- "X4=97.0 \n",
- "X5=101.0 \n",
- "X6=100.0 \n",
- "X7=103.0 \n",
- "X8=98.0 \n",
- "X9=106.0 \n",
- "X10=99.0 \n",
- "Xn_bar=(X1+X2+X3+X4+X5+X6+X7+X8+X9+X10)/10 \n",
- "Xn=101 # value of 5th measurement\n",
- "P=(1-abs((Xn-Xn_bar)/Xn_bar))*100 \n",
- "print \"Precision of the 5th measurement, P = \", round(P,2), \" %\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Precision of the 5th measurement, P = 99.5 %\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.2.i - page : 2-10"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Absolute error\n",
- "#given data :\n",
- "Ae=80.0 # in V\n",
- "Am=79.0 # in V\n",
- "e=Ae-Am \n",
- "print \"Absolute error, e = \", e, \" V\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Absolute error, e = 1.0 V\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.2.ii - page : 2-10"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Error\n",
- "#given data :\n",
- "Ae=80.0 # in V\n",
- "Am=79.0 # in V\n",
- "e=Ae-Am \n",
- "error1=(e/Ae)*100 \n",
- "print \"Error = \", error1, \" %\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Error = 1.25 %\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.2.iii - page : 2-10"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Relative accuracy\n",
- "#given data :\n",
- "Ae=80.0 # in V\n",
- "Am=79.0 # in V\n",
- "e=Ae-Am \n",
- "error1=(e/Ae)*100 \n",
- "A=(1-abs(e/Ae)) \n",
- "print \"Relative Accuracy, A = \", A"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Relative Accuracy, A = 0.9875\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.2.iv - page : 2-10"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# % accuracy\n",
- "#given data :\n",
- "Ae=80.0 # in V\n",
- "Am=79.0 # in V\n",
- "e=Ae-Am \n",
- "error1=(e/Ae)*100 \n",
- "A=(1-abs(e/Ae)) \n",
- "accuracy=A*100 \n",
- "print \"Accuracy = \", accuracy, \" %\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Accuracy = 98.75 %\n"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.2.v - page : 2-10"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# % error\n",
- "#given data :\n",
- "Ae=80.0 # in V\n",
- "Am=79.0 # in V\n",
- "e=Ae-Am \n",
- "f=100.0 #full scale deflection\n",
- "error1=(e/Ae)*100 \n",
- "A=(1-abs(e/Ae)) \n",
- "accuracy=A*100 \n",
- "P_error=(e/f)*100 \n",
- "print \"% error = \", P_error, \" %\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "% error = 1.0 %\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.3 - page : 2-11"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Maximum error\n",
- "#given data :\n",
- "V1=100.0 # in V\n",
- "V2=200.0 #in V\n",
- "V=V2-V1 \n",
- "A=0.25 #may be \u00b1 in %\n",
- "max_error=(A/100)*V \n",
- "print \"Maximum error = \u00b1 \", max_error, \" V\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Maximum error = \u00b1 0.25 V\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.4 - page : 2-12"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# sensitivity and deflection error\n",
- "#given data :\n",
- "C=4.0 # change in output in mm\n",
- "M=8.0 # magnitude of input in ohm\n",
- "S=C/M \n",
- "print \"sensitivity, S = \", S, \" mm/ohm\"\n",
- "D=M/C \n",
- "print \"Deflection factor, D = \", D, \" ohm/mm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "sensitivity, S = 0.5 mm/ohm\n",
- "Deflection factor, D = 2.0 ohm/mm\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.5 - page : 2-14"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Resolution\n",
- "#given data :\n",
- "V=200.0 # full scale reading in V\n",
- "N=100.0 # number of divisions \n",
- "Scale_div=V/N \n",
- "R=(1.0/10)*Scale_div \n",
- "print \"Resolution, R = \", R, \" V\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Resolution, R = 0.2 V\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.3.6 - page : 2-14"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Resolution\n",
- "#given data :\n",
- "V=9.999 # full scale read out in volt\n",
- "c=9999.0 # range from 0 to 9999\n",
- "R=(1/c)*V*10**3 \n",
- "print \"Resolution, R = \", R, \" mV\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Resolution, R = 1.0 mV\n"
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.6.1 - page : 2-23"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Magnitude and relative error\n",
- "#given data :\n",
- "R1=15.0 #ohm\n",
- "E1=R1*5.0/100 # \u00b1 limiting error for R1\n",
- "R2=33.0 #ohm\n",
- "E2=R2*2.0/100 # \u00b1 limiting error for R2\n",
- "R3=75.0 #ohm\n",
- "E3=R3*5.0/100 # \u00b1 limiting error for R3\n",
- "RT=R1+R2+R3 # ohm(in series)\n",
- "ET=E1+E2+E3 #\u00b1limiting error for RT\n",
- "print \"For series connection, magnitude is \", RT, \" ohm & limiting error is \u00b1 \", ET, \" ohm.\" \n",
- "Epr=ET/RT*100 #%\n",
- "print \"Percent relative error : \u00b1\", round(Epr,1),\" %\" \n",
- "\n",
- "# Answer is not accurate in the textbook."
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "For series connection, magnitude is 123.0 ohm & limiting error is \u00b1 5.16 ohm.\n",
- "Percent relative error : \u00b1 4.2 %\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.6.2 - page : 2-23"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Magnitude and relative error\n",
- "#given data :\n",
- "R1=36.0 #ohm\n",
- "E1=5.0 # \u00b1 limiting error for R1\n",
- "R2=75.0 #ohm\n",
- "E2=5.0 # \u00b1 limiting error for R2\n",
- "RT=(R1*R2)/(R1+R2) #ohm(in parallel)\n",
- "EP1=E1+E2 # \u00b1 limiting error\n",
- "EP2=((R1*E1)/(R1+R2))+((R2*E2)/(R1+R2)) \n",
- "ET=EP1+EP2 \n",
- "etm=(ET/100)*RT \n",
- "print \"Magnitude of limiting error is \u00b1\", round(etm,2), \" ohm\"\n",
- "print \"Percentage relative error is \u00b1\", ET, \" %\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Magnitude of limiting error is \u00b1 3.65 ohm\n",
- "Percentage relative error is \u00b1 15.0 %\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.6.3 page : 2-24"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# Limiting error\n",
- "vr=40.0 #reading of voltmeter in volts\n",
- "v=50.0 #rane in volts\n",
- "va=50.0 #ammeeter reading in mA\n",
- "i=125.0 #range in mA\n",
- "fsd=2.0 #accurace in percentage in \u00b1\n",
- "dv=(2.0/100)*v #limiting error of voltmeter\n",
- "da=(2./100)*i #liming error of the ammeter in mA\n",
- "erv=dv/vr #relative limiting error in voltmeter reading\n",
- "eri=da/i #relative limiting error in ammeter reading\n",
- "et=erv+eri \n",
- "pet=et*100 #percentage limiting error of the power calcultaed\n",
- "print \"Percentage limiting error of the power calcultaed is \u00b1 \",pet,\" %\"\n",
- "\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Percentage limiting error of the power calcultaed is \u00b1 4.5 %\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.6.4 - page : 2-25"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# limiting error\n",
- "r1=120.0 # ohm\n",
- "er1=0.5 #limiting error in resistance 1 in ohm \u00b1\n",
- "r2=2 #in A\n",
- "er2=0.02 #limiting error in amperes \u00b1\n",
- "e1=er2/r2 #limiting error in current\n",
- "e2=er1/r1 #limiting eror in resistance\n",
- "et=(2*e1+e2) #total error\n",
- "etp=et*100 #percentage limtimg error\n",
- "print \"Percentage limiting error in the value of power dissipation is \u00b1\",round(etp,3)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Percentage limiting error in the value of power dissipation is \u00b1 2.417\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.6.5 - page : 2-25"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#magnitude and limiting error\n",
- "r1=120 #in ohm\n",
- "er1=0.1 #limiting error in resistance 1 in ohm \u00b1\n",
- "r2=2700 #in ohm\n",
- "er2=0.5 #limiting error in resistance 2 in ohm \u00b1\n",
- "r3=470 #in ohm\n",
- "er3=0.5 #limiting error in resistance 3 in ohm \u00b1\n",
- "rxm=(r2*r3)/r1 #magnitude of unknown resistance in ohm\n",
- "rxe=(er1+er2+er3) #error\n",
- "er=(rxe*rxm)/100 #relative error \u00b1\n",
- "print \"Magnitude of unknown resistance is \",rxm,\" kohm\"\n",
- "print \"Relative limiting error is \u00b1\",er,\" ohm\"\n",
- "print \"Guranteed value of resistance is between \",rxm-er, \" ohm to \" ,rxm+er,\" ohm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Magnitude of unknown resistance is 10575 kohm\n",
- "Relative limiting error is \u00b1 116.325 ohm\n",
- "Guranteed value of resistance is between 10458.675 ohm to 10691.325 ohm\n"
- ]
- }
- ],
- "prompt_number": 14
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.6.6 - page : 2-26"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# absolute error, % error, relative error, % accuracy and % error of full scale reading\n",
- "#given data :\n",
- "Ae=80.0 # in volt\n",
- "Am=79 # in volt\n",
- "fsd=100 #full scale reading in volt\n",
- "e=Ae-Am \n",
- "print \"Absolute error, e = \",e,\" V\"\n",
- "error1=(e/Ae)*100 \n",
- "print \"Error = \",error1,\" %\"\n",
- "A=1-abs(e/Ae) \n",
- "print \"Relative accuracy, A = \",A,\" %\"\n",
- "p_accuracy=A*100 \n",
- "print \"% accuracy = \",p_accuracy,\" %\"\n",
- "error2=(e/fsd)*100 \n",
- "print \"% error expressed as percentage of full scale reading = \",error2,\" %\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Absolute error, e = 1.0 V\n",
- "Error = 1.25 %\n",
- "Relative accuracy, A = 0.9875 %\n",
- "% accuracy = 98.75 %\n",
- "% error expressed as percentage of full scale reading = 1.0 %\n"
- ]
- }
- ],
- "prompt_number": 17
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.6.7 - page : 2-27"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# limiting error\n",
- "#given data :\n",
- "fsd=100.0 # in V\n",
- "A=1.0 # (+ve or -ve) in %\n",
- "del_A=(A/100)*fsd \n",
- "As=15.0 #in V\n",
- "e1=del_A/As \n",
- "e=e1*100 \n",
- "print \"Limiting error, e = \",round(e,4),\" %\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Limiting error, e = 6.6667 %\n"
- ]
- }
- ],
- "prompt_number": 22
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.6.8 - page : 2-27 "
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# limiting value of current and % limiting error\n",
- "#given data :\n",
- "As=2.5 # in A\n",
- "fsd=10 #full scale reading in A\n",
- "A=1.5/100 \n",
- "del_A=A*fsd \n",
- "At1=As+del_A \n",
- "At2=As-del_A \n",
- "print \"Limiting value of current, At1 = \",At1,\" A\"\n",
- "print \"Limiting value of current, At2 = \",At2,\" A\"\n",
- "e=(del_A/As)*100 \n",
- "print \"Percentage limiting error, e = \",e,\" %\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Limiting value of current, At1 = 2.65 A\n",
- "Limiting value of current, At2 = 2.35 A\n",
- "Percentage limiting error, e = 6.0 %\n"
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.1.i - page : 2-30"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#ARITHEMATIC MEAN\n",
- "import numpy\n",
- "q=[49.7,50.1,50.2,49.6,49.7] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "print \"Arithematic mean is \",AM\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Arithematic mean is 49.86\n"
- ]
- }
- ],
- "prompt_number": 57
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.1.ii - page : 2-30"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#deviation\n",
- "import numpy\n",
- "q=[49.7,50.1,50.2,49.6,49.7] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM\n",
- "print \"Deviations of each value are : \"\n",
- "for dev in d:\n",
- " print dev\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Deviations of each value are : \n",
- "-0.16\n",
- "0.24\n",
- "0.34\n",
- "-0.26\n",
- "-0.16\n"
- ]
- }
- ],
- "prompt_number": 58
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.1.iii - page : 2-30"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#algebric sum of deviation\n",
- "import numpy\n",
- "q=[49.7,50.1,50.2,49.6,49.7] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM\n",
- "dtotal=sum(d)\n",
- "print \"Algebric sum of deviation is\", round(dtotal,4)\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Algebric sum of deviation is 0.0\n"
- ]
- }
- ],
- "prompt_number": 59
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.1.iv - page : 2-30"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#standard deviation\n",
- "import numpy\n",
- "q=[49.7,50.1,50.2,49.6,49.7] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM\n",
- "sigma=0\n",
- "n=5 # no. of measurements\n",
- "for dev in d:\n",
- " sigma+=dev**2\n",
- "sigma/=(n-1)\n",
- "sigma**=(1.0/2)\n",
- "print \"Standard Deviation is \",round(sigma,2)\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Standard Deviation is 0.27\n"
- ]
- }
- ],
- "prompt_number": 60
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.2.i - page : 2-31"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#ARITHEMATIC MEAN\n",
- "import numpy\n",
- "q=[101.2,101.4,101.7,101.3,101.3,101.2,101.0,101.3,101.5,101.1] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "print \"Arithematic mean is \",AM,\" V\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Arithematic mean is 101.3 V\n"
- ]
- }
- ],
- "prompt_number": 61
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.2.ii - page : 2-31"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Deviation from mean\n",
- "import numpy\n",
- "q=[101.2,101.4,101.7,101.3,101.3,101.2,101.0,101.3,101.5,101.1] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM\n",
- "print \"Deviations of each value are : \"\n",
- "for dev in d:\n",
- " print dev\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Deviations of each value are : \n",
- "-0.1\n",
- "0.1\n",
- "0.4\n",
- "0.0\n",
- "0.0\n",
- "-0.1\n",
- "-0.3\n",
- "0.0\n",
- "0.2\n",
- "-0.2\n"
- ]
- }
- ],
- "prompt_number": 62
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.2.iii - page : 2-31"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#standard deviation\n",
- "import numpy\n",
- "q=[101.2,101.4,101.7,101.3,101.3,101.2,101.0,101.3,101.5,101.1] \n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM\n",
- "sigma=0\n",
- "n=10 # no. of measurements\n",
- "for dev in d:\n",
- " sigma+=dev**2\n",
- "sigma/=(n-1)\n",
- "sigma**=(1.0/2)\n",
- "print \"Standard Deviation is \",round(sigma,2)\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Standard Deviation is 0.2\n"
- ]
- }
- ],
- "prompt_number": 63
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.2.iv - page : 2-31"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#probable error\n",
- "import numpy\n",
- "q=[101.2,101.4,101.7,101.3,101.3,101.2,101.0,101.3,101.5,101.1] \n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM\n",
- "sigma=0\n",
- "n=10 # no. of measurements\n",
- "for dev in d:\n",
- " sigma+=dev**2\n",
- "sigma/=(n-1)\n",
- "sigma**=(1.0/2)\n",
- "pe1=0.6745*sigma # Probable error of one reading\n",
- "print \"Probable error of one reading is \",pe1,\" V\"\n",
- "pm=pe1/(n-1)**(1.0/2)\n",
- "print \"Probable error of mean is \",round(pm,5)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Probable error of one reading is 0.1349 V\n",
- "Probable error of mean is 0.04497\n"
- ]
- }
- ],
- "prompt_number": 64
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.3.i - page : 2-32"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Arithmetic mean\n",
- "#given data :\n",
- "X1=147.2 # in nF\n",
- "X2=147.4 # in nF\n",
- "X3=147.9 # in nF\n",
- "X4=148.1 # in nF\n",
- "X5=148.1 # in nF\n",
- "X6=147.5 # in nF\n",
- "X7=147.6 # in nF\n",
- "X8=147.4 # in nF\n",
- "X9=147.6 # in nF\n",
- "X10=147.5 # in nF\n",
- "AM=(X1+X2+X3+X4+X5+X6+X7+X8+X9+X10)/10 \n",
- "print \"Arithmetic mean, AM = \",AM,\" nF\" "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Arithmetic mean, AM = 147.63 nF\n"
- ]
- }
- ],
- "prompt_number": 77
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.3.ii - page : 2-32"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# Average deviation\n",
- "#given data :\n",
- "n=10 \n",
- "X1=147.2 # in nF\n",
- "X2=147.4 # in nF\n",
- "X3=147.9 # in nF\n",
- "X4=148.1 # in nF\n",
- "X5=148.1 # in nF\n",
- "X6=147.5 # in nF\n",
- "X7=147.6 # in nF\n",
- "X8=147.4 # in nF\n",
- "X9=147.6 # in nF\n",
- "X10=147.5 # in nF\n",
- "AM=(X1+X2+X3+X4+X5+X6+X7+X8+X9+X10)/n \n",
- "d1=X1-AM \n",
- "d2=X2-AM \n",
- "d3=X3-AM \n",
- "d4=X4-AM \n",
- "d5=X5-AM \n",
- "d6=X6-AM \n",
- "d7=X7-AM \n",
- "d8=X8-AM \n",
- "d9=X9-AM \n",
- "d10=X10-AM \n",
- "Average_deviation=(abs(d1)+abs(d2)+abs(d3)+abs(d4)+abs(d5)+abs(d5)+abs(d6)+abs(d7)+abs(d8)+abs(d9)+abs(d10))/n \n",
- "print \"Average deviation = \",Average_deviation,\" nF\"\n",
- "# answer is wrong in book"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Average deviation = 0.289 nF\n"
- ]
- }
- ],
- "prompt_number": 79
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.3.iii - page : 2-32"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Standard deviation\n",
- "#given data :\n",
- "n=10 \n",
- "X1=147.2 # in nF\n",
- "X2=147.4 # in nF\n",
- "X3=147.9 # in nF\n",
- "X4=148.1 # in nF\n",
- "X5=148.1 # in nF\n",
- "X6=147.5 # in nF\n",
- "X7=147.6 # in nF\n",
- "X8=147.4 # in nF\n",
- "X9=147.6 # in nF\n",
- "X10=147.5 # in nF\n",
- "AM=(X1+X2+X3+X4+X5+X6+X7+X8+X9+X10)/n \n",
- "d1=X1-AM \n",
- "d2=X2-AM \n",
- "d3=X3-AM \n",
- "d4=X4-AM \n",
- "d5=X5-AM \n",
- "d6=X6-AM \n",
- "d7=X7-AM \n",
- "d8=X8-AM \n",
- "d9=X9-AM \n",
- "d10=X10-AM \n",
- "sigma=((d1**2+d2**2+d3**2+d4**2+d5**2+d6**2+d7**2+d8**2+d9**2+d10**2)/(n-1))**(1.0/2) \n",
- "print \"Standard deviation = \",round(sigma,4),\" nF\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Standard deviation = 0.3057 nF\n"
- ]
- }
- ],
- "prompt_number": 82
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.3.iv - page : 2-32"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#: Probable error\n",
- "#given data :\n",
- "n=10 \n",
- "X1=147.2 # in nF\n",
- "X2=147.4 # in nF\n",
- "X3=147.9 # in nF\n",
- "X4=148.1 # in nF\n",
- "X5=148.1 # in nF\n",
- "X6=147.5 # in nF\n",
- "X7=147.6 # in nF\n",
- "X8=147.4 # in nF\n",
- "X9=147.6 # in nF\n",
- "X10=147.5 # in nF\n",
- "AM=(X1+X2+X3+X4+X5+X6+X7+X8+X9+X10)/n \n",
- "d1=X1-AM \n",
- "d2=X2-AM \n",
- "d3=X3-AM \n",
- "d4=X4-AM \n",
- "d5=X5-AM \n",
- "d6=X6-AM \n",
- "d7=X7-AM \n",
- "d8=X8-AM \n",
- "d9=X9-AM \n",
- "d10=X10-AM \n",
- "sigma=((d1**2+d2**2+d3**2+d4**2+d5**2+d6**2+d7**2+d8**2+d9**2+d10**2)/(n-1))**(1.0/2)\n",
- "Pe1=0.6745*sigma # probable error of one reading\n",
- "probable_error=Pe1/(n-1)**(1.0/2)\n",
- "print \"Probable error of one reading = \",round(Pe1,4),\" nF\"\n",
- "print \"Probable error of mean = \",round(probable_error,4),\" nF\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Probable error of one reading = 0.2062 nF\n",
- "Probable error of mean = 0.0687 nF\n"
- ]
- }
- ],
- "prompt_number": 86
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.4.i - page : 2-34"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#ARITHEMATIC MEAN\n",
- "import numpy\n",
- "q=[10.3,10.7,10.9,9.7,9.5,9.2,10.3,11.7] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "print \"Arithematic mean is \",AM,\" kg/cm2\"\n",
- "#answer is wrong in textbook\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Arithematic mean is 10.2875 kg/cm2\n"
- ]
- }
- ],
- "prompt_number": 65
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.4.ii - page : 2-34"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#average deviation\n",
- "import numpy\n",
- "n=8 # NO. OF MEASUREMENTS\n",
- "q=[10.3,10.7,10.9,9.7,9.5,9.2,10.3,11.7] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM # deviation\n",
- "davg=sum(abs(d))/n # average deviation\n",
- "print \"Average deviation = \",round(davg,4),\" kg/cm2\"\n",
- "#answer is wrong in textbook"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Average deviation = 0.6156 kg/cm2\n"
- ]
- }
- ],
- "prompt_number": 66
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.4.iii - page : 2-34"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#standard deviation\n",
- "import numpy\n",
- "q=[10.3,10.7,10.9,9.7,9.5,9.2,10.3,11.7] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM\n",
- "sigma=0\n",
- "n=8 # no. of measurements\n",
- "for dev in d:\n",
- " sigma+=dev**2\n",
- "sigma/=(n-1)\n",
- "sigma**=(1.0/2)\n",
- "print \"Standard Deviation is \",round(sigma,4),\" kg/cm2\"\n",
- "#answer is wrong in textbook\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Standard Deviation is 0.8184 kg/cm2\n"
- ]
- }
- ],
- "prompt_number": 95
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.7.4.iv - page : 2-34"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#probable error\n",
- "n=8 # no. of measurements\n",
- "q=[10.3,10.7,10.9,9.7,9.5,9.2,10.3,11.7] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "d=q-AM\n",
- "sigma=0\n",
- "n=10 # no. of measurements\n",
- "for dev in d:\n",
- " sigma+=dev**2\n",
- "sigma/=(n-1)\n",
- "sigma**=(1.0/2)\n",
- "pe1=0.6745*sigma # Probable error of one reading\n",
- "print \"Probable error of one reading is \",round(pe1,4),\" kg/cm2\"\n",
- "pm=pe1/(n-1)**(1.0/2)\n",
- "print \"Probable error of mean is \",round(pm,4),\" kg/cm2\"\n",
- "#answer is wrong in textbook\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Probable error of one reading is 0.4868 kg/cm2\n",
- "Probable error of mean is 0.1623 kg/cm2\n"
- ]
- }
- ],
- "prompt_number": 67
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.8.1 - page : 2-34"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#ARITHEMATIC MEAN ,median value ,standard deviation and variance\n",
- "q=[25.5,30.3,31.1,29.6,32.4,39.4,28.9,30.0,33.3,31.4,29.5,30.5,31.7,33.0,29.2] #\n",
- "AM= numpy.mean(q) #arithematic mean in mm\n",
- "n=len(q) # no. of measurements\n",
- "Q=q-AM\n",
- "mv=sorted(q)[n/2] # get the median value from sorted q\n",
- "d=q-AM\n",
- "sigma=0\n",
- "for dev in d:\n",
- " sigma+=dev**2\n",
- "sigma/=(n-1)\n",
- "sigma**=(1.0/2) #standard deviation\n",
- "V=sigma**2 #variance\n",
- "print \"Arithematic mean is \",round(AM,4),\" V\"\n",
- "print \"Median value is\",round(mv,1)\n",
- "\n",
- "print \"Standard Deviation is \",round(sigma,2)\n",
- "\n",
- "print \"Variance is \",round(V,0)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Arithematic mean is 31.0533 V\n",
- "Median value is 30.5\n",
- "Standard Deviation is 3.0\n",
- "Variance is 9.0\n"
- ]
- }
- ],
- "prompt_number": 116
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.8.2 - page : 2-37"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#ARITHEMATIC MEAN\n",
- "#from __future__ import division\n",
- "v=[10,11,12,13,14] #\n",
- "f=[03,12,18,12,03] #\n",
- "xn=[a*b for a,b in zip(v,f)]\n",
- "am=sum(xn)/sum(f) # arithmetic mean\n",
- "print \"Arithematic mean is \",am,\" V\"\n",
- "dn=[x-am for x in v] # deviation\n",
- "n_dn=[a*b for a,b in zip(f,dn)]\n",
- "dn2=[a*b for a,b in zip(dn,dn)]\n",
- "n_dn2=[a*b for a,b in zip(f,dn2)]\n",
- "absn_dn=[abs(a) for a in n_dn]\n",
- "mean_dev=sum(absn_dn)/sum(f)\n",
- "print \"Mean deviation = \",mean_dev\n",
- "sigma=(sum(n_dn2)/sum(f))**(1.0/2)\n",
- "print \"Standard deviation is \", sigma\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Arithematic mean is 12.0 V\n",
- "Mean deviation = 0.75\n",
- "Standard deviation is 1.0\n"
- ]
- }
- ],
- "prompt_number": 46
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.8.3 - page : 2-37"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#ARITHEMATIC MEAN ,median value ,standard deviation \n",
- "import numpy\n",
- "q=[29.2,29.5,29.6,30.0,30.5,31.4,31.7,32.4,33.0,33.3,39.4,28.9] #\n",
- "AM= numpy.mean(q)#arithematic mean in mm\n",
- "print \"Arithematic mean is \",round(AM,2)\n",
- "mv=sorted(q)[int(len(q)/2-1)]\n",
- "print \"Median value = \",mv\n",
- "d=[x-AM for x in q]\n",
- "d2=[x**2 for x in d]\n",
- "sigma=(sum(d2)/(len(q)-1))**(1.0/2)\n",
- "print \"Standard Deviation = \",round(sigma,3)\n",
- "\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Arithematic mean is 31.57\n",
- "Median value = 30.5\n",
- "Standard Deviation = 2.886\n"
- ]
- }
- ],
- "prompt_number": 97
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.8.4 - page:2-39"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Unknown resistor \n",
- "#given data :\n",
- "S=1000.0 # ohm/V\n",
- "V=100.0 #in V\n",
- "I=5*10**-3 # in A\n",
- "# part (i)\n",
- "R_app=(V/I)*10**-3 \n",
- "print \"(i) Apparent Resistor, R_app = \",R_app, \" kohm\"\n",
- "# part (ii)\n",
- "V1=150 #in V\n",
- "Rv=S*V1*10**-3 \n",
- "Rx=Rv/6.5 #actual resistance in kohm\n",
- "print \"(ii) Actual resistance is \",round(Rx,2),\" kohm.\"\n",
- "# part(iii)\n",
- "per=(Rx-R_app)/Rx*100 # in %\n",
- "print \"(iii) Percentage error due to loading effect of voltmeter is \",round(per,1), \" %\" \n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(i) Apparent Resistor, R_app = 20.0 kohm\n",
- "(ii) Actual resistance is 23.08 kohm.\n",
- "(iii) Percentage error due to loading effect of voltmeter is 13.3 %\n"
- ]
- }
- ],
- "prompt_number": 103
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 2.8.5 - page : 2-40"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# limiting error\n",
- "#given data :\n",
- "del_A=2.5 # may be +ve or-ve in %\n",
- "As=400.0 \n",
- "FSD=600.0 # in V\n",
- "del_A1=(del_A/100)*FSD \n",
- "e=(del_A1/As)*100 # in %\n",
- "print \"Limiting error, e = \",e, \" %\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Limiting error, e = 3.75 %\n"
- ]
- }
- ],
- "prompt_number": 104
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 06:50:28 +0000