A Course In Mechanical Measurements And Instrumentation_A. K. Sawhney And P. Sawhney.pdf
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Scilab Textbook Companion for A Course In Mechanical Measurements And Instrumentation by A. K. Sawhney And P. Sawhney1 Created by Parul Instrumentation Electrical Engineering Thapar University College Teacher Dr. Sunil K Singla Cross-Checked by
September 23, 2015
1 Funded
by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in
Book Description Title: A Course In Mechanical Measurements And Instrumentation Author: A. K. Sawhney And P. Sawhney Publisher: Dhanpat Rai, New Delhi Edition: 12 Year: 2001 ISBN: 8177000233
1
Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.
2
Contents List of Scilab Codes
4
2 Static Characteristics of Instruments and Measurement systems
5
3 Errors in Measurements and Their Statistical Analysis
19
4 Dynamic Characteristics of Instruments and Measurement systems 44 5 Primary Sensing Elements and Transducers
56
6 Signal Conditioning
83
7 Display Devices and recorders
100
8 Metrology
106
9 Pressure Measurements
111
3
List of Scilab Codes Exa 2.1 Exa 2.2 Exa 2.3 Exa 2.4 Exa 2.5
Exa Exa Exa Exa
2.6 2.7 2.8 2.9
Exa 2.10 Exa 2.12 Exa 2.13 Exa 2.14 Exa 2.15 Exa 2.16 Exa 2.17 Exa 2.18
calculating static error and static correction . . . . . . calculating true value of the temperature . . . . . . . calculating Relative error expressed as a percentage of f sd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . calculating static error and static correction . . . . . . calculating maximum static error Span of the thermometer degree C Accuracy of the thermometer in terms of percentage of span . . . . . . . . . . . . . . . . . . . . calculating the pressure for a dial reading of 100 . . . calculating the noise output voltage of the amplifier . calculating the noise voltage . . . . . . . . . . . . . . . calculating the signal to noise ratio at input calculating the signal to noise ratio at output calculating the noise factor and noise figure . . . . . . . . . . . . . . . . . . calculating the ratio of output signal to noise signal . . calculating the average force and range of error . . . . calculating the sum of resistances connected in series with uncertainity of one unit . . . . . . . . . . . . . . calculating the power with uncertainity of one unit in voltage and current . . . . . . . . . . . . . . . . . . . calculating the sum of resistances connected in series with appropriate number of significant figure . . . . . calculating the voltage drop with appropriate number of significant figure . . . . . . . . . . . . . . . . . . . . calculating the sensitivity and deflection factor of wheatstone bridge . . . . . . . . . . . . . . . . . . . . . . . calculating the volume of the mercury thermometer . .
4
5 5 6 6
7 7 8 8
9 10 10 11 11 12 12 13 13
Exa 2.19 Exa Exa Exa Exa
2.20 2.22 2.23 2.24
Exa 2.25 Exa 2.26 Exa 2.27 Exa 2.28 Exa Exa Exa Exa Exa Exa
2.29 3.1 3.2 3.3 3.4 3.5
Exa 3.6 Exa 3.7 Exa 3.8 Exa 3.9 Exa Exa Exa Exa
3.10 3.11 3.12 3.13
Exa 3.14 Exa 3.15 Exa 3.16 Exa 3.17 Exa 3.18
calculating the maximum position deviation resistance deviation . . . . . . . . . . . . . . . . . . . . . . . . . calculating the dead zone . . . . . . . . . . . . . . . . calculating the Resolution . . . . . . . . . . . . . . . . calculating the Resolution . . . . . . . . . . . . . . . . calculating the reading of the multimeter and percentage error . . . . . . . . . . . . . . . . . . . . . . . . . calculating the reading of the multimeter and percentage error . . . . . . . . . . . . . . . . . . . . . . . . . calculating the loading error . . . . . . . . . . . . . . . calculating the voltage across the oscilloscope . . . . . calculating the actual value of current measured value of current and percentage error . . . . . . . . . . . . . calculating the maximum available power . . . . . . . calculating guarantee value of capacitance . . . . . . . calculating percentage limiting error . . . . . . . . . . Calculate the range of readings . . . . . . . . . . . . . Calculate the limiting error in percent . . . . . . . . . Calculate the range of readings specified interms of fsd and true value . . . . . . . . . . . . . . . . . . . . . . Calculate the magnitude and limiting error in ohm and in percentage of the resistance . . . . . . . . . . . . . calculate the value of relative limiting error in resistance Calculate the guaranteed values of the resistance . . . Calculate the percentage limiting error and range of resistance values . . . . . . . . . . . . . . . . . . . . . . Calculate the magnitude of power and limiting error . Calculate the magnitude of Force and limiting error . calculate the power loss and relative error . . . . . . . Calculate the true power as a percentage of measured power . . . . . . . . . . . . . . . . . . . . . . . . . . . calculate the total resistance error of each register and fractional error of total resistance . . . . . . . . . . . . find the error . . . . . . . . . . . . . . . . . . . . . . . calculate the Volume and relative error . . . . . . . . . calculate the per unit change in the value of spring for different temperature ranges . . . . . . . . . . . . . . Calculate apparent resistance actual resistance and error 5
14 14 14 15 15 16 16 17 17 18 19 19 20 20 21 21 22 22 23 24 25 26 26 27 27 28 29 29
Exa 3.19 Exa 3.20 Exa 3.21 Exa 3.22 Exa 3.23
Exa Exa Exa Exa Exa Exa Exa Exa
3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.31
Exa 3.32 Exa 3.34 Exa 3.35 Exa 3.37 Exa 3.38 Exa 3.39 Exa Exa Exa Exa Exa Exa Exa Exa Exa
3.40 3.41 4.1 4.2 4.4 4.5 4.6 4.8 4.9
Calculate apparent resistance actual resistance and error Calculate the error and percentage error in the measurement of deflection . . . . . . . . . . . . . . . . . . . . to find the mean deviations from the mean Average deviation standard deviation and variance . . . . . . . . to find the mean standard deviation probable error and range . . . . . . . . . . . . . . . . . . . . . . . . . . . to find the arithematic mean maen deviation standard deviation prpobable error of 1 reading standard deviation and probable error of mean standard deviation of standard deviation . . . . . . . . . . . . . . . . . . . . to find probable no of resistors . . . . . . . . . . . . . to find no of 100 rsding exceed 30mm . . . . . . . . . to find no of rods of desired length . . . . . . . . . . . to find standard deviation and probability of error . . to find no of expected readings . . . . . . . . . . . . . to calculate precision index of instrument . . . . . . . to find confidence interval for given confidence levels . to point out the reading that can be rejected by chavenets criterion . . . . . . . . . . . . . . . . . . . . . . . . . . calculate standard deviation . . . . . . . . . . . . . . . determine value of total current considering errors as limiting errors ans as standrd deviations . . . . . . . . determine probable error in the computed value of resistnce . . . . . . . . . . . . . . . . . . . . . . . . . . . to find Cq and its possible errors . . . . . . . . . . . . calculate power disipated and uncertaainity in power . to find uncertainity in combined resistance in both series and in parrallel . . . . . . . . . . . . . . . . . . . . . . to calculate uncertainity in measurement . . . . . . . . to calculate uncertainity in power . . . . . . . . . . . . calculating the temperature . . . . . . . . . . . . . . . calculate time to read half of the temperature difference Calculate the temperature after 10s . . . . . . . . . . Calculate the value of resistance after 15s . . . . . . . Calculate the depth after one hour . . . . . . . . . . . Calculate time constant . . . . . . . . . . . . . . . . . Calculate the temperature after 10s . . . . . . . . . . 6
30 30 31 32
32 33 34 34 35 35 36 37 37 38 39 39 40 41 41 42 43 44 44 45 45 46 46 47
Exa 4.10 Exa 4.11 Exa 4.12 Exa 4.13
Exa Exa Exa Exa
4.14 4.15 4.16 4.17
Exa 4.18 Exa 4.19 Exa 4.20 Exa Exa Exa Exa Exa Exa Exa
4.21 4.22 4.23 5.1 5.2 5.3 5.4
Exa 5.5 Exa 5.6 Exa 5.7 Exa Exa Exa Exa Exa Exa
5.8 5.9 5.10 5.11 5.12 5.13
Exa 5.14
Calculate the temperature at a depth of 1000 m . . . . Calculate the value of resistance at different values of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . calculate the value of damping constant and frequency of damped oscillations . . . . . . . . . . . . . . . . . . Calculate damping ratio natural frequency frequency of damped oscillations time constant and steady state error for ramp signal . . . . . . . . . . . . . . . . . . . . . . Calculate the natural frequency . . . . . . . . . . . . . Calculate natural frequency and setteling time . . . . Calculate time lag and ratio of output and input . . . Calculate the maximum allowable time constant and phase shift . . . . . . . . . . . . . . . . . . . . . . . . Calculate maximum value of indicated temperature and delay time . . . . . . . . . . . . . . . . . . . . . . . . Find the output . . . . . . . . . . . . . . . . . . . . . Calculate maximum and minimum value of indicated temperature phase shift time lag . . . . . . . . . . . . determine damping ratio . . . . . . . . . . . . . . . . . Calculate the frequency range . . . . . . . . . . . . . . determine the error . . . . . . . . . . . . . . . . . . . Calculate the deflection at center . . . . . . . . . . . . Calculate the angle of twist . . . . . . . . . . . . . . . Calculate the Torque . . . . . . . . . . . . . . . . . . . Calculating the displacement and resolution of the potentiometer . . . . . . . . . . . . . . . . . . . . . . . . plot the graph of error versus K . . . . . . . . . . . . . Calculating the output voltage . . . . . . . . . . . . . Calculating the maximum excitation voltage and the sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . Calculating the resolution of the potentiometer . . . . Checking the suitability of the potentiometer . . . . . Checking the suitability of the potentiometer . . . . . Calculating the possion ratio . . . . . . . . . . . . . . Calculating the value of the resistance of the gauges . calculate the percentage change in value of the gauge resistance . . . . . . . . . . . . . . . . . . . . . . . . . Calculating the Gauge factor . . . . . . . . . . . . . . 7
47 47 48
49 50 50 51 52 52 53 53 54 54 55 56 56 57 57 58 58 59 59 59 60 60 61 61 62
Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa
5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.30 5.31 5.32 5.33
Exa 5.34 Exa 5.35 Exa 5.36 Exa Exa Exa Exa Exa
5.37 5.40 5.41 5.42 5.43
Exa 5.44 Exa 5.45
Exa 5.46
Calculating the change in length and the force applied Calculate the linear approximation . . . . . . . . . . . Calculate the linear approximation . . . . . . . . . . . Calculate the resistance and the temperature . . . . . Calculate the resistance . . . . . . . . . . . . . . . . . Calculate the time . . . . . . . . . . . . . . . . . . . . Calculate the resistance . . . . . . . . . . . . . . . . . find resistance . . . . . . . . . . . . . . . . . . . . . . calculating the change in temperature . . . . . . . . . calculating the frequencies of oscillation . . . . . . . . Calculating the sensitivity and maximum output voltage Calculating the temperature . . . . . . . . . . . . . . . Calcating the series resistance and approximate error . Calculate the values of resistance R1 and R2 . . . . . Calculate the percentage linearity . . . . . . . . . . . . Calculate senstivity of the LVDT . . . . . . . . . . . . calculate the deflection maximum and minimum force calculating the sensitivity of the transducer . . . . . . Calculate the value of the capacitance afte the application of pressure . . . . . . . . . . . . . . . . . . . . . . Calculate the change in frequency of the oscillator . . Calculate the dielectric stress change in value of capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the value of time constant phase shift series resistance amplitude ratio and voltage sensitivity . . . Calculate the change in capacitance and ratio . . . . . Calculate the output voltage and charge sensitivity . . Calculate the force . . . . . . . . . . . . . . . . . . . . Calculate the strain charge and capacitance clc . . . . calculate peak to peak voltage swing under open and loaded conditions calculate maximum change in crystal thickness . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the minimum frequency and phase shift . . . calculate sensitivity of the transducer high frequency sensitivity Lowest frequency Calculate external shunt capacitance and high frequency sensitivity after connecting the external shunt capacitance . . . . . . . . . calculate op volatge . . . . . . . . . . . . . . . . . . . 8
62 63 63 64 64 65 65 65 66 66 67 67 67 68 69 69 70 70 71 71 72 72 73 74 74 75
75 76
77 78
Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa
5.47 5.48 5.49 5.50 5.51 5.52 5.53 5.54 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11
Exa 6.12 Exa 6.13 Exa 6.14 Exa 6.15 Exa 6.16 Exa Exa Exa Exa Exa Exa Exa Exa
6.17 6.19 6.20 6.21 6.22 6.23 6.24 6.25
to prove time constant should be approximately 20T . calculate op volatge . . . . . . . . . . . . . . . . . . . Calculate the threshold wavelength . . . . . . . . . . . Calculate maximum velocity of emitted photo electrons Calculate the resistance of the cell . . . . . . . . . . . Calculate incident power and cut off frequency . . . . Calculate the internal resistance of cell and open circuit voltage . . . . . . . . . . . . . . . . . . . . . . . . . . Find the value of current . . . . . . . . . . . . . . . . calculating feedback resistance . . . . . . . . . . . . . calculating the closed loop gain . . . . . . . . . . . . . calculating the maximum output voltage . . . . . . . . calculating output voltage due to offset voltage . . . . calculating Amplification factor . . . . . . . . . . . . . calculating output voltage due to offset voltage . . . . calculating gain and feedback resistance . . . . . . . . Calculating the values of resistances . . . . . . . . . . Calculating the value of resistance and capacitance . . Calculating Difference mode gain and output voltage . Calculating Difference mode Common mode gain and CMRR . . . . . . . . . . . . . . . . . . . . . . . . . . Calculating Signal to noise ratio and CMRR . . . . . . Calculating sensitivity and output voltage . . . . . . . calculating minimum maximum time constants and value of frequencies . . . . . . . . . . . . . . . . . . . . . . . calculating time constant and value of capacitance . . calcuating the passband gain and upper and lower cut off frequencies . . . . . . . . . . . . . . . . . . . . . . calcuating the value of C . . . . . . . . . . . . . . . . calculate the output voltage and sensitivity . . . . . . calculate the output voltage for different values of K . calculating the resistance and output voltage . . . . . Calculating the bridge output . . . . . . . . . . . . . . Calculating the resistance of unknown resistance . . . calculating the current . . . . . . . . . . . . . . . . . . Calculating maximum permissible current through strain gauge supply voltage and Power dissipation in series resistance . . . . . . . . . . . . . . . . . . . . . . . . . . 9
78 79 79 80 80 80 81 81 83 83 84 84 84 85 85 86 86 86 87 88 88 89 89 90 90 90 91 92 92 93 93
94
Exa 6.26 Exa 6.27 Exa 6.28 Exa 6.29 Exa 6.30
Exa 6.31 Exa 6.32 Exa 6.33 Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa
6.34 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 8.1 8.2 8.3 8.4
Exa 8.5 Exa Exa Exa Exa Exa Exa Exa
8.6 8.7 9.1 9.2 9.3 9.4 9.6
Calculating the maximum voltage sensitivity of the bridge Calculating the resolution of the instrument quantization error and decesion levels . . . . . . . . . . . . . . Calculating the weight of MSB and LSB . . . . . . . . Calculating reference voltage and percentage change . Calculating the number of bits Value of LSB Quantization error minimum sampling rate Aperature time and dynamic range . . . . . . . . . . . . . . . . . . . . . . Calculating the value of resistance and smallest output current . . . . . . . . . . . . . . . . . . . . . . . . . . Calculating the output voltage . . . . . . . . . . . . . Calculate the output of successive approximation A to D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . to calculate op dc voltage . . . . . . . . . . . . . . . . calculating resolution . . . . . . . . . . . . . . . . . . calculating resolution . . . . . . . . . . . . . . . . . . calculating Total possible error and percentage error . calculating frequency . . . . . . . . . . . . . . . . . . . calculating maximum error . . . . . . . . . . . . . . . calculating number of turns and current . . . . . . . . calculating speed of the tape . . . . . . . . . . . . . . calculating number density of the tape . . . . . . . . . Calculating possible phase angles . . . . . . . . . . . . Calculating possible phase angles . . . . . . . . . . . . calculate the arrangement of slip gauges . . . . . . . . calculate the sensitivity . . . . . . . . . . . . . . . . . calculate uncertainity in displacement . . . . . . . . . calculate difference between height of workpieces and pile of slip gauges . . . . . . . . . . . . . . . . . . . . calculate seperation distance between two surfaces and angle of tilt . . . . . . . . . . . . . . . . . . . . . . . . Calculate the difference in two diameters . . . . . . . . Calculate the change in thickness along its length . . . calculating the length of mean free path . . . . . . . . Calculate Pressure of air source . . . . . . . . . . . . . Calculate Pressure head . . . . . . . . . . . . . . . . . calculate height . . . . . . . . . . . . . . . . . . . . . . calculate error interms of pressure . . . . . . . . . . . 10
94 95 95 96
96 97 97 98 98 100 100 101 102 102 102 103 104 104 104 106 107 108 108 109 109 110 111 112 112 113 113
Exa 9.7 Exa 9.8 Exa 9.9 Exa Exa Exa Exa
9.10 9.11 9.12 9.13
Exa 9.14 Exa 9.15 Exa Exa Exa Exa Exa
9.16 9.17 9.18 9.19 9.20
calculate angle to which tube is incliend to vertical . . calculate angle to which tube is incliend to horizontal calculate Length of scale angle to which tube is incliend to horizontal . . . . . . . . . . . . . . . . . . . . . . . calculate diameter of the tube . . . . . . . . . . . . . . calculate amplification ratio and percentage error . . . calculate value of counter weight required . . . . . . . calculate damping factor time constant error and time lag calculate damping factor natural frequency time constant error and time lag . . . . . . . . . . . . . . . . . calculate thickness of diaphram and natural frequency calculate the natural length of the spring and dispacement . . . . . . . . . . . . . . . . . . . . . . . . . . . calculate the open circuit voltage . . . . . . . . . . . . calculate the optimum setting . . . . . . . . . . . . . . calculate the output voltage of bridge . . . . . . . . . calculate attenuation . . . . . . . . . . . . . . . . . . . calculate error . . . . . . . . . . . . . . . . . . . . . .
11
113 114 114 115 115 116
116 117 118 118 119 120 121 121
Chapter 2 Static Characteristics of Instruments and Measurement systems
Scilab code Exa 2.1 calculating static error and static correction 1 blue//blue blue c a l c u l a t i n g blue blue s t a t i c blue blue e r r o r
blue blueandblue blue s t a t i c blue blue c o r r e c t i o n 2 redclc ; 3 reddisp ( ’ c a l c u l a t i n g 4 5 6 7 8 9
s t a t i c e r r o r and s t a t i c
correction ’) Am = 127.50; At = 127.43; e = Am - At ; reddisp (e , ’ S t a t i c e r r o r (V)= ’ ) ; Sc = - e ; reddisp ( Sc , ’ S t a t i c C o r r e c t i o n (V)= ’ ) ;
Scilab code Exa 2.2 calculating true value of the temperature
12
1 blue//blue blue c a l c u l a t i n g blue blue t r u e blue blue v a l u e 2 3 4 5 6 7
blue blue o f blue blue t h e blue blue t e m p e r a t u r e redclc ; reddisp ( ’ c a l c u l a t i n g t r u e v a l u e o f t h e t e m p e r a t u r e ’ ) Am = 95.45; Sc = -0.08; At = Am + Sc ; reddisp ( At , ’ True T e m p e r a t u r e ( D e g r e e C)= ’ ) ;
Scilab code Exa 2.3 calculating Relative error expressed as a percentage of f s d 1 blue//blue blue c a l c u l a t i n g blue blue R e l a t i v e blue blue e r r o r
2 3 4 5 6 7 8 9 10 11 12 13
blue blue ( blue e x p r e s s e d blue blue a s blue blueablue blue p e r c e n t a g e blue blue o f blue blue f blue . blue s blue . blued blue ) redclc ; reddisp ( ’ c a l c u l a t i n g R e l a t i v e e r r o r ( e x p r e s s e d a s a percentage of f . s . d) ’) Am = 1.46; At =1.50; e = Am - At ; reddisp (e , ’ A b s o l u t e e r r o r (V)= ’ ) ; Sc = - e ; reddisp ( Sc , ’ A b s o l u t e C o r r e c t i o n (V)= ’ ) ; RE =( e / At ) *100; reddisp ( RE , ’ R e l a t i v e E r r o r i n t e r m s o f t r u e v a l u e ( i n p e r c e n t a g e )= ’ ) ; REF =( e /2.5) *100; reddisp ( REF , ’ R e l a t i v e E r r o r i n t e r m s o f t r u e v a l u e ( i n p e r c e n t a g e )= ’ ) ;
Scilab code Exa 2.4 calculating static error and static correction 13
1 blue//blue blue c a l c u l a t i n g blue blue s t a t i c blue blue e r r o r
blue blueandblue blue s t a t i c blue blue c o r r e c t i o n 2 redclc ; 3 reddisp ( ’ c a l c u l a t i n g 4 5 6 7 8 9
s t a t i c e r r o r and s t a t i c correction ’) Am = 0.000161; At = 0.159*10^ -3; e = Am - At ; reddisp (e , ’ S t a t i c e r r o r (m3/ s )= ’ ) ; Sc = - e ; reddisp ( Sc , ’ S t a t i c C o r r e c t i o n (m3/ s )= ’ ) ;
Scilab code Exa 2.5 calculating maximum static error Span of the thermometer degree C Accuracy of the thermometer in terms of percentage of span 1 blue//blue c a l c u l a t i n g blue bluemaximumblue blue s t a t i c blue 2 3 4 5
6 7 8
blue e r r o r reddisp ( ’ c a l c u l a t i n g maximum s t a t i c e r r o r ’ ) ; blue//blueSpanblue blue o f blue blue t h e blue blue t h e r m o m e t e r blue ( blue d e g r e e blue blueCblue ) S =200 -150; blue//blue A c c u r a c y blue blue o f blue blue t h e blue blue t h e r m o m e t e r blue ( blue i n blue blue t e r m s blue blue o f blue blue p e r c e n t a g e blue blue o f blue blue s p a n blue ) A =0.0025; e= A*S; reddisp (e , ’ Maximum S t a t i c e r r o r ( d e g r e e C)= ’ ) ;
Scilab code Exa 2.6 calculating the pressure for a dial reading of 100
14
1 blue//blue blue c a l c u l a t i n g blue blue t h e blue blue p r e s s u r e
blue blue f o r blue blueablue blue d i a l blue blue r e a d i n g blue blue o f blue blue100 2 redclc ; 3 reddisp ( ’ c a l c u l a t i n g t h e p r e s s u r e f o r a d i a l r e a d i n g o f 100 ’ ) 4 P =((27.58 -6.895) /150) *100+6.895; 5 6 reddisp (P , ’ p r e s s u r e
f o r a d i a l r e a d i n g o f 1 0 0 ( kN/m2)=
’ );
Scilab code Exa 2.7 calculating the noise output voltage of the amplifier 1 blue//blue blue c a l c u l a t i n g blue blue t h e blue blue n o i s e blue
2 3 4 5 6 7 8 9 10 11 12
blue o u t p u t blue blue v o l t a g e blue blue o f blue blue t h e blue blue a m p l i f i e r redclc ; reddisp ( ’ c a l c u l a t i n g t h e n o i s e o u t p u t v o l t a g e o f t h e amplifier ’) Bw =100*10^3; Sn =7*10^ -21; R =50*10^3; A =( Sn * R * Bw ) ^0.5; En =2* A ; reddisp ( En , ’ N o i s e v o l t a g e a t i n p u t (V)= ’ ) ; Ga =100; Eno = En * Ga ; reddisp ( Eno , ’ N o i s e v o l t a g e a t o u t p u t (V)= ’ ) ;
Scilab code Exa 2.8 calculating the noise voltage 1 blue//blue blue c a l c u l a t i n g blue blue t h e blue blue n o i s e blue
blue v o l t a g e 15
2 3 4 5 6 7
redclc ; reddisp ( ’ c a l c u l a t i n g t h e n o i s e v o l t a g e ’ ) Sn =20; Vs =3; Vn = Vs /( Sn ) ^0.5; reddisp ( Vn , ’ n o i s e V o l t a g e (mV)= ’ )
Scilab code Exa 2.9 calculating the signal to noise ratio at input calculating the signal to noise ratio at output calculating the noise factor and noise figure 1 blue//blue blue c a l c u l a t i n g blue blue t h e blue blue s i g n a l
2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
blue blue t o blue blue n o i s e blue blue r a t i o blue blue a t blue blue i n p u t blue//blue blue c a l c u l a t i n g blue blue t h e blue blue s i g n a l blue blue t o blue blue n o i s e blue blue r a t i o blue blue a t blue blue o u t p u t blue//blue c a l c u l a t i n g blue blue t h e blue blue n o i s e blue blue f a c t o r blue blueandblue blue n o i s e blue blue f i g u r e redclc ; reddisp ( ’ s i g n a l t o n o i s e r a t i o a t i n p u t ’ ) Sni =(3*10^ -6/(1*10^ -6) ) ^2; reddisp ( Sni , ’ s i g n a l t o n o i s e r a t i o a t i n p u t= ’ ) reddisp ( ’ s i g n a l t o n o i s e r a t i o a t o u t p u t ’ ) Sno =(60*10^ -6/(20*10^ -6) ) ^2; reddisp ( Sno , ’ s i g n a l t o n o i s e r a t i o a t o u t p u t= ’ ) reddisp ( ’ New s i g n a l t o n o i s e r a t i o a t o u t p u t ’ ) Snno =(60*10^ -6/(25*10^ -6) ) ^2; reddisp ( Snno , ’ s i g n a l t o n o i s e r a t i o a t o u t p u t= ’ ) F = Sni / Snno ; reddisp (F , ’ n o i s e F a c t o r= ’ ) nf =10*redlog10 ( F ) ; reddisp ( nf , ’ n o i s e F i g u r e ( dB )= ’ )
16
Scilab code Exa 2.10 calculating the ratio of output signal to noise signal 1 blue//blue blue c a l c u l a t i n g blue blue t h e blue blue r a t i o blue
2 3 4 5 6 7 8 9 10 11 12 13 14
blue o f blue blue o u t p u t blue blue s i g n a l blue blue t o blue blue n o i s e blue blue s i g n a l redclc ; reddisp ( ’ The n o i s e v o l t a g e i s ’ ) Bw =100*10^3; K =1.38*10^ -23; T =300; R =120; A =( K * T * R * Bw ) ^0.5; En =2* A ; reddisp ( En , ’ N o i s e v o l t a g e (V)= ’ ) ; Eno =0.12*10^ -3; reddisp ( Eno , ’ N o i s e v o l t a g e a t o u t p u t (V)= ’ ) ; Ra = Eno / En ; reddisp ( Ra , ’ R a t i o o f s i g n a l v o t a g e t o N o i s e v o l t a g e = ’ );
Scilab code Exa 2.12 calculating the average force and range of error 1 blue//blue c a l c u l a t i n g blue blue t h e blue blue a v e r a g e blue
2 3 4 5 6 7 8
blue f o r c e blue blueandblue blue r a n g e blue blue o f blue blue e r r o r redclc ; F1 =10.03; F2 =10.10; F3 =10.11; F4 =10.08; Fav =( F1 + F2 + F3 + F4 ) /4; reddisp ( Fav , ’ A v e r a g e F o r c e (N) = ’ ) ; 17
9 Fmax = F3 ; 10 MaxR = Fmax - Fav ; 11 Fmin = F1 ; 12 MinR = Fav - Fmin ; 13 AvgR =( MaxR + MinR ) /2; 14 reddisp ( AvgR , ’ A v e r a g e r a n g e o f
e r r o r (N)= ’ )
Scilab code Exa 2.13 calculating the sum of resistances connected in series with uncertainity of one unit 1 blue//blue c a l c u l a t i n g blue blue t h e blue bluesumblue blue o f
blue blue r e s i s t a n c e s blue blue c o n n e c t e d blue blue i n blue blue s e r i e s blue blue w i t h blue blue u n c e r t a i n i t y blue blue o f blue blueoneblue blue u n i t redclc ; R1 =72.3; R2 =2.73; R3 =0.612; R =( R1 + R2 + R3 ) ; reddisp (R , ’ sum o f r e s i s t a n c e s ( ohm ) = ’ ) ;
2 3 4 5 6 7 8 9 reddisp ( ’ t h e
as f i r s t
r e s u l t a n t r e s i s t a n c e i s 7 5 . 6 ohm w i t h 6 doutful figure ’)
Scilab code Exa 2.14 calculating the power with uncertainity of one unit in voltage and current 1 blue//blue c a l c u l a t i n g blue blue t h e blue bluepowerblue
blue w i t h blue blue u n c e r t a i n i t y blue blue o f blue blueone blue blue u n i t blue blue i n blue blue v o l t a g e blue blueand blue blue c u r r e n t 2 redclc ; 3 V =12.16; 18
4 5 6 7 8
I =1.34; P=V*I; reddisp (P , ’ Power (W) = ’ ) ; reddisp ( ’ t h e r e s u l t a n t doutful figure ’)
i s 16.2 W with 2 as f i r s t
Scilab code Exa 2.15 calculating the sum of resistances connected in series with appropriate number of significant figure 1 blue//blue c a l c u l a t i n g blue blue t h e blue bluesumblue blue o f
blue blue r e s i s t a n c e s blue blue c o n n e c t e d blue blue i n blue blue s e r i e s blue blue w i t h blue blue a p p r o p r i a t e blue bluenumberblue blue o f blue blue s i g n i f i c a n t blue blue f i g u r e 2 redclc ; 3 R1 =28.7; 4 R2 =3.624; 5 6 R =( R1 + R2 ) ; 7 reddisp (R , ’ sum o f r e s i s t a n c e s ( ohm ) = ’ ) ; 8 9 reddisp ( ’ t h e r e s u l t a n t r e s i s t a n c e i s 3 2 . 3 ohm a s one
of the r e s i s t a n c e i s accurate to three significant figure ’)
Scilab code Exa 2.16 calculating the voltage drop with appropriate number of significant figure 1 blue//blue c a l c u l a t i n g blue blue t h e blue blue v o l t a g e blue
blue d r o p blue blue w i t h blue blue a p p r o p r i a t e blue bluenumberblue blue o f blue blue s i g n i f i c a n t blue blue f i g u r e 19
2 3 4 5 6 7 8 9
redclc ; R =31.27; I =4.37; E=I*R; reddisp (E , ’ v o l t a g e d r o p (V) = ’ ) ; reddisp ( ’ t h e v o l t a g e d r o p i s 137 V a s one o f t h e r e s i s t a n c e i s accurate to three s i g n i f i c a n t figure ’)
Scilab code Exa 2.17 calculating the sensitivity and deflection factor of wheatstone bridge 1 blue//blue c a l c u l a t i n g blue blue t h e blue blue s e n s i t i v i t y
2 3 4 5 6 7 8
blue blueandblue blue d e f l e c t i o n blue blue f a c t o r blue blue o f blue blue w h e a t s t o n e blue blue b r i d g e redclc ; Mo =3; Mi =7; Sen = Mo / Mi ; reddisp ( Sen , ’ s e n s i t i v i t y (mm p e r ohm ) = ’ ) ; Df = Mi / Mo ; reddisp ( Df , ’ d e f l e c t i o n f a c t o r ( ohm p e r mm) = ’ ) ;
Scilab code Exa 2.18 calculating the volume of the mercury thermometer 1 blue//blue c a l c u l a t i n g blue blue t h e blue bluevolumeblue 2 3 4 5
blue o f blue blue t h e blue blue m e r c u r y blue blue t h e r m o m e t e r redclc ; Ac =( %pi /4) *0.25^2; reddisp ( Ac , ’ Area o f m e r c u r y t h e r m o m e t e r ’ ) Lc =13.8*10^3; 20
6 Vc = Ac * Lc ; 7 reddisp ( Vc , ’ Volume o f m e r c u r y t h e r m o m e t e r (mm3) ’ )
Scilab code Exa 2.19 calculating the maximum position deviation resistance deviation 1 blue//blue c a l c u l a t i n g blue blue t h e blue bluemaximumblue
2 3 4 5 6 7 8 9
blue p o s i t i o n blue blue d e v i a t i o n blue , blue blue r e s i s t a n c e blue blue d e v i a t i o n redclc ; Pl =0.001; FSD =320; R =10000; MDD =( Pl * FSD ) ; reddisp ( MDD , ’ Maximum d i s p l a c e m e n t d e v i a t i o n ( d e g r e e )= ’ ); MRD = Pl * R ; reddisp ( MRD , ’ Maximum d i s p l a c e m e n t d e v i a t i o n ( ohm )= ’ ) ;
Scilab code Exa 2.20 calculating the dead zone 1 blue//blue c a l c u l a t i n g blue blue t h e blue bluedeadblue 2 3 4 5 6
blue z o n e redclc ; reddisp ( ’ s p a n s= ’ ) s =600; Dz =0.00125* s ; reddisp ( Dz , ’ Dead z o n e ( d e g r e e C)= ’ ) ;
Scilab code Exa 2.22 calculating the Resolution 21
1 2 3 4 5 6 7
blue//blue c a l c u l a t i n g blue blue t h e blue blue R e s o l u t i o n redclc ; Fs =200; D =100; SD = Fs / D ; R = SD /10; reddisp (R , ’ r e s o l u t i o n (V)= ’ )
Scilab code Exa 2.23 calculating the Resolution 1 2 3 4 5 6 7
blue//blue c a l c u l a t i n g blue blue t h e blue blue R e s o l u t i o n redclc ; Fs =9.999; D =9999; SD = Fs / D ; R = SD ; reddisp (R , ’ r e s o l u t i o n (V)= ’ )
Scilab code Exa 2.24 calculating the reading of the multimeter and percentage error 1 blue//blue c a l c u l a t i n g blue blue t h e blue blue r e a d i n g blue
2 3 4 5 6 7 8 9
blue o f blue blue t h e blue blue m u l t i m e t e r blue blueandblue blue p e r c e n t a g e blue blue e r r o r redclc ; Zl =20000; Zo =10000; Eo =6; El = Eo /(1+ Zo / Zl ) ; reddisp ( El , ’ R e a d i n g o f t h e m u l t i m e t e r (V)= ’ ) PE =(( El - Eo ) / Eo ) *100; reddisp ( PE , ’ P e r c e n t a g e e r r o r= ’ ) 22
Scilab code Exa 2.25 calculating the reading of the multimeter and percentage error 1 blue//blue c a l c u l a t i n g blue blue t h e blue blue r e a d i n g blue
2 3 4 5 6 7 8 9
blue o f blue blue t h e blue blue m u l t i m e t e r blue blueandblue blue p e r c e n t a g e blue blue e r r o r redclc ; Zl =20000; Zo =1000; Eo =6; El = Eo /(1+ Zo / Zl ) ; reddisp ( El , ’ R e a d i n g o f t h e m u l t i m e t e r (V)= ’ ) PE =(( El - Eo ) / Eo ) *100; reddisp ( PE , ’ P e r c e n t a g e e r r o r= ’ )
Scilab code Exa 2.26 calculating the loading error 1 blue//blue c a l c u l a t i n g blue blue t h e blue blue l o a d i n g blue 2 3 4 5 6 7 8 9 10 11
blue e r r o r redclc ; Zl =1000; Zo =200*200/400; Eo =100*200/400; El = Eo /(1+ Zo / Zl ) ; reddisp ( El , ’ R e a d i n g o f t h e m u l t i m e t e r (V)= ’ ) PE =(( El - Eo ) / Eo ) *100; reddisp ( PE , ’ P e r c e n t a g e l o a d i n g e r r o r= ’ ) Ac =100+ PE ; reddisp ( Ac , ’ A c c u r a c y= ’ )
23
Scilab code Exa 2.27 calculating the voltage across the oscilloscope 1 blue//blue c a l c u l a t i n g blue blue t h e blue blue v o l t a g e blue 2 3 4 5 6 7 8 9 10 11 12 13
blue a c r o s s blue blue t h e blue blue o s c i l l o s c o p e redclc ; C =50*10^ -6; f =100000; reddisp (f , ’ f r e q u e n c y= ’ ) Xc =1/(2* %pi * f * C ) ; R =10^6; Zl =( R * - %i * Xc ) /( R - %i * Xc ) ; Eo =1; Zo =10*10^3; El = Eo /(1+ Zo / Zl ) ; reddisp ( El , ’ R e a d i n g o f t h e m u l t i m e t e r (V)= ’ )
Scilab code Exa 2.28 calculating the actual value of current measured value of current and percentage error 1 blue//blue c a l c u l a t i n g blue blue t h e blue blue a c t u a l blue
blue v a l u e blue blue o f blue blue c u r r e n t blue , blue blue m e a s u r e d blue blue v a l u e blue blue o f blue blue c u r r e n t blue blueandblue blue p e r c e n t a g e blue blue e r r o r 2 redclc ; 3 4 5 6 7 8 9 10 11 12
Eo =10 -((10*1000) /(1000+1000) ) ; Zo =((1000*1000) /(1000+1000) ) +500; Io = Eo / Zo ; reddisp ( Io , ’ A c t u a l v a l u e o f c u r r e n t (A)= ’ ) Zl =100; Il = Eo /( Zo + Zl ) ; reddisp ( Il , ’ Measured v a l u e o f c u r r e n t (A)= ’ ) PE =(( Il - Io ) / Io ) *100; reddisp ( PE , ’ P e r c e n t a g e l o a d i n g e r r o r= ’ ) 24
Scilab code Exa 2.29 calculating the maximum available power 1 blue//blue c a l c u l a t i n g blue blue t h e blue bluemaximumblue
blue a v a i l a b l e blue bluepower 2 redclc ; 3 4 5 6 7 8 9 10
Eo =80*10^ -3; Il =5*10^ -9; Rl =6*10^6; Ro =( Eo / Il ) - Rl ; Pmax =( Eo ^2) /(4* Ro ) ; reddisp ( Pmax , ’ Maximum a v a i l a b l e Power (W)= ’ )
25
Chapter 3 Errors in Measurements and Their Statistical Analysis
Scilab code Exa 3.1 calculating guarantee value of capacitance 1 blue//blue blue c a l c u l a t i n g blue blue g u a r a n t e e blue 2 3 4 5 6 7 8
blue v a l u e blue blue o f blue blue c a p a c i t a n c e redclc ; As = 1; Er =0.05; Aau = As *(1+ Er ) ; reddisp ( Aau , ’ Upper l i m i t ( m i c r o F )= ’ ) ; Aal = As *(1 - Er ) ; reddisp ( Aal , ’ Lower l i m i t ( m i c r o F )= ’ ) ;
Scilab code Exa 3.2 calculating percentage limiting error 1 blue//blue blue c a l c u l a t i n g blue blue p e r c e n t a g e blue
blue l i m i t i n g blue blue e r r o r 2 redclc ; 3 As = 150; 26
4 5 6 7 8
Er =0.01; dA = As * Er ; As1 =75; Er =( dA / As1 ) *100; reddisp ( Er , ’ P e r c e n t a g e l i m i t i n g e r r o r = ’ ) ;
Scilab code Exa 3.3 Calculate the range of readings 1 blue//blue blue C a l c u l a t e blue blue t h e blue blue r a n g e blue 2 3 4 5 6 7 8 9 10
blue o f blue blue r e a d i n g s redclc ; fsd =1000; TP =100; Efsd =(1/100) *1000; reddisp ( Efsd , ’ m a g n i t u d e o f E r r o r when s p e c i f i e d i n t e r m s o f f u l l s c a l e d e f l e c t i o n (w)= ’ ) reddisp ( ’ Thus t h e m e t e r w i l l r e a d b e t w e e n 90W and 110 W’ ) Etv =(1/100) *100; reddisp ( Etv , ’ m a g n i t u d e o f E r r o r when s p e c i f i e d i n t e r m s o f t r u e v a l u e (w)= ’ ) reddisp ( ’ Thus t h e m e t e r w i l l r e a d b e t w e e n 99W and 101 W’ )
Scilab code Exa 3.4 Calculate the limiting error in percent 1 blue//blue blue C a l c u l a t e blue blue t h e blue blue l i m i t i n g 2 3 4 5 6
blue blue e r r o r blue blue i n blue blue p e r c e n t redclc ; dA =0.05*5*10^ -6; As =2.5*10^ -6; Er =( dA / As ) *100; reddisp ( Er , ’ p e r c e m t a g e l i m i t i n g e r r o r =+/− ’ ) 27
Scilab code Exa 3.5 Calculate the range of readings specified interms of fsd and true value 1 blue//blue blue C a l c u l a t e blue blue t h e blue blue r a n g e blue
2 3 4 5 6 7 8 9 10 11 12 13 14
blue o f blue blue r e a d i n g s blue blue s p e c i f i e d blue blue i n t e r m s blue blue o f blue blue f blue . blue s blue . blued blue . blue blueandblue blue t r u e blue blue v a l u e redclc ; reddisp ( ’ Range when s p e c i f i e d i n t e r m s o f f . s . d . ’ ) Error_fsd =1*1000/100 ’ Range_lower_value =100 - Error_fsd ; reddisp ( Range_lower_value , ’ Lower v a l u e o f r a n g e ( kN/ m2) ’ ) Range_upper_value =100+ Error_fsd ; reddisp ( Range_upper_value , ’ Upper v a l u e o f r a n g e ( kN/ m2) ’ ) reddisp ( ’ Range when s p e c i f i e d i n t e r m s o f True v a l u e ’ ) Error_true =1*100/100 ’ Range_lower_value =100 - Error_true ; reddisp ( Range_lower_value , ’ Lower v a l u e o f r a n g e ( kN/ m2) ’ ) Range_upper_value =100+ Error_true ; reddisp ( Range_upper_value , ’ Upper v a l u e o f r a n g e ( kN/ m2) ’ )
Scilab code Exa 3.6 Calculate the magnitude and limiting error in ohm and in percentage of the resistance 1 blue//blue blue C a l c u l a t e blue blue t h e blue blue m a g n i t u d e
blue blueandblue blue l i m i t i n g blue blue e r r o r blue blue i n blue blueohmblue blueandblue blue i n blue blue p e r c e n t a g e blue blue o f blue blue t h e blue blue r e s i s t a n c e 28
2 3 4 5 6 7 8 9 10 11 12 13 14
redclc ; R1 =37; R1_le =5* R1 /100; R2 =75; R2_le =5* R2 /100; R3 =50; R3_le =5* R3 /100; R = R1 + R2 + R3 ; reddisp (R , ’ V a l u e o f r e s i s t a n c e ( ohm )= ’ ) R_le = R1_le + R2_le + R3_le ; reddisp ( R_le , ’ L i m i t i n g V a l u e o f r e s i s t a n c e ( ohm )= ’ ) Limiting_error_percentage = R_le *100/ R ; reddisp ( Limiting_error_percentage , ’ L i m i t i n g V a l u e o f r e s i s t a n c e ( p e r c e n t a g e )=+/− ’ )
Scilab code Exa 3.7 calculate the value of relative limiting error in resistance 1 blue//blue blue c a l c u l a t e blue blue t h e blue blue v a l u e blue
2 3 4 5 6
blue o f blue blue blue r e l a t i v e blue blue l i m i t i n g blue blue e r r o r blue blue i n blue blue r e s i s t a n c e redclc ; Re_P =1.5; Re_I =1; Re_resistance =( Re_P +2* Re_I ) ; reddisp ( Re_resistance , ’ t h e v a l u e o f relative l i m i t i n g e r r o r o f r e s i s t a n c e i n p e r c e n t a g e (+/−)= ’ )
Scilab code Exa 3.8 Calculate the guaranteed values of the resistance
29
1 blue//blue blue C a l c u l a t e blue blue t h e blue blue g u a r a n t e e d
2 3 4
5 6 7 8 9 10 11
blue blue v a l u e s blue blue o f blue blue t h e blue blue r e s i s t a n c e redclc ; R1 =100; R1_le_perunit =0.5; blue//blue blue R 1 l e p e r u n i t blue blue i n d i c a t e s blue bluedR1blue/blueR1blue blue=blue blue 0 . 5 blue% R2 =1000; R2_le_perunit =0.5; R3 =842; R3_le_perunit =0.5; Rx = R2 * R3 / R1 ; reddisp ( Rx , ’ V a l u e o f r e s i s t a n c e ( ohm )= ’ ) Rx_le_perunit = R1_le_perunit + R2_le_perunit + R3_le_perunit ;
12 13 reddisp ( Rx_le_perunit , ’ L i m i t i n g V a l u e o f 14 15 16 17 18 19
resistance
p e r u n i t ( dRx/Rx )= ’ ) Er_Le = Rx_le_perunit * Rx /100; reddisp ( Er_Le , ’ L i m i t i n g V a l u e o f r e s i s t a n c e ( ohm )=+/− ’) reddisp ( ’ G u a r a n t e e v a l u e o f t h e r e s i s t a n c e ( ohm )= ’ ) G1 = Rx + Er_Le ; G2 = Rx - Er_Le ; reddisp ( G1 , G2 , ’ ’ )
Scilab code Exa 3.9 Calculate the percentage limiting error and range of resistance values 1 blue//blue blue C a l c u l a t e blue blue t h e blue blue p e r c e n t a g e
blue blue l i m i t i n g blue blue e r r o r blue blueandblue blue r a n g e blue blue o f blue blue r e s i s t a n c e blue blue v a l u e s 2 redclc ; 3 reddisp ( ’ d e c a d e a i s s e t a t 4 0 0 0 ohm , so , e r r o r i n 30
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
d e c a d e a= ’ ) Er_a =4000*0.1/100; reddisp ( Er_a ) reddisp ( ’ d e c a d e b i s s e t a t 600 ohm , so , e r r o r i n d e c a d e b= ’ ) Er_b =600*0.1/100; reddisp ( Er_b ) reddisp ( ’ d e c a d e c i s s e t a t 30 ohm , so , e r r o r i n d e c a d e c= ’ ) Er_c =30*0.1/100; reddisp ( Er_c ) reddisp ( ’ d e c a d e d i s s e t a t 9 ohm , so , e r r o r i n d e c a d e d= ’ ) Er_d =9*0.1/100; reddisp ( Er_d ) Er_total = Er_a + Er_b + Er_c + Er_d ; Re_le_percentage = Er_total *100/4639; reddisp ( Re_le_percentage , ’ P e r c e n t a g e R e l a t i v e l i m i t i n g e r r o r= ’ ) Range_lower =4639 - Er_total ; reddisp ( Range_lower , ’ Lower v a l u e o f r a n g e ( ohm )= ’ ) Range_upper =4639+ Er_total ; reddisp ( Range_upper , ’ u p p e r v a l u e o f r a n g e ( ohm )= ’ )
Scilab code Exa 3.10 Calculate the magnitude of power and limiting error 1 blue//blue blue C a l c u l a t e blue blue t h e blue blue m a g n i t u d e
2 3 4 5 6 7
blue blue o f blue bluepowerblue blueandblue blue l i m i t i n g blue blue e r r o r redclc ; F =4.58; L =397; R =1202*10^ -9; t =60; P =(2* %pi *9.81* F * L * R ) /( t *10^6) ; 31
8 reddisp (P , ’ Magnitude o f power (W)= ’ ) 9 dF_pu =0.02/ F ; blue//blue blue p e r blue blue u n i t blue 10 11 12 13 14 15
blue e r r o r blue blue i n blue blue f o r c e dL_pu =1.3/ L ; blue//blue blue p e r blue blue u n i t blue blue e r r o r blue blue i n blue blue Length dR_pu =1/ R ; blue//blue blue p e r blue blue u n i t blue blue e r r o r blue blue i n blue blue r e v o l u t i o n dt_pu =0.5/ t ; blue//blue blue p e r blue blue u n i t blue blue e r r o r blue blue i n blue blue t i m e dP_pu = dF_pu + dL_pu + dR_pu + dt_pu ; dP_le = dP_pu * P ; reddisp ( dP_le , ’ Magnitude o f l i m i t i n g e r r o r i n power ( W) ’ )
Scilab code Exa 3.11 Calculate the magnitude of Force and limiting error 1 blue//blue blue C a l c u l a t e blue blue t h e blue blue m a g n i t u d e
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
blue blue o f blue blue F o r c e blue blueandblue blue l i m i t i n g blue blue e r r o r redclc ; E =200*10^9; L =25*10^ -3; b =4.75*10^ -3; d =0.9*10^ -3; I =( b * d ^3) /12; x =2.5*10^ -3; F =(3* E * I * x ) /( L ^3) ; reddisp (F , ’ Magnitude o f F o r c e (N)= ’ ) dE_pu =0/ E ; blue//blue blue p e r blue blue u n i t blue blue e r r o r blue blue i n blue blueE db_pu =0.0075/ b ; dd_pu =0.0075/ d ; dx_pu =0.025/ x ; dL_pu =0.025/ L ; dF_pu = ( dE_pu + db_pu +3* dd_pu + dx_pu +3* dL_pu ) *10^ -3; 32
17 18 reddisp ( dF_pu , ’ l i m i t i n g
e r r o r i n f o r c e (N)=+/− ’ )
Scilab code Exa 3.12 calculate the power loss and relative error 1 blue//blue blue c a l c u l a t e blue blue t h e blue bluepowerblue 2 3 4 5 6 7 8
blue l o s s blue blueandblue blue r e l a t i v e blue blue e r r o r redclc ; I =64*10^ -3; R =3200; P =( I ^2) * R ; reddisp (P , ’ Power (W)= ’ ) Re =2*0.75+0.2; reddisp ( Re , ’ R e l a t i v e e r r o r (%)= ’ )
Scilab code Exa 3.13 Calculate the true power as a percentage of measured power 1 blue//blue blue C a l c u l a t e blue blue t h e blue blue t r u e blue
2 3 4 5 6 7 8 9 10
bluepowerblue blue a s blue blueablue blue p e r c e n t a g e blue blue o f blue blue m e a s u r e d blue bluepower redclc ; I =30.4; R =0.015; I_true = I *(1+0.012) ; R_true = R *(1 -0.003) ; P_true =( I_true ^2) * R_true ; P_measured =( I ^2) * R ; R = P_true *100/ P_measured ; reddisp (R , ’ t r u e power a s a p e r c e n t a g e o f m e a s u r e d power (%)= ’ )
33
Scilab code Exa 3.14 calculate the total resistance error of each register and fractional error of total resistance 1 blue//blue c a l c u l a t e blue blue t h e blue blue t o t a l blue
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
blue r e s i s t a n c e blue , blue blue e r r o r blue blue o f blue blue e a c h blue blue r e g i s t e r blue blueandblue blue f r a c t i o n a l blue blue e r r o r blue blue o f blue blue t o t a l blue blue r e s i s t a n c e redclc ; R1 =250; R2 =500; R3 =375; R_true =1/((1/ R1 ) +(1/ R2 ) +(1/ R3 ) ) ; reddisp ( R_true , ’ True v a l u e o f r e s i s t a n c e ( ohm )= ’ ) dR1 = 0.025* R1 ; dR2 = -0.36* R2 ; dR3 =0.014* R3 ; R1_effective = R1 + dR1 ; R2_effective = R2 + dR2 ; R3_effective = R3 + dR3 ; R_effective =1/((1/ R1_effective ) +(1/ R2_effective ) +(1/ R3_effective ) ) ; reddisp ( R_effective , ’ E f f e c t i v e v a l u e o f r e s i s t a n c e ( ohm )= ’ ) Fractional_error =( R_true - R_effective ) / R_true ; reddisp ( Fractional_error , ’ F r a c t i o n a l e r r o r ’ )
Scilab code Exa 3.15 find the error 1 blue// 2 redclc ;
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3 reddisp ( ’ When a l l 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
t h e c o m p o n en t s have 0% e r r o r t h e n r e s o n a n t f r e q u e n c y ( Hz ) ’ ) L =160*10^ -6; C =160*10^ -12; fr =[1/(2* %pi ) ]*[1/( L * C ) ]^0.5; reddisp ( fr ) reddisp ( ’ When a l l t h e c o m p o n en t s have +10% e r r o r t h e n r e s o n a n t f r e q u e n c y ( Hz ) ’ ) L_new =(160*10^ -6) +0.1* L ; C_new =(160*10^ -12) +0.1* C ; fr_new =[1/(2* %pi ) ]*[1/( L_new * C_new ) ]^0.5; reddisp ( fr_new ) rederror =( fr_new - fr ) / fr ; reddisp (rederror , ’ e r r o r= ’ ) reddisp ( ’ When a l l t h e c o m p o n en t s have −10% e r r o r t h e n r e s o n a n t f r e q u e n c y ( Hz ) ’ ) L_new =(160*10^ -6) -0.1* L ; C_new =(160*10^ -12) -0.1* C ; fr_new =[1/(2* %pi ) ]*[1/( L_new * C_new ) ]^0.5; reddisp ( fr_new ) rederror =( fr_new - fr ) / fr ; reddisp (rederror , ’ e r r o r= ’ )
Scilab code Exa 3.16 calculate the Volume and relative error 1 blue//blue blue c a l c u l a t e blue blue t h e blue blueVolumeblue 2 3 4 5 6 7 8
blueandblue blue r e l a t i v e blue blue e r r o r redclc ; L =250; d =50; V =(( %pi /4) * d ^2) * L ; reddisp (V , ’ Volume (mm3)= ’ ) Re =2*0.2 -0.5; reddisp ( Re , ’ R e l a t i v e e r r o r (%)= ’ )
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Scilab code Exa 3.17 calculate the per unit change in the value of spring for different temperature ranges 1 blue//blue blue c a l c u l a t e blue blue t h e blue blue p e r blue
2 3 4 5 6 7 8 9 10 11 12
blue u n i t blue blue c h a n g e blue blue i n blue blue t h e blue blue v a l u e blue blue o f blue blue s p r i n g blue blue f o r blue blue d i f f e r e n t blue blue t e m p e r a t u r e blue blue r a n g e s redclc ; dG_pu = -240*10^ -6; dD_pu =11.8*10^ -6; reddisp ( ’ f o r t e m p e r a t u r e c h a n g e o f 20 d e g r e e C t o 50 d e g r e e C (%) = ’ ) d_th =30; dK_pu =( dG_pu + dD_pu ) * d_th *100; reddisp ( dK_pu ) reddisp ( ’ f o r t e m p e r a t u r e c h a n g e o f 20 d e g r e e C t o −50 d e g r e e C (%) = ’ ) d_th = -70; dK_pu =( dG_pu + dD_pu ) * d_th *100; reddisp ( dK_pu )
Scilab code Exa 3.18 Calculate apparent resistance actual resistance and error 1 blue//blue blue C a l c u l a t e blue blue a p p a r e n t blue
2 3 4 5 6
blue r e s i s t a n c e blue , blue blue a c t u a l blue blue r e s i s t a n c e blue blueandblue blue e r r o r redclc ; Et =100; It =5*10^ -3; Rt = Et / It ; reddisp ( Rt , ’ a p p a r e n t v a l u e o f r e s i s t a n c e ( ohm )= ’ ) 36
7 8 9 10 11
Rv =1000*150; Rx = Rt * Rv /( Rv - Rt ) ; reddisp ( Rx , ’ t r u e v a l u e o f r e s i s t a n c e ( ohm ) ’ ) Er_percentage =[( Rt - Rx ) / Rx ]*100; reddisp ( Er_percentage , ’ p e r c e n t a g e e r r o r= ’ )
Scilab code Exa 3.19 Calculate apparent resistance actual resistance and error 1 blue//blue blue C a l c u l a t e blue blue a p p a r e n t blue
2 3 4 5 6 7 8 9 10 11
blue r e s i s t a n c e blue , blue blue a c t u a l blue blue r e s i s t a n c e blue blueandblue blue e r r o r redclc ; Et =40; It =800*10^ -3; Rt = Et / It ; reddisp ( Rt , ’ a p p a r e n t v a l u e o f r e s i s t a n c e ( ohm )= ’ ) Rv =1000*150; Rx = Rt * Rv /( Rv - Rt ) ; reddisp ( Rx , ’ t r u e v a l u e o f r e s i s t a n c e ( ohm ) ’ ) Er_percentage =[( Rt - Rx ) / Rx ]*100; reddisp ( Er_percentage , ’ p e r c e n t a g e e r r o r= ’ )
Scilab code Exa 3.20 Calculate the error and percentage error in the measurement of deflection 1 blue//blue C a l c u l a t e blue blue t h e blue blue e r r o r blue blueand
blue blue p e r c e n t a g e blue blue e r r o r blue blue i n blue blue t h e blue bluemeasurementblue blue o f blue blue d e f l e c t i o n 2 redclc ; 3 l =0.2; 4 E =200*10^9; 37
5 6 7 8 9 10 11 12 13 14 15 16
b =20*10^ -3; d =5*10^ -3; D =(4* l ^3) /( E * b * d ^3) ; F =1*9.81; x_true = D * F ; reddisp ( x_true , ’ True v a l u e o f d e f l e c t i o n ’ ) x_indicated = D *10.31/(1+.1* D ) ; reddisp ( x_indicated , ’ I n d i c a t e d v a l u e o f d e f l e c t i o n ’ ) Er = x_indicated - x_true ; reddisp ( Er , ’ e r r o r= ’ ) Er_percentage = Er *100/ x_true ; reddisp ( Er_percentage , ’ P e r c e n t a g e e r r o r= ’ )
Scilab code Exa 3.21 to find the mean deviations from the mean Average deviation standard deviation and variance 1 blue//blue t o blue blue f i n d blue blue t h e blue bluemeanblue ,
blue d e v i a t i o n s blue bluefromblue blue t h e blue bluemean blue , blue blue A v e r a g e blue blue d e v i a t i o n blue , blue blue s t a n d a r d blue blue d e v i a t i o n blue blueandblue blue v a r i a n c e 2 3 4 5 6 7 8 9 10 11 12 13 14 15
redclc ; x =[532 548 543 535 546 531 543 536]; X =redsum ( x ) ; n =8; a =0; Mean = X / n ; reddisp ( X /n , ’ mean ( kHZ ) ’ ) ; redfor i =1: n , d ( i ) = x ( i ) - Mean reddisp ( d ( i ) , ’ d e v i a t i o n s = ’ ) a = a +(redabs ( d ( i ) ) ) redend d_average = a / n ; 38
16 17 18 19 20 21
reddisp ( d_average , ’ A v e r a g e d e v i a t i o n ( kHz )= ’ ) d_2 =redsum ( d ^2) ; s =redsqrt ( d_2 /( n -1) ) reddisp (s , ’ s t a n d a r d d e v i a t i o n ( kHz ) ’ ) ; V = s ^2; reddisp (V , ’ v a r a i n c e ( kHZ ) 2= ’ )
Scilab code Exa 3.22 to find the mean standard deviation probable error and range 1 blue//blue t o blue blue f i n d blue blue t h e blue bluemeanblue ,
blue s t a n d a r d blue blue d e v i a t i o n blue , blue blue p r o b a b l e blue blue e r r o r blue blueandblue blue r a n g e 2 3 4 5 6 7 8 9 10 11 12 13 14 15
redclc ; x =[41.7 42 41.8 42 42.1 41.9 42 41.9 42.5 41.8]; X =redsum ( x ) ; reddisp ( X ) ; d =[ -.27 .03 -.17 .03 .13 -.07 .03 -.07 .53 -.17]; d_2 =redsum ( d ^2) ; n =10; reddisp ( X /n , ’ mean l e n g t h ( deg C) ’ ) ; reddisp (redsqrt ( d_2 / n ) , ’ s t a n d a r d d e v i a t i o n ( i f d a t a i s i n f i n i t e ) ( deg C) ’ ) ; reddisp (redsqrt ( d_2 /( n -1) ) , ’ s t a n d a r d d e v i a t i o n ( deg C) ’ ); r1 =.6745*redsqrt ( d_2 /( n -1) ) ; reddisp ( r1 , ’ p r o b a b l e e r r o r o f 1 r e a d i n g ( deg C) ’ ) ; reddisp ( r1 /redsqrt (n -1) , ’ p r o b a b l e e r r o r o f mean ( deg C ) ’ ); reddisp (redmax ( x ) -redmin ( x ) , ’ r a n g e ( deg C) ’ ) ;
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Scilab code Exa 3.23 to find the arithematic mean maen deviation standard deviation prpobable error of 1 reading standard deviation and probable error of mean standard deviation of standard deviation 1 blue//blue t o blue blue f i n d blue blue t h e blue blue a r i t h e m a t i c
blue bluemeanblue , blue bluemaenblue blue d e v i a t i o n blue , blue s t a n d a r d blue blue d e v i a t i o n blue , blue blue p r p o b a b l e blue blue e r r o r blue blue o f blue blue1blue blue r e a d i n g blue , blue blue s t a n d a r d blue blue d e v i a t i o n blue blueand blue blue p r o b a b l e blue blue e r r o r blue blue o f blue bluemean blue , blue blue s t a n d a r d blue blue d e v i a t i o n blue blue o f blue blue s t a n d a r d blue blue d e v i a t i o n 2 3 4 5 6 7 8 9 10 11 12
13 14
redclc ; T =[397 398 399 400 401 402 403 404 405]; f =[1 3 12 23 37 16 4 2 2]; Tf =redsum (redabs ( T .* f ) ) ; reddisp ( Tf /redsum ( f ) , ’ mean temp ( deg C) ’ ) ; d =[ -3.78 -2.78 -1.78 -.78 .22 1.22 2.22 3.22 4.22]; reddisp (redsum ( f .* d ) /redsum ( f ) , ’ mean d e v i a t i o n ( deg C) ’ ); reddisp (redsqrt (redsum ( f .* d ^2) /redsum ( f ) ) , ’ s t a n d a r d d e v i a t i o n ( deg C) ’ ) ; reddisp (.6745*redsqrt (redsum ( f .* d ^2) /redsum ( f ) ) , ’ p r o b a b l e e r r o r o f 1 r e a d i n g ( deg C) ’ ) ; reddisp ((.6745*redsqrt (redsum ( f .* d ^2) /redsum ( f ) ) ) / redsqrt (redsum ( f ) ) , ’ p r o b a b l e e r r o r o f mean ( deg C) ’ ); reddisp ((redsqrt (redsum ( f .* d ^2) /redsum ( f ) ) ) /redsqrt ( redsum ( f ) ) , ’ s t a n d a r d d e v i a t i o n o f mean ( deg C) ’ ) ; reddisp ((redsqrt (redsum ( f .* d ^2) /redsum ( f ) ) ) /redsqrt ( redsum ( f ) *2) , ’ s t a n d a r d d e v i a t i o n o f s t a n d a r d d e v i a t i o n ( deg C) ’ ) ;
Scilab code Exa 3.24 to find probable no of resistors 40
1 blue//blue t o blue blue f i n d blue blue p r o b a b l e blue bluenoblue
blue o f blue blue r e s i s t o r s 2 3 4 5 6 7
redclc ; x =.15; blue blue//blue d e v i a t i o n o =.1; blue blue//blue s t a n d a r d blue blue d e v i a t i o n t=x/o; A =.4432 blue blue//blue a r e a blue blue u n d e r blue blue g a u s s i a n blue blue c u r v e blue blue c o r r e s p o n d i n g blue blue t o blue blue t 8 n =2* A *1000; 9 reddisp (redfloor ( n ) , ’ no o f r e s i s t o r s ’ ) ;
Scilab code Exa 3.25 to find no of 100 rsding exceed 30mm 1 blue//blue t o blue blue f i n d blue bluenoblue blue o f blue blue100
blue blue r s d i n g blue blue e x c e e d blue blue30bluemm 2 3 redclc ; 4 x =30 -26.3; blue
blue//bluemeanblue blue v a l u e blue
blue 2 6 . 3 r =2.5; o = r /.6745; t=x/o; A =.3413;blue//blue a r e a blue blue u n d e r blue blue g a u s s i a n blue blue c u r v e blue blue c o r r e s p o n d i n g blue blue t o blue blue t 9 n =2* A *100; 10 nn =100 -redfloor ( n ) ; 11 reddisp ( nn /2 , ’ no o f r e a d i n g s e x c e e d ’ ) ; 5 6 7 8
Scilab code Exa 3.26 to find no of rods of desired length 41
1 blue//blue t o blue blue f i n d blue bluenoblue blue o f blue
blue r o d s blue blue o f blue blue d e s i r e d blue blue l e n g t h 2 3 4 5 6 7 8 9 10 11 12 13
redclc ; n =25000; blue blue//bluenoblue blue o f blue blue r o d s n1 =12500; blue//blue l e n g t h blue>10bluemm n2 =2000; blue blue//blue l e n g t h blue > 1 0 . 2 5 a = n1 - n2 ; blue blue//blue10 3 . 1 2 5 s o d1=1 ’ ) reddisp ( ’ S e t d0=1 ’ ) Output =(5/2^1) +(5/2^3) +(5/2^4) ; reddisp ( ’ s i n c e 3 . 2 1 7 < 3 . 4 3 7 5 s o d0=0 ’ ) reddisp ( ’ Output o f s u c c e s s i v e a p p r o x i m a t i o n A/D = 1010 ’ )
Scilab code Exa 6.34 to calculate op dc voltage 105
1 blue//blue t o blue blue c a l c u l a t e blue blueoblue/bluepblue
bluedcblue blue v o l t a g e 2 3 4 5 6 7 8 9 10 11
redclc ; t =400; T = t /4; C =1*10^ -6; v =20; i = C *100* v /( T ) ; R =1*10^3; e_o = i * R ; reddisp ( e_o , ’ o u t p u t v o l t a g e (V) ’ ) ;
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Chapter 7 Display Devices and recorders
Scilab code Exa 7.1 calculating resolution blue//blue blue c a l c u l a t i n g blue blue r e s o l u t i o n redclc ; N = 4; R =1/10^ N ; reddisp (R , ’ R e s o l u t i o n o f t h e m e t e r= ’ ) ; VR =1; R1 = VR * R ; reddisp ( R1 , ’ R e s o l u t i o n o f t h e m e t e r f o r v o l t a g e r a n g e 1V= ’ ) ; 9 VR1 =10; 10 R2 = VR1 * R ; 11 reddisp ( R2 , ’ R e s o l u t i o n o f t h e m e t e r f o r v o l t a g e r a n g e 10V= ’ ) ; 1 2 3 4 5 6 7 8
Scilab code Exa 7.2 calculating resolution 1 blue//blue blue c a l c u l a t i n g blue blue r e s o l u t i o n 2 redclc ;
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3 4 5 6 7 8 9 10 11 12 13 14
N = 3; R =1/10^ N ; reddisp (R , ’ R e s o l u t i o n o f t h e m e t e r= ’ ) ; reddisp ( ’ 1 2 . 9 8 w i l l be d i s p l a y e d a s 1 2 . 9 8 0 on 10V scale ’) VR =1; R1 = VR * R ; reddisp ( R1 , ’ R e s o l u t i o n o f t h e m e t e r f o r v o l t a g e r a n g e 1V= ’ ) ; reddisp ( ’ 0 . 6 9 7 3 w i l l be d i s p l a y e d a s 0 . 6 9 7 3 on 1V scale ’) VR1 =10; R2 = VR1 * R ; reddisp ( R2 , ’ R e s o l u t i o n o f t h e m e t e r f o r v o l t a g e r a n g e 10V= ’ ) ; reddisp ( ’ 0 . 6 9 7 3 w i l l be d i s p l a y e d a s 0 0 . 6 9 7 on 10V scale ’)
Scilab code Exa 7.3 calculating Total possible error and percentage error 1 blue//blue blue c a l c u l a t i n g blue blue T o t a l blue blue p o s s i b l e
2 3 4 5 6 7 8 9 10 11 12 13
blue blue e r r o r blue blueandblue blue p e r c e n t a g e blue blue e r r o r redclc ; R =5; V =0.005* R ; reddisp (V , ’ 0 . 5 p e r c e n t o f t h e r e a d i n g ’ ) TPE = V +0.01; reddisp ( TPE , ’ T o t a l p o s s i b l e e r r o r (V)= ’ ) R1 =0.10; V1 =0.005* R1 ; TPE1 = V1 +0.01; reddisp ( TPE1 , ’ T o t a l p o s s i b l e e r r o r (V)= ’ ) PE =( TPE1 /0.1) *100; reddisp ( PE , ’ P e r c e n t a g e e r r o r= ’ ) 108
Scilab code Exa 7.4 calculating frequency 1 2 3 4 5 6
blue//blue blue c a l c u l a t i n g blue blue f r e q u e n c y redclc ; N =034; t =10*10^ -3; f=N/t; reddisp (f , ’ f r e q u e n c y ( Hz )= ’ )
Scilab code Exa 7.5 calculating maximum error 1 2 3 4 5 6 7 8 9 10 11 12 13 14
blue//blue blue c a l c u l a t i n g blue bluemaximumblue blue e r r o r redclc ; R =5*10^6; V =0.00005* R ; reddisp (V , ’ 0 . 0 0 5 p e r c e n t o f t h e r e a d i n g ( m i c r o s e c )= ’ ) ; LSD =1; ME = V +1; reddisp ( ME , ’ Maximum e r r o r ( m i c r o s e c )= ’ ) R =500; V =0.00005* R ; reddisp (V , ’ 0 . 0 0 5 p e r c e n t o f t h e r e a d i n g ( s e c )= ’ ) ; LSD =1; ME = V +1; reddisp ( ME , ’ Maximum e r r o r ( s e c )= ’ )
Scilab code Exa 7.6 calculating number of turns and current
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1 blue//blue blue c a l c u l a t i n g blue bluenumberblue blue o f blue 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
blue t u r n s blue blueandblue blue c u r r e n t redclc ; D =8*10^ -3; A = D ^2; reddisp (A , ’A= ’ ) J =8*10^ -3; K =16*10^ -3; B =4* J * K ; reddisp (B , ’B= ’ ) reddisp ( ’ s i n c e A
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