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EKT212/4 Principles of Measurement and Instrumentation
(sem.2 2014/15)
Tutorial 1
Question 1
(a).
Differentiate between measurement and instrument.
Measurement is the process of determining the amount, degree, or capacity by comparison (direct or
indirect) with the accepted standards of the system units being used.
Instrument is a device or mechanism used to determine the present value of the quantity under
measurement
(b). A Digital Clamp Meter is used to measure the current flow into a machine at different
interval. The results are shown in Table 1. Calculate:
Arithmetic mean;
Deviation for each reading;
Average deviation;
Standard deviation;
Precision for most frequent reading.
Table 1
No. of measurement Frequency of reading Current, I (A)
1
1
2.002
2
3
1.997
3
1
2.001
4
4
1.996
5
1
1.998
Sol:
No. of
measurement
Frequency
of
reading(n)
Current,
I (A)
(xn)
nxI
(ii)Deviati
on
d n  xn  x
|n x dn|
n x| dn|2
1
1
2.002
2.002
0.0044
0.0044
12.25µ
2
3
1.997
5.991
-0.0006
0.0018
9.72µ
3
1
2.001
2.001
0.0034
0.0034
11.56µ
4
4
1.996
7.984
-0.0016
0.0064
10.24µ
5
1
1.998
1.998
0.0004
0.0004
0.16µ
  0.0164
  43.93
∑n=10
∑=19.976
(i)Arithmetic mean
x
 n  I  1.9976
n
(iii)Average deviation
(iv)Standard deviation

Dav = 0.00164
43 .93 
 0.00221
9
EKT212/4 Principles of Measurement and Instrumentation
(vi)
(sem.2 2014/15)
Precision for the most frequent reading= P  1 
1.996  1.9976
 0.9992
1.9976
Question 2
(a) Compare accuracy, precision and sensitivity.
Accuracy is the degree of exactness (closeness) of a measurement compared to the expected
(desired) value.
Precision measure of the consistency or repeatability of measurements, i.e. successive
reading does not differ.
Sensitivity is the ratio of the change in output (response) of the instrument to a
change of input or measured variable.
(b)
The expected value of the current through a resistor is 22 mA. However the
measurement yields a current value of 19 mA. Calculate
(i)
(ii)
(iii)
(iv)
Absolute error,
Percentage of error,
Relative accuracy, and
Percentage of accuracy
Yn  22 mA,
X n  19 mA
Absolute error , e  Yn  X n  (22  19 )mA  3mA
%E 
e
3
 100 
 100  13 .64 %
Yn
22
Relative accuracy, A  1 
e
 1  0.1364  0.9864
Yn
% of accuracy, a  A  100  98 .64 %
(c)
The output voltage of an amplifier was measured at eight different intervals using the
same digital voltmeter with the following results: 20.00, 19.80, 19.85, 20.05, 20.10,
19.90, 20.25, 19.95. Which is the most precise measurement?
Pr ecision  1 
Xn  Xn
Xn
n
voltage
deviation
Precision
1
20.00
0.0125
0.9994
2
19.80
-0.1875
0.9906
3
19.85
-0.1375
0.9931
4
20.05
0.0625
0.9969
5
20.10
0.1125
0.9944
6
19.90
-0.0875
0.9956
7
20.25
0.2625
0.9869
8
19.95
-0.0375
0.9981
n=8
∑=159.9
Xn bar=19.9875
The nearest precision value to 1 is the most precise value, or The lowest deviation is the most precise value..
Hence the 1st measurement is the most precise measurement.
EKT212/4 Principles of Measurement and Instrumentation
(sem.2 2014/15)
Question 3
(a) Discuss the difference between random error and systematic error of a measurement.
Systematic Error is the deviation of the true value from the desired value
Random Error occurs when different results in magnitude or sign obtained on repeated measurement of
one or the same quantity.
(b)
In a calibration test, 10 measurements using a digital voltmeter have been made of the
battery voltage that is known to have a true voltage of 6.11 V. The results are shown
in Table 2. Calculate:
(i)
(ii)
(iii)
(iv)
Arithmetic mean,
Systematic error,
Deviation for each reading
Maximum random error.
Table 2
Number of measurement Reading (V)
1
5.98
2
6.05
3
6.10
4
6.06
5
5.99
6
5.96
7
6.02
8
6.09
9
6.03
10
5.99
Solution:
Number of measurement
Reading (V)
(iii)Deviation
1
5.98
-0.047
2
6.05
0.023
3
6.10
0.073
4
6.06
0.033
5
5.99
-0.037
6
5.96
-0.067
7
6.02
-0.007
8
6.09
0.063
9
6.03
0.003
10
5.99
-0.037
N =10
∑=60.27
(i) Arithmetic mean= 60.27/10=6.027
(ii)Systematic Error = Mean – True = 6.027 - 6.11= -0.083
(iv)Maximum random error = Higher deviation – mean =6.10– 6.027= 0.073
EKT212/4 Principles of Measurement and Instrumentation
(sem.2 2014/15)
Question 4
(a)
Define absolute error.
Absolute error is the difference between the expected value of the variable and the
measured value of the variable.
(b)
The expected value of the voltage across a resistor is 100 V. However, the
measurement gives a value of 98 V. Calculate
(i)
(ii)
(iii)
(iv)
Absolute error,
Percentage of error,
Relative accuracy, and
Percentage of accuracy.
Yn  100V ,
X n  98V
Absolute error , e  Yn  X n  (100  98 )V  2V
%E 
e
2
 100 
 100  2%
Yn
100
Relative accuracy, A  1 
e
 1  0.02  0.98
Yn
% of accuracy, a  A  100  98 %
(c)
A 600 mA ammeter is specified to be accurate with ±2%. Calculate the limiting error
when instrument is used to measure 300 mA.
A 500 mA ammeter with accuracy ±2%
Magnitude of limiting error on given ammeter  2%  600 mA  12 mA
Limiting error when measure 300mA 
12
100  4%
300
Question 5
(a)
A voltmeter reading 185 V on its 200 V range and an ammeter reading 350 mA on its
500 mA range are used to determine the power dissipated in a resistor. Both these
instruments are guaranteed to be accurate within 1.5% at full scale deflection.
(i)
(ii)
Briefly discuss limiting errors in a measurement.
Calculate the limiting error of the power.
A 200 V voltmeter with accuracy ±1.5%
Magnitude of limiting error on given volt meter  1.5%  200V  3V
Limiting error when measure 185V 
A 500 mA ammeter with accuracy ±1.5%
3
 100  1.622%
185
EKT212/4 Principles of Measurement and Instrumentation
(sem.2 2014/15)
Magnitude of limiting error on given ammeter  1.5%  500mA  7.5mA
Limiting error when measure 300mA 
7.5
 100  2.143%
350
Limiting error of the power = 1.622% + 2.143% = 3.765%
(b) With a suitable block diagram, briefly explain each of the main components in
instrumentation system.
 Transducers
 Device that converts a change in physical quantity into a change of electrical
signal magnitude.
 Power Supply
 Provide energy to drive the transducers.
 Signal Conditioning Circuits
 Electronic circuits that manipulate, convert the output from transducers into
more usable electrical signal.
 Amplifiers
 Amplify low voltage signal from transducers or signal conditional circuit.
 Recorders
 Used to display the measurement for easy reading and interpretation.
 Data Processors
 Can be a microprocessor or microcontroller.
 Process Controllers
 Used to monitor and adjust any quantity of the specified level or value.
 Command Generator
 Provide control voltage that represents the difference of the parameter in a
given process.