1. Introduction to Electrical Measurement
Chapter 1
Introduction to Electrical Measurement
ELECTRICAL MEASUREMENTS
(BEF 23903)
INSTRUMENTATION & MEASUREMENTS (BEE 1313)

2. ELECTRICAL MEASUREMENTS
Objectives
At the end of this chapter, you should be able to:
explain units and quantities in electrical field
discuss and calculate various types of error in measurement
ELECTRICAL MEASUREMENTS
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3. ELECTRICAL MEASUREMENTS
Chapter outline
The outline of this chapter is as follows:
1.1 Principles of Measurements
1.2 System of Measurement
1.3 SI Systems
1.4 Accuracy of Measurements
1.5 Instruments Accuracy
1.6 Reading Resolution
1.7 Errors in Instruments
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4. 1.1 Principle of Measurements
A process to present an observer with a numerical value corresponding to the variable being measured by using appropriate instrument
Basically used to monitor a process or operation, or as well as the controlling process
Eg: thermometers, multimeter, etc
Measurement
system
Input
Output
True value
of variable
Measured value
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INSTRUMENTATION & MEASUREMENTS (BEE 1313)

5. 1.1 Principle of Instrumentation & measurements
The major problem encountered with any measuring instrument is the error
Therefore, it is necessary to select the appropriate measuring instrument & measurement method which minimises error
To avoid errors in any experimental work, careful planning, execution & evaluation of the experiment are essential
ELECTRICAL MEASUREMENTS
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6. 1.1 Principle of Instrumentation & Measurements
Before measurement process we have to
ensure:
Methods/procedures of measurement
Characteristics of the parameter
Quality: time and cost, instrument capabilities, knowledge of measurement, acceptable result
What instrument to use
ELECTRICAL MEASUREMENTS
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7. 1.1 Principle of Measurements
During the measurements we have to ensure:
Quality- best instrument chosen, suitable position when taking the data, etc..
Safety- electric shock, overloaded, instrument limits, read instruction manual
Sampling – observe parameter changing, taking enough sample
After measurement
Analyse the data mathematically/statistically
Full result must be reported completely and accurately
ELECTRICAL MEASUREMENTS
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8. 1.1 Principle of Measurements
Electrical Units
i) Fundamental Quantity…
Quantity
Symbol
Unit
Unit Abbre.
Length l
meter m
Mass
kilogram kg
Time t
second s
Temperature T
Kelvin oK
Electric current I
Ampere A
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9. 1.1 Principle of Measurements
ii) Derived Quantity…
Quantity
Symbol
Unit
Unit Abbre.
emf/ voltage V
volt
charge Q
coulomb C
resistance R
Ohm Ω
capacitance
farad F
inductance L
hendry H
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10. 1.2 Error in Measurement Error:
is defined as the difference between the measured value and the expected value (true value) of the measured parameter
Various types of error in measurement:
i) absolute error
ii) gross error
iii) systematic error
iv) random error
v) limiting error
**static error = numerical difference between the true value of a quantity and its value as obtained by measurement (i.e. repeated measurement of the same quantity gives different indications.
Static errors

11. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
i) Absolute error:
The difference between the expected value of the variable and the measured value of the variable, or e = Yn – Xn
where:
e = absolute error
Yn = expected value
Xn = measured value
ELECTRICAL MEASUREMENTS
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12. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
To express error in percentage
% error = , e = Yn - Xn
We also derived relative accuracy, A;
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13. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
Percentage accuracy, a:
a = 100% - % error or
a = A x 100%
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14. ELECTRICAL MEASUREMENTS
Example 1.1
The expected value of the voltage across a resistor is 5.0 V. However, measurement yields a value of 4.9 V. Calculate:
a) absolute error
b) % error
c) relative accuracy
d) % accuracy
ELECTRICAL MEASUREMENTS
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15. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
ii) Gross Error
Due to human mistakes
Example: incorrect reading, incorrect recording, improper use of instruments, etc
To minimize:
take at least 3 separate reading
take proper care in reading & recording
ELECTRICAL MEASUREMENTS
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16. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
Instrumental errors
iii) Systematic Error
due to instrument’s problem or environmental effects or observational errors
example…???
defective or worn parts
ageing
parallax error
wrong estimation reading scale
Environmental errors
Observational errors
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17. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
Instrumental errors :
due to friction in the bearings of the meter movement, incorrect spring tension, improper calibration, or faulty instruments
can be reduced by proper maintenance, use, and handling of instruments
Environmental errors :
due to external condition of the measuring
eg: effects of change in temperature, humidity, barometric pressure, electrostatic fields etc
can be avoided by: air conditioning, hermetically sealing certain components in the instrument and using magnetic shields
Observational errors :
Errors that introduced by the observer
The two most common observational errors are probably the parallax error introduced in reading a meter scale and the error of estimation when obtaining a reading from a meter scale
ELECTRICAL MEASUREMENTS
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18. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
iv) Random Errors
Errors that remain after gross and systematic errors have been substantially reduced
Are generally the accumulation of a large number of small effects
May be of real concern only in measurements requiring a high degree of accuracy
such errors can only be analyzed statistically
Due to unknown causes
ELECTRICAL MEASUREMENTS
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19. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
v) Limiting Errors
Most manufacturers of instruments state that an instrument is accurate within a certain percentage of a full-scale reading
Eg: a voltmeter is accurate within ±2% at full-scale deflection (limiting errors)
however, with reading less than full-scale, the limiting error will increase
therefore, it is important to obtain measurements as close as possible to full scale
ELECTRICAL MEASUREMENTS
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20. ELECTRICAL MEASUREMENTS
Example 1.2
A 300-V voltmeter is specified to be accurate within ±2% at full scale. Calculate the limiting error when the instrument is used to measure a 120-V source?
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21. INSTRUMENTATION &ELECTRICAL MEASUREMENTS
Example 1.2
Solution
The magnitude of the limiting error is:
2/100 x 300 = 6V
Therefore, the limiting error at 120 V is:
6/120 x 100 = 5%
(reading < full scale, limiting error increased)
INSTRUMENTATION &ELECTRICAL MEASUREMENTS
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22. INSTRUMENTATION &ELECTRICAL MEASUREMENTS
Example 1.3
A voltmeter and an ammeter are to be used to determine the power dissipated in a resistor. Both instruments are guaranteed to be accurate within ±1% at full scale. If the voltmeter reads 80V on its 150-V range and the ammeter reads 70mA on its 100-mA range, calculate the limiting error for the power calculation.
** The limiting error for the power calculation is the sum of individual limiting errors involved
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23. INSTRUMENTATION &ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
Precision of measurement
A measure of the consistency or repeatability of measurements
where
Xn = the value of the nth measurement
Xn = the average of the set of n measurements
= sum of the nth measurement values / nth
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24. ELECTRICAL MEASUREMENTS
Example 1.4
Table below gives the set of 10 measurement that were recorded in the laboratory. Calculate the precision of the 6th measurement.
= ??
Precision = ??
Measurement number
Measurement value Xn 1 98 2
101 3
102 4 97 5 6
100 7
103 8 9
106 10 99
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25. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
STATISTICAL ANALYSIS OF MEASUREMENT DATA
Important because it allows an analytical determination of the uncertainty of the final result
A large number of measurements is usually required
can be divided into 4:
Arithmetic mean / average
deviation
average deviation
standard deviation
ELECTRICAL MEASUREMENTS
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26. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
Arithmetic mean/average:
- the most probable value of measured variable
n = total number of reading
xn = nth reading taken
xi = set of number
ELECTRICAL MEASUREMENTS
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27. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
ii) Deviation:
- The difference between each piece of data and
arithmetic mean
- Algebraic sum of deviation,
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28. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
iii) Average deviation (D):
- precision of a measuring instrument
- high D low precision
- low D  high precision
ELECTRICAL MEASUREMENTS
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29. ELECTRICAL MEASUREMENTS
1.2 Error in Measurement
iv) Standard deviation:
- also known as root mean square deviation
- the most important factor in statistical analysis
- reduction means improvement in measurement
ELECTRICAL MEASUREMENTS
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30. ELECTRICAL MEASUREMENTS
Example 1.5
For the following data compute
(a) The arithmetic mean (49.9)
(b) The deviation of each value (0.2,-0.2,-0.3,0.3)
(c) The algebraic sum of the deviation (0)
(d) The average deviation (0.25)
(e) The standard deviation (0.294)
x1= x2= 49.7
x3= 49.6 x4= 50.2
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31. 1.3 Measurement Standards
Standards are defined in 4 categories:
i) international standards
ii) primary standards
iii) secondary standards
iv) working standards
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32. ELECTRICAL MEASUREMENTS
1.3 Measurement Standard
i) International Standards
Defined by international agreements
These standards are maintained at the International Bureau of Weight and Measures in Paris, Frances
They are periodically evaluated and checked by absolute measurements in term of the fundamental units of physics
They represent certain units of measurement to the closest possible accuracy attained by the science and technology of measurement and used for comparison with primary standards
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33. ELECTRICAL MEASUREMENTS
1.3 Measurement Standard
ii) Primary Standard
Are maintained at institution in various countries around the world, such as the National Bureau of Standard In Washington D.C, SIRIM in Malaysia
The primary standards are not available for use outside the national laboratories
Their principle function is to calibrate and verify the secondary standards
Also known as National Standard
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34. ELECTRICAL MEASUREMENTS
1.3 Measurement Standard
iii) Secondary Standard
Use as the basic reference standards used by measurement & calibration laboratories in industry
Each industrial laboratory is completely responsible for its own secondary standards
Each laboratory sends its secondary standards to the national standards ( primary standards) laboratory for calibration
After calibration, the secondary standards are returned to the industrial users with the certification
Needs to check periodically (e.g. once in six months ..)
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35. ELECTRICAL MEASUREMENTS
1.3 Measurement Standard
iv) Working Standard
Working standard is the principle tools of a measurement laboratory and the lowest level of standards
Used to check and calibrate the instruments used in the laboratory or to make comparison measurement in industrial application
Example: the standard resistor, capacitors, inductor which usually found in an electronics laboratory are classified as working standards.
ELECTRICAL MEASUREMENTS
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36. ELECTRICAL MEASUREMENTS
Summary
Some terms + definitions are as below:
Error – ---???
Accuracy – The degree of exactness of a measurement compared to the expected value
Precision – A measure of consistency, or repeatability of measurements.
ELECTRICAL MEASUREMENTS
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37. ELECTRICAL MEASUREMENTS
Summary
Instrument – a device or mechanism used to determine the present value of a quantity
Measurement – a process of comparing an unknown quantity with an accepted standard quantity.
Standard – an instrument or device having a recognized permanent (stable) value that is used as a reference.
ELECTRICAL MEASUREMENTS
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38. ELECTRICAL MEASUREMENTS
Summary
expected value – the most probable value we should expect to obtain.
deviation – the difference between any piece of data in a set of numbers and the arithmetic mean of the set of numbers.
transducer – a device that converts one form of energy into another form
ELECTRICAL MEASUREMENTS
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39. ELECTRICAL MEASUREMENTS
Evaluation
Electrical Quantity…
Quantity
Symbol
Unit
Unit Abbre. l
meter
Capacitance F
Time
second T
Kelvin oK
Charge
ELECTRICAL MEASUREMENTS
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40. ELECTRICAL MEASUREMENTS
ANY
QUESTIONS?
ELECTRICAL MEASUREMENTS
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