Units, Standards and Their
Classifications
Introduction
by
Dr. Arnab Ghosh
Dept. of Electrical Engineering,
NIT Rourkela, Odisha, India
E-mail: ghosha@nitrkl.ac.in
aghosh.ee@gmail.com
INTRODUCTION
❖ Measurement is the act, or the result, of a quantitative comparison between a given quantity and a quantity of the same
kind chosen as a unit.
❖ The result of the measurement is expressed by a pointer deflection over a predefined scale or a number representing the
ratio between the unknown quantity and the standard.
❖ A standard is defined as the physical personification of the unit of measurement or its submultiple or multiple values.
❖ The device or instrument used for comparing the unknown quantity with the unit of measurement or a standard quantity is
called a measuring instrument.
❖ The value of the unknown quantity can be measured by direct or indirect methods.
❖ In direct measurement methods, the unknown quantity is measured directly instead of comparing it with a standard.
Examples of direct measurement are current by ammeter, voltage by voltmeter, resistance by ohmmeter, power by
wattmeter, etc.
❖ In indirect measurement methods, the value of the unknown quantity is determined by measuring the functionally
related quantity and calculating the desired quantity rather than measuring it directly. Suppose the resistance as (R)
of a conductor can be measured by measuring the voltage drop across the conductor and dividing the voltage (V) by
the current (I) through the conductors, by Ohm’s Law.
FUNDAMENTAL AND DERIVED UNITS
❖ At the time of measuring a physical quantity, we must express the magnitude of that quantity in terms of a unit and a
numerical multiplier, i.e.,
Magnitude of a physical quantity = (Numerical ratio) × (Unit)
❖ The numerical ratio is the number of times the unit occurs in any given amount of the same quantity and, therefore, is
called the number of measures. The numerical ratio may be called numerical multiplier.
❖ In science and engineering, two kinds of units are used:
❖ Fundamental units
❖ Derived units
STANDARDS AND THEIR CLASSIFICATIONS
A standard of measurement is a physical representation of a unit of measurement. A unit is realised by reference to an
arbitrary material standard or to natural phenomena including physical and atomic constants. The term ‘standard’ is applied
to a piece of equipment having a known measure of physical quantity.
The classifications of standards are
1. International standards: International Bureau of Weights and Measures
2. Primary standards: National Bureau of Standards (NBS) in Washington, National Physical Laboratory (NPL) in Great Britain
3. Secondary standards
4. Working standards
5. Current standards
6. Voltage standards
7. Resistance standards
8. Capacitance standards
9. Time and frequency standards
METHODS OF MEASUREMENT
The measurement methods can be classified as
❑Direct comparison methods:
In direct measurement methods, the unknown quantity is measured directly. Direct methods of measurement are of
two types, namely, deflection methods and comparison methods.
➢The value of the unknown quantity is measured by the help of a measuring instrument having a calibrated scale
indicating the quantity under measurement directly, such as measurement of current by an ammeter.
➢The value of the unknown quantity is determined by direct comparison with a standard of the given quantity, such
as measurement of emf by comparison with the emf of a standard cell. Comparison methods can be classified as null
methods, differential methods, etc. In null methods of measurement, the action of the unknown quantity upon the
instrument is reduced to zero by the counter action of a known quantity of the same kind, such as measurement of
weight by a balance, measurement of resistance, capacitance, and inductance by bridge circuits
❑Indirect comparison methods:
➢ In indirect measurement methods, the comparison is done with a standard through the use of a calibrated system.
❑Indirect comparison methods:
➢These methods for measurement are used in those cases where the desired parameter to be measured is difficult to
be measured directly, but the parameter has got some relation with some other related parameter which can be easily
measured.
➢Example: the elimination of bacteria from some fluid is directly dependent upon its temperature. Thus, the bacteria
elimination can be measured indirectly by measuring the temperature of the fluid.
➢In indirect methods of measurement, it is general practice to establish an empirical relation between the actual
measured quantity and the desired parameter.
MEASUREMENT SYSTEM AND ITS ELEMENTS
➢ A measurement system may be defined as a systematic arrangement for the measurement or determination of an
unknown quantity and analysis of instrumentation.
➢ The generalized measurement system and its different components/elements are shown in Figure
Important Topics:
➢ Primary Sensing Elements
➢ Variable Conversion Elements
➢ Manipulation Elements
➢ Data Transmission Elements
➢ Data Presentation Elements
Figure: Generalised measurement system
THE STAGES OF A TYPICAL MEASUREMENT SYSTEM
Figure: Steps of a typical measurement system
CLASSIFICATION OF INSTRUMENTS
The measuring instruments may be classified as follows:
1. Absolute and Secondary Instruments
❖ Absolute Instruments: Absolute instruments are mostly used in standard laboratories, deflection, tangent galvanometer.
❖ Secondary Instruments
▪ Indicating instruments: Ordinary ammeters, voltmeters, wattmeters, frequency meters, power factor meters, etc..
▪ Integrating instruments: ampere-hour meters and energy meters
▪ Recording instruments: a curve is traced which shows the variations in the magnitude of the electrical quantity
under observation over a definite period of time. Such instruments are generally used in powerhouses where the
current, voltage, power, etc., are to be maintained within certain acceptable limit.
2. Analog and Digital Instruments
❖ Analog Instruments: The signals of an analog unit vary in a continuous fashion and can take on infinite number of values
in a given range. Fuel gauge, ammeter and voltmeters, wrist watch, speedometer
❖ Digital Instruments: Signals varying in discrete steps and taking on a finite number of different values in a given range
are digital signals and the corresponding instruments are of digital type. Digital instruments have some advantages over
analog meters, in that they have high accuracy and high speed of operation. It eliminates the human operational errors. A
digital multimeter is the example of a digital instrument.
3. Mechanical, Electrical and Electronics Instruments
❖ Mechanical Instruments
❖ Electrical Instruments
❖ Electronic Instruments
4. Manual and Automatic Instruments: measurement of temperature by a resistance thermometer incorporating a Wheatstone bridge
5. Self-operated and Power-operated Instruments: Electromechanical instruments
6. Deflection and Null Output Instruments: Physical effect mechanical displacement, Permanent Magnet Moving Coil (PMMC), Moving
Classification of Measuring Instruments
Electromechanical measurement system
DEFINITIONS OF SOME STATIC CHARACTERISTICS
1. Accuracy
Accuracy is the closeness with which the instrument reading approaches the true value of the variable under
measurement. Accuracy is determined as the maximum amount by which the result differs from the true value.
The true value is not indicated by any measurement system due to the loading effect, lags and mechanical problems
(e.g., wear, hysteresis, noise, etc.).
Accuracy of the measured signal depends upon the following factors:
▪ Intrinsic accuracy of the instrument itself;
▪ Accuracy of the observer;
▪ Variation of the signal to be measured; and
▪ Whether or not the quantity is being truly impressed upon the instrument.
2. Precision
Precision is a measure of the reproducibility of the measurements, i.e., precision is a measure of the degree to
which successive measurements differ from one another.
3. Resolution
If the input is slowly increased from some arbitrary value it will be noticed that the output does not change at all until
the increment exceeds a certain value called the resolution or discrimination of the instrument.
Resolution is sometimes referred as sensitivity.
The largest change of input quantity for which there is no output of the instrument is called the dead zone of that
instrument.
4. Speed of Response
The quickness of an instrument to read the measure and variable is called the speed of response. Alternately, speed of
response is defined as the time elapsed between the start of the measurement to the reading taken.
This time depends upon the mechanical moving system, friction, etc.
Example 1
A moving coil ammeter has a uniform scale with 50 divisions and gives a full-scale reading of 5 A. The instrument
can read up to 1/4 th of a scale division with a fair degree of certainty. Determine the resolution of the instrument
in mA.
Example 2
A 0-25 A ammeter has a guaranteed accuracy of 1 percent of full scale reading. The current measured by this instrument is 10
A. Determine the limiting error in percentage.
MEASUREMENT OF ERRORS
In practice, it is impossible to measure the exact value of the measurand. There is always some difference
between the measured value and the absolute or true value of the unknown quantity (measurand), which may be
very small or may be large. The difference between the true or exact value and the measured value of the
unknown quantity is known as the absolute error of the measurement.
If δA be the absolute error of the measurement, Am and A be the measured and absolute value of the unknown
equantity then δA may be expressed as
δA= Am - A
Sometimes, δA is denoted by ε0.
The relative error is the ratio of absolute error to the true value of the unknown quantity to be measured,
When the absolute error ε0 (=δA) is negligible, i.e., when the difference between the true value A and the
measured value Am of the unknown quantity is very small or negligible then the relative error may be expressed
as,
The relative error is generally expressed as a fraction, i.e., 5 parts in 1000 or in percentage value,
The limits of these deviations from specified values are defined as limiting or guarantee errors. The magnitude of
a given quantity having a specified magnitude Am and a maximum or a limiting error ±δA must have a
magnitude between the limits
For example, the measured value of a resistance of 100 Ω has a limiting error of ±0.5 Ω. Then the true value of the
resistance is between the limits 100 ± 0.5, i.e., 100.5 and 99.5 Ω.
TYPES OF ERRORS
The origination of error may be in a variety of ways. They are categorized in three main types.
➢ Gross error: The errors occur because of mistakes in observed readings, or using instruments and in recording
and calculating measurement results.
➢ Systematic error: These are the errors that remain constant or change according to a definite law on repeated
measurement of the given quantity.
There are two types of systematic errors:
• Instrumental error
• Environmental error
➢ Random error: These errors are of variable magnitude and sign and do not maintain any known law.
Discussion
