Note for ELECTRICAL MEASUREMENTS AND MEASURING INSTRUMENTS - EMMI By Amity Kumar

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1 TABLE OF CONTENTS Chapter 1(a) Units and Dimensions 1.1 Art of measurements 1.2 Methods of Measurements and Measuring Instruments 1.2.1 Requirements of Instruments 1.2.2 Classification of Instruments 1.2.3 Accuracy and Precision 1.2.4 Resolution and Overshoot 1.3 Review of fundamental and derived units 1.3.1 Fundamental Units 1.3.2 MKSA and SI Units 1.3.3 Derived Units 1.4 Dimensional Analysis 1.4.1 Dimension of a Physical Quantity 1.4.2 Dimensional Equations 1.5 Solved Problems 1.5.1 Solved Problems on Units 1.5.2 Solved Problems on Dimensions 1.6 Exercises

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2 CHAPTER 1 UNITS AND DIMENSIONS 1.1 ART OF MEASUREMENTS Measurement of a quantity is the result of a comparison between the unknown quantity and its predefined standard. A measuring system is required to quantify the parameters involved and establish clear rules about their relative values. Early systems of measurements were based on imprecise units, while the modern measurement systems are based on accurately defined units. Many standard measuring units have been established at different levels of measurements. The significance of electrical measurements and measuring instruments is evident from the rapid developments in the field of electrical engineering owing to the developments in their measuring devices. The measurement is meaningful only if the standards are accurately defined, reliable and commonly accepted, the methods used are well proven and the circuit conditions are little affected by the introduction of the measuring systems. The parameter under measurement is referred as measurand and it is always measured in terms of its numeric value. The process of measurement through a meter is referred as Instrumentation. Electrical measuring instruments are the most common devices used not only for the measurement of electrical quantities, but also for all other quantities, which could be transformed into an electrical signal. The usual quantities to be measured are current, voltage, power, energy, frequency, power factor, etc. The various circuit parameters also need to be measured such as resistance, inductance, capacitance, etc. An umpteen number and varieties of measuring instruments have been developed for measurement purposes. In other words, measurement and instrumentation are based on different methods depending upon the characteristic features of the quantity being measured. 1.2 METHODS OF MEASUREMENTS AND MEASURING INSTRUMENTS The measurement methods can be analog or digital methods, deflection or null methods, active or passive methods, direct or indirect methods and absolute or secondary methods. Measurement generally involves an instrument as a physical means of determining an unknown quantity or a variable called the parameter. The instrument is a means for determining the value or magnitude of the measurand. The instruments can also be divided into separate classes according to several criteria as, analog or digital instruments, deflection or null type instruments, power operated (active) or self generating (passive) instruments, contacting or non-contacting instruments, mechanical or electrical instruments and monitoring or control instruments. • Signals which vary continuously with the change in the measurand are analog signals and the devices producing them are analog instruments. The deflection type dynamometer type wattmeter is a good example of an analog instrument. As the input

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3 • • • • • • value changes, the moving system or pointer exhibits a smooth continuous motion. The signals which vary in discrete steps and have only finite number of values in any given range are digital signals and the associated devices are digital instruments. A digital instrument has an output varying in discrete steps. An electronic counter is an example of a digital instrument. If the quantity is to be directly measured, then deflection methods are used. For e.g., ammeter, voltmeter, etc. acting as meters indicating the value of the measurand by the deflection of a pointer over a graduated and calibrated scale. Alternatively, if the value is measured based on the null balance conditions, then it is a null method. Null methods are used only to detect the null condition of a measurand through a given path or circuit. AC/DC Bridge measurements for measurement of resistance, inductance, capacitance, frequency, etc. are null methods. They involve balance detection by using null detectors, such as, Galvanometer, Vibration Galvanometers and Head Phones. Null instruments are more accurate than the deflection instruments. If the output of the instrument is entirely produced by the measurand, then it is an active instrument. These are the power operated instruments requiring some source of auxiliary power for their operation such as compressed air, electricity and hydraulic supply. On the other hand, if the measurand modulates the magnitude of some external power source, then it is a passive instrument. Passive instruments are self generating instruments where the energy requirements are met entirely from the input signal. The direct methods involve measuring the measurand by comparison against its own standard. They are very common for measurement of physical quantities such as length, mass and time. They are less sensitive and inaccurate since they involve human operators. Thus direct methods are not usually preferred. On the other hand, indirect methods use measuring systems, which are the systems having a transducer to convert the measurand into its analogous form. This converted signal is processed, fed to the end devices to obtain the results. Absolute methods give the magnitude of the quantity under measurement in terms of the physical constants of the instrument. They do not require calibration. They are used only for calibration of other instruments. For e.g., Tangent Galvanometer, Rayleigh's current balance and potentiometers. Secondary methods are so constructed that the desired quantity is measured only by observing the output of the instrument, which needs to be calibrated. Thus, they measure the quantity in terms of their deflection, for which they are already calibrated. These are the ones which are the most commonly used. For e.g., Voltmeters, Thermometer, Pressure gauge, etc. Secondary methods work on either Analog mode or Digital mode and hence lead to analog or digital methods. Contacting type instruments are those which are kept in the measuring medium itself. For e.g., clinical thermometer. A non-contacting or proximity type instrument measures the desired input even though it is not in close contact with the measuring medium. For e.g., optical pyrometer measuring the temperature of a blast furnace, variable reluctance tachometer measuring the speed of a rotating body, etc. Mechanical instruments are very reliable for static conditions. Their parts are very bulky, rigid and have a heavy mass. Hence they cannot respond rapidly to measurements of dynamic and transient conditions. Besides, many of them are the potential sources of noise. On the other hand, electrical instruments are very rapid in

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4 • response. However, their operating mechanism normally depends on a mechanical meter movement as an indicating device. Monitoring instruments are useful for monitoring functions. If their output is in a form that can be directly included as part of an automatic control system, then they become control instruments. 1.2.1 Requirements of Instruments A measuring instrument should possess some of the following important characteristic features: • It should have a very high instrument efficiency which is the ratio of the quantity being measured to the power utilized by the instrument at full scale. • It should have a high sensitivity which is the ratio of the magnitude of the output signal to the magnitude of the quantity being measured. The inverse of this ratio is the Inverse Sensitivity or Deflection Factor. • The output of the instrument should be linearly proportional to the input. In such cases, the scale will be uniform and hence easier to calibrate. • It should have a very low threshold which is the minimum value of below which the change in output cannot be detected by the instrument. • It should have lowest dead time which is the minimum time required for the instrument to respond to a change in the quantity being measured. • It should virtually have no dead zone where dead zone is the largest change of the input quantity for which there is no output of the instrument. Dead zone is caused due to friction, hysterisis, backlash, etc. • It should have perfect reproducibility (precision) which is specified in terms of the scale readings over a given period of time. This is different from repeatability which is defined as the variation of scale readings and is random in nature. • It should not have any drift. For an instrument, perfect reproducibility means that the instrument has no drift. This means that for a given input, the measured values are constant and do not vary with time. • It should have minimum noise. Noise is any signal that does not convey any useful information. Noise is due to extraneous disturbances caused by many sources such as stray fields, shocks and thermal stresses. • It should be modifiable and properly priced. All the indicating instruments require three important torques for their operation: deflecting torque-Td, controlling torque-Tc and damping torque-TD.
The deflecting torque is responsible for the movement of the pointer in proportion to the value of the measurand. It is provided by the different effects of electric current on which the operation of the given instrument depends.
The controlling torque is responsible for controlling the movements of the pointer. It is very high at the null position of the pointer. When the pointer gets deflected due to the deflecting torque exerted on it, the controlling torque provides the retarding torque and the two torques are equal at the equilibrium position of the