# Measurement & Electrical Quantities-1 Study notes for GATE EE Exam

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Measurement & Electrical Quantities-1 Study notes for GATE EE Exam are an invaluable resource for aspiring candidates aiming to excel in the field of electrical engineering. With comprehensive coverage of key topics and concepts, these study notes offer a systematic approach to understanding measurement techniques and electrical quantities. Designed specifically for the GATE EE Exam, these study notes provide a focused and structured learning experience to help candidates optimize their preparation.

These Measurement & Electrical Quantities-1 Study notes for GATE EE Exam delve into the fundamental principles and applications of electrical measurements, equipping candidates with the necessary knowledge and skills to tackle related questions in the exam. The notes cover essential topics such as measurement errors, and measurement of voltage, current, power, energy, and impedance. By thoroughly studying these notes, candidates can develop a strong foundation in measurement techniques and electrical quantities, enabling them to approach GATE EE Exam questions with confidence and accuracy. With their comprehensive content and emphasis on exam relevance, these study notes serve as a valuable tool to enhance preparation and maximize performance in the GATE EE Exam.

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## Electrical Instruments and Measurement

Electrical Instruments and Measurement play a crucial role in the field of electrical engineering, enabling accurate and precise measurements of various electrical quantities. Understanding the principles and operation of electrical instruments is essential for engineers and technicians working in industries such as power systems, electronics, and telecommunications. This knowledge is also vital for aspiring candidates preparing for competitive exams like the GATE EE Exam.

## Classification of Electrical Instrument

Electrical instruments can be classified into various categories based on their working principles, the electrical quantities they measure, and their applications. Here are some common classifications of electrical instruments:

Absolute Instrument: It gives the value of the parameters under measurement in terms of the instrument.

e.g., Tangent galvanometer, and Rayleigh’s current balance.

Secondary Instrument: This instrument gives the value of parameters directly under measurement.

e.g., Voltmeter, thermometer, pressure gauge etc.

Note – Absolute instruments are more highly accurate than secondary instruments as they contain a fewer number of moving mechanical parts resulting in lower operational power consumption.

Analog Instrument: Its output varies continuously with respect to time all the while maintaining a constant relationship with the input.

Deflecting Instrument: This instrument gives the value of the parameters under measurement in terms of the deflection of the pointer away from the zero position. e.g., PMMC

Null Deflection: Null-deflecting types of instruments indicate their end of measurement with a zero deflection. e.g., Bridge circuit, DC potentiometer etc.

Note: Null deflecting instrument is highly accurate in comparison to the deflecting instrument as their operational power consumption at zero deflection is zero.

Indicating Instrument: This instrument gives the instantaneous value of the parameters under measurement. e.g., Ammeter, voltmeter, wattmeter, galvanometer.

Integrating Instrument: It gives the sum total of the electrical parameter consumed over a specified period of time. e.g., Energy meter

Recording Instrument: e.g., Recording voltmeter.

### Key Points:

• PMMC-type instruments are used only in DC voltage and current.
• Induction-type instruments are used only in AC (voltage and current) measurement.
• An electrodynamometer-type instrument can be used to measure DC well as AC voltage.

• Electro Magnetic Effect Moving iron coil type, PMMC type, electro dynamometer type instrument.
• Induction Effect Energy meter
• Heating Effect Hot wire type, thermocouple, bolometer.
• Electrostatic Effect Electrostatic type of instrument.
• Halls Effect Fluxmeter, Poynting vector type wattmeter.

## Essentials of Indicating Instrument

Deflecting Torque/Force: Deflecting torque is proportional to the quantity under measurement. The benefit of this torque is to deflect the pointer away from the zero position.

Controlling Torque/Force (TC): It controls the deflection by bringing the pointer to rest at the steady-state position.

It brings the pointer back to the zero position when the parameter under measurement is removed.

Note: If control force is absent then the pointer will be deflected beyond the maximum scale.

Damping Torque/Force (TD): This torque is damp out the oscillation of the pointer due to inertia.

Construction Details of Indicating Instrument: A moving system of indicating instruments produces the deflecting torque.

Various types of supports for the moving systems as Suspension

• Used in galvanometer class instrument.
• Used only in the vertically held instrument.

Taut Suspension: It is used in PMMC-type instruments that require low friction and high sensitivity.

Pivot and Jewel Bearing Type of Supports: The weight of the moving system decide the sensitivity of the instrument directly.

Note: Torque to weight ratio of the moving system should be high and equal to 0.1

Control System: There are two types of mechanisms is considered here. The first one is spring control and the other one is gravity control mechanism as given below.

Spring Control Mechanism

Control torque TCS = kθ

where k = spring constant

θ = deflection

as Td ∞ l

at steady state position Td = Tc; θ ∞ l

Where Td = Deflection torque

Tcg = Control torque of gravity control mechanism

Note: The gravity control mechanism has an initial scale.

### Key Points:

• If damping torque Td is absent then the pointer oscillates around the mean position.
• Fatigue in spring is avoided by annealing and ageing.

Damping System: A damping system is provided in the instrument which helps the moving system of the instrument to reach the final position at the earliest.

Eddy Current Damping: Mechanism Used in a strong operating field. e.g., PMMC (Permanent Magnet Moving Coil instrument) type.

Air Friction Damping: Used when the operating field is weak as used in moving iron and electrodynamometer-type instruments.

Fluid Friction Damping: Used in high voltage measurement. Used in the vertically mounted instrument. e.g., Electrostatic type instrument.

Measuring Current: Ammeters

For measurement of current, the circuit should be broken at the point where we want that current is to be measured, and the ammeter inserted at that point. An ammeter must be connected in series with the load under test.

As it is important that the insertion of the ammeter into a network has a small effect on the circuits existing resistance and, thus alter the current normally flowing in the circuit, ammeters are manufactured with very small values of internal resistance.

Because ammeters have a very small internal resistance, it is vitally important that they are never connected in parallel with any circuit component —and particularly with the supply. It will result in a short-circuit current flowing through the instrument which may damage the ammeter.

Measuring Voltage: Voltmeters

To measure potential difference or voltage, a voltmeter should be connected between two points at different potentials. So, a voltmeter must always be connected in parallel with the part of the network under test.

In order to operate, a voltmeter must, of course, draw some current from the circuit under test, and this can lead to inaccurate results because it can interfere with the normal condition of the circuit. We call this the ‘loading effect and, to minimise this ‘loading effect (and, therefore, improve the accuracy of a reading), this operating current must be as small as possible and, for this reason, voltmeters are manufactured with a very high value of internal resistance —usually many megohms.

Types of Instruments Used for Ammeter and Voltmeter

PMMC (Permanent Magnet Moving Coil) Only for DC current measurement.

Moving Iron Type For both AC and DC

Electro Dynamometer Type For both AC and DC

Electro Thermic Type For both AC and DC

Also for hot wire type, thermocouple type and bolometer.

Induction Type Only for AC measurement.

Electrostatic Type Both AC and DC

Rectifier Type Both AC and DC

## Permanent Magnet Moving Coil (PMMC)Type Instrument

It is used for the measurement of DC only. The material used for magnets in PMMC is Alnico (AI + Ni + Co) and Alcomax (Al + Co + max….). The field strength in PMMC varies from 0.1 Wb/m2 to 1Wb/m2.

• Concentric magnetic construction is used to get the longer angular movement of the pointer.
• Due to the strong operating field of the permanent magnet, the eddy current damping mechanism is used to produce the damping torque.
• The control torque in PMMC is provided with a spiral-shaped hair-type phosphor-bronze spring.
Td = NBIA due to magnetic field
TC = Kθ due to the control spring
At balance
As θ ∞ I
The scale of the PMMC instrument is a uniform scale

where N = number of turns of the moving coil

B = Flux density of permanent magnet in Wb/m2

A = Area of the coil in m2

I = Current in amp

G = NBA = Displacement constant of the galvanometer

### Key Points:

• The control spring in PMMC has dual utility, they not only produce controlling torque but are also used to lead the current into the system.
• Due to the strong operating torque at the permanent magnet, an eddy current damping is used to produce damping torque.

• High torque to weight ratio.
• High accuracy and sensitivity.
• Magnetic shielding is not required due to a strong operating field.
• Low power consumption (25 – 200 μ W).

• High cost.
• Used for measurement of DC only.
• Limited current carrying capacity (100 mA) approx.

### Sources of Errors:

• Ageing effect of the permanent magnet (can be compensated by using a pre-edged magnet.
• Ageing effect of the spring.
• Temperature effect of the coil and the control spring.

## Application of PMMC Instrument

#### Ammeter Shunt:

Shunt resistance

Where, Rsh = Shunt resistance (Ω)

Rm = Internal resistance of the movement (Ω)

Im = Ifs = Full-scale deflection current of the movement (A)

I = Full-scale current of the ammeter including the shunt.

### Key Points:

• The shunt should have a small and constant temperature coefficient.
• The material used for the shunt in PMMC is Magnin as it gives a small thermal emf with copper.
• Constantin is used for the construction of shunt in AC ammeter.

## Effect of Temperature Change on Ammeter Reading

As temperature increases the resistance of copper increases and this result in a change of reading of the instrument. To reduce the effect of temperature a resistance having a very small temperature coefficient made up of Magnin is connected in series with the coil and this is known as swamping resistance.

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