Title

: SSC : Junior Engineers - Electrical Engineering - Guide

Language

: English

Editor’s Name : Vinit Garg Copyright ©

: 2022 G.K. Publications (P) Ltd.

No part of this book may be reproduced in a retrieval system or transmitted, in any form or by any means, electronics, mechanical, photocopying, recording, scanning and or without the written permission of the Author/Publisher. Published & Marketed by : G.K. Publications (P) Ltd. Plot No. 9A, Sector-27A, Mathura Road, Faridabad, Haryana-121003 ISBN

: 978-93-92837-22-7

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For product information : Visit www.gkpublications.com or email to [email protected]

Preface SSC JE is a combined three-stage examination conducted by Staff Selection Commission for the recruitment of Junior Engineer for government departments such as CPWD, CWC & MES. Every year a large number of candidates appear for this exam, competing for a limited number of posts. Thus SSC JE is considered one among the toughest exam in India due to its low selection ratio and technical nature. GK Publications has been the ‘‘publisher of choice'' to students preparing for GATE, PSUs, ESE, SSC JE and various other technical examinations in the country. GKP's SSC JE series provides a wide range of study material classified into 10 books, with 4 study guides, 3 practice papers book each in English and Hindi for Mechanical, Civil & Electrical. These books have been thoroughly updated as per the latest pattern and syllabus to provide everything you need to prepare for the exam. Like every other exam, SSC JE was also conducted for the first time in an online mode this year. We at GKP had taken an effort to reach out a good number of students to help them prepare for the exam in an actual exam environment with our online test series both in English and Hindi. As today's students have easy access to technology, the concept of a monologue within the classroom has changed to dialogue where students come prepared with concepts and then discuss topics. They learn a lot of things on the go with their mobile devices and practice with online mock tests. We, as a leading publisher of Technical Test Prep Books, have also embraced change. Today, our books are no more guides only but come with a fully supported mobile app and a web portal. Our mobile app provides access to short tests, report analysis and regular updates about the exam. The web portal in additional to what is available on the app provides full length mock tests to mimic the actual exam and help you gauge your level of preparedness both in English & Hindi. The combination of practice content in print, short and full length tests on mobile and web makes this product a complete courseware for the SSC JE preparation. We hope this little effort of ours will be helpful in achieving your dreams. If you have any suggestions on improvement of this book, you can write to us at [email protected].

All the Best! Team GKP

Contents x Exam Pattern x Syllabus

1. Basic Electrical

1.1 – 1.22

Inductances In series and Parallel

3.6 3.7

Types of Electricity

1.1

Magnetic Hysteresis

Coulomb’s Law

1.1

Determination of Hystersis Loss

3.7

Electric Field Intensity

1.1

Eddy Current

3.8

Electric Dipole Moment

1.1

Flux of an Electric Field

1.2

Exercise – I 3.9 – Answers 3.16 Exercise – II 3.17 (Questions From Previous SSC CPWD Exams) – Answers 3.22 – Explanations 3.22

Electric Field of Many Charges

1.2

Gauss’s Law

1.2

Electric Potential

1.3

Electric Potential due to a Charge

1.3

Potential due to Group of Charges

1.3

Potential due to an Electric Dipole

1.3

Electric Potential Energy

1.4

4. AC Fundamentals

4.1 – 4.26

Alternating Quantity

4.1

Power of an A.C. circuit

4.3

Unit of Current

1.4

Advantages and disadvantages of a.c. over d.c.4.3

Electromotive force

1.4

Resistance

1.4

Resistance, Capacitance and Inductance Resistance

Electrical power

1.5

4.3

Capacitance (C)

4.3 4.4

Resistance in series and parallel

1.5

Inductance

Drift Velocity

1.5

Resonance

4.4

1.5

Measurement of Three Phase Power

4.5

Super- Conductivity

Non Linear Devices 1.5 Exercise – I 1.6 – Answers 1.17 Exercise – II 1.18 (Questions From Previous SSC CPWD Exams) – Answers 1.20 – Explanations 1.20

Exercise – I 4.8 – Answers 4.16 Exercise – II 4.17 (Questions From Previous SSC CPWD Exams) – Answers 4.22 – Explanations 4.23

2.1 – 2.37

5. Measurement and Measuring Instruments 5.1 – 5.63

Kirchhoff’s Law

2.1

Measurement of Electric Voltage and current 5.1

Series and Parallel Networks

2.1

Extension of Instrument Range

Commercial Resistor

2.2

Devices Commonly Used

5.1

Source Transformation

2.2

Shunts

5.1

Magnetic Coupling

2.2

Shunts for AC Instruments

5.2

Network Theorems

2.3

Galvanometers

5.4

2. Circuit Law

Exercise – I 2.6 – Answers 2.27 Exercise – II 2.28 (Questions From Previous SSC CPWD Exams) – Answers 2.33 – Explanations 2.33

3. Magnetic Circuit

3.1 – 3.24

5.1

Sensitivity

5.4

Moving Iron instruments

5.5

Errors Occuring in Moving Iron Instruments 5.5 Moving coil Instruments

5.5

Thermal Instruments

5.6

Rectifier Instruments

5.7

Magnetic materials

3.1

Electrostatic Instruments

5.7

Magnetic Force

3.1

Induction Type Instruments

5.8

Solenoid

3.3

Instrument Transformers

Electro-magnetic Induction

3.5

Measurement of Power

5.9 5.12

Wattmeters

5.12

Transformer Tests

6.13

Types of Wattmeters

5.14

Per Unit System

6.14

Measurement of Resistance

5.16

Voltage Regulation of a Transformer

6.14

Measurement of Medium Resistance

5.18

Transformer Losses and Efficiency

6.15

Measurement of High Resistance

5.19

Auto – Transformer

6.15

Electronic Instruments

5.20

Parallel Operation of Transformers

6.16

Electronic Voltmeters

5.20

Three Phase Transformer

6.17

Electronic Galvanometers

5.22

Alternators and Synchronous Motors

6.18

Cathode Ray Oscilloscope

5.22

Synchronous Machine

6.18

Various Controls of CRO

5.22

Rotors

6.18

AC Signal Source

5.23

Space Phasors

6.18

Oscillators

5.23

Voltage Regulation of an Alternator

6.20

Signal Generators

5.24

Electro Magnetic Torque

6.20

Sweep Frequency Generator

5.24

Phasor Diagram of Alternator

6.20

Function Generators

5.24

Synchronous Motor Phasor Diagram

6.20

Harmonic Distortion

5.25

Power Flow Equation

6.21

Digital Instruments

5.25

Maximum Power Condition

6.21

Analog Electronic Voltmeter

5.25

Hunting

6.24

5.26

Induction Motors

6.24

Induction Motor Phasor Diagram

6.26

Digital Voltmeters (DVM)

Exercise – I 5.28 – Answers 5.49 Exercise – II 5.56 (Questions From Previous SSC CPWD Exams) – Answers 5.61 – Explanations 5.61

6. Electrical Machines

6.1 – 6.157

D. C. Machines

6.1

Working of D.C. Motors

6.1

Power Stages in Induction Motor

6.27

Single Phase Induction Motors

6.30

Approximate Equivalent Circuit

6.32

Split Phase Starting

6.33

Exercise – I 6.39 – Answers 6.137 Exercise – II 6.142 (Questions From Previous SSC CPWD Exams) – Answers 6.153 – Explanations 6.153

Importance of Back EMF

6.1

Speed Control of D.C. Motors

6.3

Speed Control of Shunt Motor

6.3

Speed Control of Series Motors

6.4

Hydro–electric Power Plants

Power Stages in Generators

6.5

Classification

7.1

Power Stages in Motors

6.5

Water Turbines

7.2

Various Losses in D.C. Machines

6.5

Steam Power Plants

7.2

Condition for Maximum Efficiency

6.5

Nuclear Power plants

7.3

Testing of D.C. Machines

6.5

Nuclear Reactor

7.4

Electrical Braking

6.6

Diesel-Electric Power Plants

7.5

D.C. Generators

6.7

Base Load and Peak Load

7.7

Induced Voltage

6.7

Costs of Power Generation

7.7

Characteristics of DC Generators

6.8

Economics of Generation

7.8

Characteristics Curves

6.9

Tariff

Conditions For Self Excited

6.9

Common Types of Tariffs

6.9

Parallel Operation of D.C. Generators

7. Generation, Transmission and Distribution 7.1 – 7.72 7.1

7.9 7.10

Power Factor Improvement

7.11

Armature Reaction

6.10

Medium Lines

7.16

Commutation

6.10

Surge Impedance Loading (SIL)

7.17

Transformer

6.11

Symmetrical Fault Analysis

7.20

Phasor Diagram

6.12

Symmetrical Components

7.22

Switches

7.25

Fuses

7.25

Protective Relay

7.26

Methods of Discrimination

7.27

Relay Classification

7.28

Over Current Relay

7.29

Transformer Protection

7.32

Circuit Breaker

7.33

HVDC Transmission

7.37

Exercise – I 7.38 – Answers 7.64 Exercise – II 7.65 (Questions From Previous SSC CPWD Exams) – Answers 7.70 – Explanations 7.70

8. Estimation and Costing, Utilization and Electrical Energy 8.1 – 8.28

Exercise – I 8.11 – Answers 8.25 Exercise – II 8.26 (Questions From Previous SSC CPWD Exams) – Answers 8.28 – Explanations 8.28

9. Basic Electronics

9.1 – 9.30

Intrinsic Semiconductors

9.1

Forward Bias

9.2

Semiconductor-diode

9.2

Biasing of Diodes

9.2

Some Special Diodes

9.3

Junction Diode as a Rectifier

9.3

Key Points

9.3

LASER

9.5

Electronic Test Instruments

9.5

Rectification

9.8

Filter Circuit

9.9

Industrial Drives

8.1

LED

Selection of Electric Motor

8.1

Enclosures

8.2

Bearings

8.2

Transmission of Power

8.2

Electric Braking

8.3

Exercise – I 9.15 – Answers 9.27 Exercise – II 9.28 (Questions From Previous SSC CPWD Exams) – Answers 9.30 – Explanations 9.30

Electric Heating

8.4

Electric Heating Methods

8.4

Electric Welding

8.6

Resistance Welding

8.6

Electric Arc Welding

8.7

Illumination

8.8

Types of Electric Lamps

8.9

Electrolytic Processes

8.10

9.11

SOLVED

PAPER 2017 SOLVED PAPER 2018 SOLVED PAPER 2019 (Set 1) SOLVED PAPER 2019 (Set 2) SOLVED PAPER 2020 (Set 1) SOLVED PAPER 2020 (Set 2) SOLVED PAPER 2021 (Set 1) SOLVED PAPER 2021 (Set 2)

Exam Pattern Papers Paper – I Objective Type

Subject (i) General Intelligence & Reasoning (ii) General Awareness (iii) General Engineering

Maximum Marks

Duration

50 50 100

2 Hours

300

2 Hours

Paper – II Conventional Type

General Engineering

1-26 1-22 1-25 1-24 1-34 1-38 1-40 1-41

Syllabus Paper-I General Intelligence & Reasoning The Syllabus for General Intelligence would include questions of both verbal and non-verbal type. The test may include questions on analogies, similarities, differences, space visualization, problem solving, analysis, judgement, decision making, visual memory, discrimination, observation, relationship concepts, arithmetical reasoning, verbal and figure classification, arithmetical number series etc. The test will also include questions designed to test the candidate’s abilities to deal with abstract ideas and symbols and their relationships, arithmetical computations and other analytical functions.

General Awareness Questions will be aimed at testing the candidate’s general awareness of the environment around him/her and its application to society. Questions will also be designed to test knowledge of current events and of such matters of everyday observations and experience in their scientific aspect as may be expected of any educated person. The test will also include questions relating to India and its neighbouring countries especially pertaining to History, Culture, Geography, Economic Scene, General Polity and Scientific Research, etc. These questions will be such that they do not require a special study of any discipline.

General Engineering Electrical Engineering Basic concepts, Circuit law, Magnetic Circuit, AC Fundamentals, Measurement and Measuring instruments, Electrical Machines, Fractional Kilowatt Motors and single phase induction Motors, Synchronous Machines, Generation, Transmission and Distribution, Estimation and Costing, Utilization and Electrical Energy, Basic Electronics.

Paper-II Basic Concepts Concepts of resistance, inductance, capacitance, and various factors affecting them. Concepts of current, voltage, power, energy and their units.

Circuit Law Kirchhoff’s law, Simple Circuit solution using network theorems.

Magnetic Circuit Concepts of flux, mmf, reluctance, Different kinds of magnetic materials, Magnetic calculations for conductors of different configuration e.g. straight, circular, solenoidal, etc. Electromagnetic induction, self and mutual induction.

AC Fundamentals Instantaneous, peak, R.M.S. and average values of alternating waves, Representation of sinusoidal wave form, simple series and parallel AC Circuits consisting of R.L. and C, Resonance, Tank Circuit. Poly Phase system – star and delta connection, 3 phase power, DC and sinusoidal response of R-L and R-C circuit.

Measurement and Measuring Instruments Measurement of power (1 phase and 3 phase, both active and re-active) and energy, 2 wattmeter method of 3 phase power measurement. Measurement of frequency and phase angle. Ammeter and voltmeter (both moving oil and moving iron type), extension of range wattmeter, Multimeters, Megger, Energy meter AC Bridges. Use of CRO, Signal Generator, CT, PT and their uses. Earth Fault detection.

Electrical Machines D.C. Machine – Construction, Basic Principles of D.C. motors and generators, their characteristics, speed control and starting of D.C. Motors. Method of braking motor, Losses and efficiency of D.C. Machines. (b) 1 phase and 3 phase transformers – Construction, Principles of operation, equivalent circuit, voltage regulation, O.C. and S.C. Tests, Losses and efficiency. Effect of voltage, frequency and wave form on losses. Parallel operation of 1 phase /3 phase transformers. Auto transformers. (c) 3 phase induction motors, rotating magnetic field, principle of operation, equivalent circuit, torque-speed characteristics, starting and speed control of 3 phase induction motors. Methods of braking, effect of voltage and frequency variation on torque speed characteristics. Fractional Kilowatt Motors and Single Phase Induction Motors: Characteristics and applications. (a)

Synchronous Machines Generation of 3-phase e.m.f. armature reaction, voltage regulation, parallel operation of two alternators, synchronizing, control of active and reactive power. Starting and applications of synchronous motors.

Generation, Transmission and Distribution Different types of power stations, Load factor, diversity factor, demand factor, cost of generation, inter-connection of power stations. Power factor improvement, various types of tariffs, types of faults, short circuit current for symmetrical faults. Switchgears – rating of circuit breakers, Principles of arc extinction by oil and air, H.R.C. Fuses, Protection against earth leakage / over current, etc. Buchholtz relay, Merz-Price system of protection of generators & transformers, protection of feeders and bus bars. Lightning arresters, various transmission and distribution system, comparison of conductor materials, efficiency of different system. Cable – Different type of cables, cable rating and derating factor.

Estimation and Costing Estimation of lighting scheme, electric installation of machines and relevant IE rules. Earthing practices and IE Rules.

Utilization of Electrical Energy Illumination, Electric heating, Electric welding, Electroplating, Electric drives and motors.

Basic Electronics Working of various electronic devices e.g. P N Junction diodes, Transistors (NPN and PNP type), BJT and JFET. Simple circuits using these devices.

1

Basic Electrical

CHAPTER TYPES OF ELECTRICITY It is of two types. (i) Static electricity : It is developed on bodies when they are rubbed with each other. (ii) Dynamic electricity : It is the flow of electric charge through a conductor in form of current. Electric charge. It is of two types (i) Negative charge (ii) Positive charge Charge on a body is always some integral multiple of smallest charge e, i.e. ne where n = ±1, ±2, ±3, ......; and e = 1.6 × 10–19 C. COULOMB’S LAW Charges of same polarity repel one another and that of opposite polarity attract each other. The force (F) between the two charges q1 and q2 as shown in the figure is (i) directly proportional to the product of the charges q1 and q2 (ii) inversely proportional to the square of distance d between them (iii) depends on the nature of medium surrounding the charges. q1

q2 d

Mathematically,

F∝ F=

q1 . q 2 d2 q1 . q 2

. ar

4 πε r . ε 0d 2

Field intensity, E =

(a) (b) Thus field intensity is a vector in the direction of the force. Its value is given by q iR Newton/Coulomb E = 4π ε r ε 0R 2 where iR is the unit factor along the distance R and directed away from the charge. ELECTRIC DIPOLE MOMENT It is a vector p whose magnitude is 2aq and direction is from negative to the positive charge. When the dipole is placed in a uniform external electric field E , as shown in the figure below, the two charges experience equal and opposite forces.

F = qE Thus net force on the dipole is zero but there is a net torque τ about an axis at point P at right angles to the plane of the paper. τ = 2F (asin θ) = 2 (qE) (a sinθ)

ar Newton

where ε0 = permittivity of air and its value is 8.854 × 10–12 F/m

εr = relative permittivity of surrounding medium with respect to air and ar = unit vector pointing in direction of line joining the two charges. ELECTRIC FIELD INTENSITY The space around the charge which is under stress, and experiences a force on another charge when placed there, is known as electrostatic field. This is illustrated in Fig (a). If the force F experienced by a resting positive charge q0 placed at a point as shown in Fig. (b) at a distance R metres from the charge of q, then

F q0

= 2aqE sin θ = pE sin θ Thus torque is product of magnitude of force and the perpendicular distance between the forces. In vector form, τ = p×E In order to change the orientation of the electric dipole placed in an external field, some amount of work is to be done and this work is stored as potential energy in the system. If the dipole is to be rotated from its reference vertical position (i.e. θ = 90°) to angle θ, then Potential energy, U = or

θ

θ

90°

90°

z τdθ = z pE sinθ = – pE cos θ

U = –p.E

1.2

Basic Electrical

FLUX OF AN ELECTRIC FIELD

GAUSS’S LAW

It refers to a hypothetical surface, closed or open and is measured by the numbers of lines of force cut through the surface. An arbitrary closed surface can be divided into a large number of infinitesimal surfaces represented by a vector Δ S whose direction is at right angel to the small surface as illustrated in figure. Then its flux can be defined as

The surface integral of the normal component of electric field intensity E over a closed surface containing point charge q as shown in the figure above is given by

z E . dS = εq

0

This can be interpreted as the net flux of electric field emanating from the surface S containing a point charge q is equal to q/ε0. If this arbitrary surface does not enclose the point charge, the net electric field flux emanating from the surface must be zero, i.e.

z E . dS = 0 ΔΦe = E . Δ S = E ΔS cos θ which means it is the product of ΔS and component of E parallel to vector Δ S or at right angels to the surface. If both vectors point in the same direction, the flux is positive otherwise negative. For the whole surface,

If there are more than one point charges enclosed, then the above equation can be generated as follows

z E . dS = z E . dS + z E 1

s

s

2

z

. dS + E3 . dS + .......

s

s

q + q2 +.... qn = 1 ε0

Φe= E . dS

z

=

s

charge enclosed by the surface S ε0

The electric field intensity of a point charge is thus directed everywhere radically away from the point charge, and on any spherical surface at the point charge, its magnitude is constant.

An important outcome of this law is that excess charge placed on an insulated conductor resides entirely on its outer surface.

ELECTRIC FIELD OF MANY CHARGES

Gauss’s Law in Differential Form.

If there are several point charges q1, q2, q3....qn located

Consider a volume distribution with the charge density ρ . The charge enclosed by arbitrary closed surface S is given by volume integral of charge density throughout the volume V enclosed by surface, i.e ρdv .

at different points, then by superposition, the force F experienced by a test charge situated at a point, is the vector sum of the forces experienced by the test charge due to the individual charges.

F=

q1 q 4π ε 0 R12

iR1 +

q 2q 4π ε 0 R 22

iR2 + .....

q nq 4 ε 0 R 2n

q1 q2 F qn = i + i + .... iR 4π ε 0 R 12 R1 4π ε 0 R 22 R2 q 4 π ε 0 R 2n n

=

n

qj

j= l

4 π ε 0 R 2j

∑

According to Gauss’s law,

v

z E . dS = ε1 z ρdv

iRn

The electric field intensity at point P will be

E =

z

0 V

s

If the volume is shrunk to a very small Δv, then surface area becomes very small ΔS

FG IJ z H K

1 ρdv ε0 E. dS = Lim Lim ΔV → 0 ΔV → 0 Δs ΔV ΔV

z

iR j

= or

ΔE =

ρ ΔV 1 1 = .ρ Lim ε 0 Δv → 0 ΔV ε0 1 ρ ε0

This equation is Gauss’s law in differential form. It states that the divergence of electric field intensity at any point is equal to 1/ε0 times the volume charge density at that point. This is Maxwell’s divergence equation for electric field.

Basic Electrical

1.3

ELECTRIC POTENTIAL

ELECTRIC POTENTIAL DUE TO A CHARGE

The electric field is a force field so far the charges are concerned, there is work associated with the movement of the charges in an electric field. If a force exerted by the field on the charge is in the direction moved against the direction of the field, and external agent has to supply the energy to overcome the force exerted on the charge by the field. This force is opposite to the direction of movement of the charge. Consider the displacement of test charge q by an

If point A is taken to be at infinity and potential at infinity is taken to be zero, then the potential V at a point B will be

infinitesimal distance dl from A to B at an angle with the electric field E at a point A as shown in figure. The force exerted on the test charge by the field has magnitude qE and is directed along E. Its component along the line from A to B is qE cos α. If the charge is moved from A to B, the amount of work done dW by the field is the product of force and displacement.

r

B

V= –

z

∞

E . dl = –

z 4π ε qε r

∞

LM OP NQ

1 q =– . r 4π ε r ε 0

r

r ∞

=

0

2

dr

q 4π ε r ε 0 r

Since field intensity is the variation of potential with the distance, it can also be visualised as potential gradient. If potential for all points of space are known, the components of E and thus E itself can be found by taking the following derivatives. Ex =

–∂V –∂V –∂V , Ey = E2 = ∂y ∂x ∂z

FG H

∂V ∂V ∂V i + j +k E = – ∂x ∂y ∂z

∴

IJ K

Thus the unit of electric field is volt/metre. POTENTIAL DUE TO GROUP OF CHARGES The potential at a point due to a group of point charges q1, q2, qn, is the algebraic sum of the potentials due to each charge, i.e. V=

dW = qE cosα dl = qE . dl where dl is the vector from A to B. The work done WAB by the field in moving a test charge q from A to B along a given path can be obtained by dividing the path into several segments of infinitesimal length dl.The result is a line integral expression given by B

z

WAB = q E. dl The test charge has certain potential energy associated with it by virtue of its location in the electric field. WAB as given by the above equation is then the loss of potential energy associated with the movement of the charge from A to B . Dividing WAB by q gives the potential energy per unit charge. This quantity denoted by VAB is known as the potential difference between the points A and B. Thus

VAB

1

+

1

q2 q +.... n r2 rn

IJ = 1 K 4π ε

0

∑ n

qn rn

If the charge distribution is continuous, then potential at a point is given by V=

z dqr

1 4π ε 0

where dq is infinitesimal element of charge at a distance r from the point. POTENTIAL DUE TO AN ELECTRIC DIPOLE

A

WAB = = q

FG q Hr

1 4π ε 0

The potential at a point P due to the dipole shown in figure will be V=

=

E. dl

A

If VAB is positive, there is a potential energy associated with the movement of the charge from A to B, that is, the field does the work. If VAB is negative, there is a gain in potential energy associated with the moment of the charge from A to B, that is an external agent has to do the work.

q 4π ε 0

2

1

1 2

Now if r >> 2a, then

B

z

FG IJ H K FG r – r IJ H rr K

q q 1 . – 4 π ε 0 r1 r2

θ=α ∴

(r2 –r1) = 2a cos α

≅ 2a cos θ and Thus

r1r2 ≅ r2 V=

bq2ag cos θ = 4π ε 0 r 2

1 . p cos θ 4π ε 0 r2

1.4

Basic Electrical

ELECTRIC POTENTIAL ENERGY

Resistance of a conductor depends on

For two charges +q1 and –q2 placed at a distance r apart, energy is stored in the system because a definite amount of work has to be done to move away these charges. If the charges are of opposite polarity, their potential energy will change into kinetic energy and as a result, they will accelerate towards each other.

(i)

Thus potential energy of a system of point charges is the work required to assemble these charges by bringing them together from infinity. Now, potential due to q1 is, V=

q 1 . 1 4π ε 0 r

(ii) cross-sectional area of the conductor – it varies inversely with the cross-sectional area (iii) resistivity i.e. the nature of composition, etc., of the material of which the conductor is made up and (iv) temperature of the conductor – it almost varies directly with the temperature, thus l resistance of a conductor, R = ρ A where ρ = specific resistance or resistivity of the material,

Work done required to move q2 from infinity to distance r by definition of potential will be W = Vq2

∴

Electric potential energy, U = Vq2 =

1 q1 q2 4π ε 0 r

l = length of the conductors, A = cross– sectional area of conductor. Ohm’s Law. If the temperature and other conditions remain constant, then current through a conductor is proportional to the applied potential difference and it remains constant. Thus Current =

UNIT OF CURRENT The charge on an electron is measured in terms of coulomb. The unit of current is coulomb per second and is called ampere. Thus I(Ampere) =

coulomb second

Δq = . Δt One coulomb is equivalent to the charge of 6.28 × 1018 electrons.

length of the conductor — it varies directly with the length

Resistance =

Applied voltage Resistance of the circuit Applied voltage Current in the circuit

Potential across resistance = Current × Resistance Conditions for Ohm’s Law: (i)

Ohm’s law can be applied either to the entire circuit or a part of a circuit.

ELECTROMOTIVE FORCE

(ii) When Ohm’s law is applied to a part circuit, part resistance and the potential across the part resistance should be use

Electromotive force or potential of a body is the work done in joules to bring a unit electric charge from infinity to the body. It is expressed in terms of volts.

(iii) The Ohm’s law can be applied to dc as well as ac circuits. However, in case of ac circuits impedance Z, is used in place of resistance. Thus

The potential difference is defined as that which causes current to flow in the closed circuit. RESISTANCE Resistance is the property of a substance due to which it opposes the flow of electrons (i.e., electric current) through it. The unit of resistance is ohm (Ω) . Some substances offer relatively greater difficulty or hindrance to the passage of these electrons. Such substances are called poor conductors or insulators of electricity. e.g. glass, bakelite, mica , rubber, polyvinyl chloride (P.V. C.), dry wood , etc.

I= =

E Z

Applied voltage . Impedance in the circuit

Conductance (G). It is the reciprocal of resistance (R) and is measure of the ease with which the current will flow through a substance. Thus 1 G= . R The unit of conductance is mho ( ).

Ω

1 emu of current = 3 ×1010 esu of current.

Basic Electrical

1.5

ELECTRICAL POWER

Temperature coefficient of resistance.

Electrical power is expressed in terms of watts (W) and is given by W=E×I = I2 R

Temperature coefficient is the increase in resistance per ohm original resistance per °C rise in temperature.

E2 R Power is also expressed in terms of kW (kilowatt) (= 1000 W) or MW (megawatt) which is 1000 kW or 1000,000 W.

=

Electrical Energy is expressed in terms of kilowatt hours (kWh). Thus 1 kWh = 1 kW × 1 hour = 1000 watt – hours = 1000 × 60 × 60 watt – sec RESISTANCE IN SERIES AND PARALLEL Resistances in series . When resistances are connected in series, same current flows through all the resistance. Overall resistance, R = R 1 + R2 + R3 Also,

V = V 1 + V2 + V 3 = IR1 + IR2 + IR3

Resistance in Parallel . When conductors are joined in parallel, then I = I1 + I2 + I3

∴ or

1 1 1 1 = + + R R1 R2 R3 R =

R1R 2R 3 R1R 2 + R 2R 3 + R 3R1

G = G1 + G2 + G3

∴

α =

Rt – R0 R 0.t

where R0 is resistance at 0° C, Rt is resitstance at t°C, and t is temperature rise in °C Usually α is of the order of 10–4 Ω/ Ω° C for most of the metals. In case of insulators and electrolytes, α is usually negative. DRIFT VELOCITY Drift velocity vd of charge carriers is related to current I as I = n α evd where n = density of charge carriers in conductor,

α = area of cross-section of conductor, e = charge on each carrier A large amount of energy has to be supplied to pull an electron from inside to outside of the metal surface. This energy is called work function. This energy is the characteristic of the metal. SUPER- CONDUCTIVITY As temperature of metallic conductor decreases, their resistivity decreases. In certain metallic conductors as temperature decreases, the resistivity falls to zero at a certain temperature called super-conducting temperature. It happens for mercury at 4K and for tin at 3.72 K. This phenomenon is called superconductivity. Resistivity of semiconductors decreases with increase in temperature. resistivity at TK, ρT = ρ o e

– E g / kT

where, Eg = band gap energy, k = Boltzman constant NON LINEAR DEVICES The devices for which potential difference V Vs current I curve is not a straight line are called non-linear devices. These do not obey Ohm’s law and resistance of these devices is a function of V or I

Effect of temperature on resistance.

e.g. vacuum tubes, junction diodes, thermistors etc.

Resistance of all materials is affected by the variations in temperature.

The dynamic resistance of such devices is given as

•

Resistance of most of the metallic ocnductors increases with rising temperature.

•

Resistance of non-conductors or insulators usually decreases with rising temperature.

ΔV r = ΔILt →0 ΔI dV dI where Δ V is the change in p.d. =

1.6

Basic Electrical

EXERCISE - I 1. Ampere is the current which, if maintained in two straight parallel conductors of infinite length, of neglible circular cross-section, and placed 1 m apart in a vacuum, would produce between these conductors a force of (a) 2 × 10–7 N/m length (b) 1 N/m length (c) 1 × 10–7 N/m length (d) 2 × 107 N/m length 2. Current velocity through a copper conductor is (a) nearly 3 × 109 m/s. (b) of the order of a few μ m/s. (c) independent of current strength. (d) the same as propagation velocity of electric energy. 3. Draft velocity of electrons is (a) larger than speed of light. (b) almost equal to speed of light. (c) equal to speed of light. (d) very small in comparison to speed of light. 4. Ratio of the voltage and electric current in a closed circut (a) remains constant (b) varies (c) increases (d) decreases 5. Condition for the validity under Ohm’s law is that the (a) temperature should remain constant. (b) current should be proportional to voltage. (c) resistance must be wire wound type. (d) all of the above. 6. Ohm’s law is applicable to (a) semi-conductors. (b) vacuum tubes. (c) electrolytes. (d) none of these 7. Resistance of a wire always increases if (a) temperature is reduced. (b) temperature is increased. (c) number of free electrons available become less. (d) number of free electrons available become more. 8. The resistance of wire varies inversely as (a) area of cross-section (b) length (c) resistivity (d) temperature 9. For a fixed supply voltage, the current flowing through a conductor will increase when its (a) area of cross-section is reduced. (b) length is reduced. (c) length is increased. (d) length is increased and x-sectional area is reduced.

10. Two wires A and B of the same material and length l and 2l have radius r and 2r respectively. The ratio of their specific resistances will be (a) 1:1.

(b) 1:2.

(c) 1:4.

(d) 1:8.

11. Electrical conductivity of metals is typically of the order of (in ohm–1m–1) (a) 107

(b) 105

(c) 10–4

(d) 10–6

12. Pure metals generally have (a) high conductivity and low temperature coefficient. (b) high conductivity and large temperature coefficient. (c) low conductivity and zero temperature coefficient. (d) low conductivity and high temperature coefficient. 13. A wire of length l and of circular cross section of radius r has a resistance of R ohms. Another wire of same material and of cross-sectional radius 2r will have the same resistance R if the length is (a) 2 l

(b) l/2

(c) 4 l

(d) l2

14. Specific resistance of a conductor depends upon (a) dimensions of the conductor. (b) composition of conductor material. (c) resistance of the conductor. (d) all of the above 15. Which of the following materials possesses the least specific resistivity ? (a) Aluminium

(b) Copper

(c) Silver

(d) Iron

16. Resistivity or specific resistance is measured in (a) Ω – m.

(b) Ω /m.

(c) Ω/m .

(d) Ω/m2.

3

17. Specific resistance of copper is (a) 1.76 × 10–6 Ω-m.

(b) 1.68 × 10–8 Ω-m.

(c) 1.68 × 108 Ω-m.

(d) 1.76 × 106 Ω/m.

18. Electrical conductivity is measured in (a) mho/m.

(b) mho-m.

(c) mho/m3.

(d) mho/m2.

19. Substances having a large number of free electrons and offering low resistance are called the (a) insulator

(b) conductors.

(c) semi-conductors.

(d) insulators.

Basic Electrical

20. Materials having a few number of free electrons and offering very high resistance to the flow of electric current are known as (a) conductors.

(b) insulators.

(c) semi-conductors.

(d) none of these.

21. With the increase in temperature, the resistance of pure metals (a) increases. (b) decreases. (c) first increases and then decreases. (d) remains constant.

(a) increases.

(b) decreases.

(c) becomes zero.

(d) remains unchanged.

23. With the rise in temperature the insulating property of an insulator (b) gains.

(c) remains unchanged. (d) none of these 24. With the rise in temperature, the temperature coefficient of resistance (a) remains unaffected. (b) increases.

(a) 48 Ω.

(b) 18 Ω.

(c) 36 Ω.

(d) 24 Ω.

30. When one leg of a parallel circuit gets opened out, the current drawn from the supply will (a) reduce.

(b) increase.

(c) remain the same.

(d) uncertain

(d) uncertain.

25. The values of temperature coefficient of resistance of a given conductor

(a) Resistance’s are additive. (b) Powers are additive. (c) Currents are additive. (d) Voltage drops are additive. 32. Twelve identical wires of resistance 6 Ω each are arranged to form the edges of a cube. The effective resistance between the opposite corners of the cube is (a) 6 Ω.

(b) 5 Ω.

(c) 8 Ω.

(d) 4.5 Ω.

33. The equivalent resistance of the given circuit above is (a) 2 Ω.

(a) are the same at different temperatures

(b) 4 Ω.

(b) are higher at higher temperatures

(c) 5 Ω.

(c) are different at different temperatures

(d) 10 Ω.

26. Temperature coefficient of resistance is defined as (a) increase in resistance per ohm per °C. (b) increase in resistance per °C. (c) decrease in resistance per ohm per°C. (d) the ratio of decrease in resistance per °C to the resistance at 0°C. 27. In case of a series circuit (a) current flowing through each resistor is the same. (b) applied voltage is equal to the sum of voltage drops across individual resistors.

34. The current drawn from the battery given in circuit for Q 33 is (a) 1.5 A.

(b) 2.0 A.

(c) 2.5 A.

(d) 5 A.

35. The current flowing through branch AB of the circuit shown for Q 33 is (a) 5/12 A.

(b) 0.25 A.

(c) 5/6 A.

(d) 5/3 A.

36. When all the resistances in the circuit are of 1 Ω each, the equivalent resistance across the points A and B will be 1Ω

(d) none of the above

1Ω

B

A

1Ω

=

=

1Ω

R

28. Two resistances of equal value, when connected in parallel, give an equivalent resistance of R. If these resistors are connected in series, the equivalent resistance will be (c) 2R.

=

R

(d) all of the above

(a) R.

R

=

(c) resistors are additive.

R

(c) decreases.

29. The resistance of a parallel circuit consisting of two resistors is 12 Ω . One of the resistance wires breaks and the effective resistance becomes 18 Ω . The resistance of the broken wire is

31. For a series as well as a parallel circuit

22. With the rise in temperature, the resistance of carbon

(a) weakens.

1.7

(b) 4R.

(a) 1 Ω.

(b) 0.5 Ω.

(d) R/2.

(c) 2 Ω.

(d) 1.5 Ω.