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BASIC ELECTRICAL AND

INSTRUMENTATION ENGINEERING

ABOUT THE AUTHORS

S. Salivahanan is the Principal of SSN College of Engineering, Chennai. He obtained

his B.E. degree in Electronics and Communication Engineering from PSG College of

Technology, Coimbatore, M.E. degree in Communication Systems from NIT, Trichy

and Ph.D. in the area of Microwave Integrated Circuits from Madurai Kamaraj

University. He has four decades of teaching, research, administration and industrial

experience both in India and abroad. He has taught at NIT, Trichy, A.C. College of

Engineering and Technology, Karaikudi, RV College of Engineering, Bangalore, and

Mepco Schlenk Engineering College, Sivakasi. He has industrial experience as Sci-

entist/Engineer at Space Applications Centre, ISRO, Ahmedabad, Telecommunication

Engineer at State Organization of Electricity, Iraq and Electronics Engineer at Electric Dar Establishment,

Kingdom of Saudi Arabia.

He is the author of 40 popular books which include all-time bestsellers such as Basic Electrical and

Electronics Engineering, Electronic Devices and Circuits, Linear Integrated Circuits, and Digital Signal

Processing, all published by McGraw Hill Education. He has also authored the books on Digital Circuits

and Design, Electromagnetic Field Theory, Circuit Theory, Network Analysis and Synthesis and Control

Systems Engineering. He has published several papers at national and international levels.

Professor Salivahanan is the recipient of Bharatiya Vidya Bhavan National Award for Best Engineering

College Principal for 2011 from ISTE, and IEEE Outstanding Branch Counsellor and Advisor Award in

the Asia-Pacific region for 1996–97. He was the Chairman of IEEE Madras Section for two years 2008 and

2009 and Syndicate Member of Anna University.

He is a Senior Member of IEEE, Fellow of IETE, Fellow of Institution of Engineers (India), Life Mem-

ber of ISTE and Life Member of Society for EMC Engineers. He is also a member of IEEE societies in

Microwave Theory and Techniques, Communications, Signal Processing, and Aerospace and Electronics.

R. Rengaraj is Associate Professor in the Department of Electrical and Electronics

Engineering, SSN College of Engineering, Chennai. He obtained his B.E. degree in

Electrical and Electronics Engineering from Manonmaniam Sundaranar University,

Tirunelveli, M.E. degree in Power Systems Engineering and Ph.D. in the area of Com-

bined Heat and Power, both from Anna University, Chennai. He has authored a book

on Control Systems Engineering. He has more than 13 years of teaching and research

experience. He has published several research publications in refereed international

journals and in the proceedings of international conferences. He has received TATA

Rao Gold Medal from the Institution of Engineers (India) in 2011. He is a Life Member

of ISTE and a Member of IEEE.

G.R. Venkatakrishnan is Assistant Professor in the Department of Electrical and

Electronics Engineering, SSN College of Engineering, Chennai. He obtained his B.E.

degree in Electrical and Electronics Engineering and M.E. degree in Control Systems

from Anna University, Chennai. He has authored a book on Control Systems Engineer-

ing and has published many research papers in national and international journals and

conferences. He is a Life Member of ISTE and a Member of IEEE.

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Basic Electrical and Instrumentation Engineering

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CONTENTS

4.11 Relation Between P 2

, P c

and P m

• 1. AC Circuits and Power Systems Preface ix
  • 1.1 Introduction
  • 1.2 Three-Phase Supply
  • 1.3 Basics of a Three-Phase Power System
  • 1.4 Generation of Three-Phase Voltages
  • 1.5 Analysis of the Three-Phase System
  • 1.6 Steps to Draw Phasor Diagram
  • 1.7 Star–Delta Conversion
  • 1.8 Power Measurment in a Three-Phase System
  • 1.9 Introduction to Electric Power System
  • 1.10 Introduction to Power System Protection
  • 1.11 Circuit Breaker
  • 1.12 Fuse
  • 1.13 Protective Relays
  • 1.14 Introduction to Tariff
  • 1.15 Power Factor
  • 1.16 Power Factor Improvement or Correction
  • Two-Mark Questions and Answers
  • Review Questions
• 2. Transformers
  • 2.1 Introduction
  • 2.2 Single-Phase Transformer
  • 2.3 EMF Equation of the Transformer
  • 2.4 Reasons for not Using DC Supply as a Source
  • 2.5 Types of Transformers
  • 2.6 Ideal Transformer
  • 2.7 Accounting for Finite Permeability and Core Loss
  • 2.8 Transformer on Load
  • 2.9 Effect of Winding Resistances vi Contents
  • 2.10 Effect of Leakage Reactance
  • 2.11 Winding Impedance
  • 2.12 Transformer on Load with Winding Impedances
  • 2.13 Circuit Model or Equivalent Circuit of Transformer
  • 2.14 Per Unit System
  • 2.15 Voltage Regulation
  • 2.16 Name Plate Rating of a Transformer
  • 2.17 Losses in a Transformer
  • 2.18 Efficiency of the Transformer
  • 2.19 All-Day Efficiency
  • 2.20 Determination of Parameters of Circuit Model of Transformer
  • 2.21 Auto-Transformer
  • 2.22 Three-Phase Transformer
  • 2.23 Voltage and Current Relationship for Different Connections
  • Two Mark Questions and Answers
  • Review Questions
• 3. DC Machines
  • 3.1 Introduction
  • 3.2 DC Generator
  • 3.3 Armature Reaction
  • 3.4 Commutation
  • 3.5 Types of DC Generators
  • 3.6 Electrical Equivalent Circuits, Current and Voltage Equations of DC Generators
  • 3.7 Characteristics of DC Generators
  • 3.8 Applications of DC Generators
  • 3.9 DC Motor
  • 3.10 Types of DC Motor
  • 3.11 Characteristics of DC Motors
  • 3.12 Speed Control of DC Motors
  • 3.13 Losses in DC Machines
  • 3.14 Power-Flow Diagram
  • 3.15 Starting DC Motors
  • 3.16 Applications of DC Motors
  • 3.17 Universal Motor
  • Two Mark Questions and Answers
  • Review Questions
• 4. AC Machines Contents vii
  • 4.1 Introduction
  • 4.2 Three-Phase Induction Motor
  • 4.3 Slip of an Induction Motor
  • 4.4 Effect of Slip on Rotor Parameters
  • 4.5 Three-Phase Induction Motor vs Transformer
  • 4.6 Torque Equation
  • 4.7 Effect of Change in Rotor Resistance on Torque
  • 4.8 Effect of Change in Rotor Reactance on Torque
  • 4.9 Losses in Induction Motors
  • 4.10 Power Flow in Induction Motor
  • 4.12 Efficiency of an Induction Motor
  • 4.13 Equivalent Circuit of an Induction Motor
  • 4.14 Phasor Diagram of an Induction Motor
  • 4.15 Starters
  • 4.16 Speed Control of a Three-Phase Induction Motor
  • 4.17 Single-Phase Induction Motor
  • 4.18 Types of Single-Phase Induction Motors
  • 4.19 Equivalent Circuit of a Single-Phase Induction Motor
  • 4.20 Alternator or a Three-Phase AC Generator
  • 4.21 EMF Equation of an Alternator
  • 4.22 Parameters of Armature Winding
  • 4.23 Synchronous Reactance and Synchronous Impedance
  • 4.24 Equivalent Circuit of an Alternator
  • 4.25 Voltage Equation of the Alternator
  • 4.26 Phasor Diagram of the Loaded Alternator
  • 4.27 Voltage Regulation of an Alternator
  • 4.28 Synchronous Motor
  • 4.29 Methods of Starting Synchronous Motors
  • 4.30 Behaviour of a Synchronous Motor on Loading
  • 4.31 Phasor Diagram
  • 4.32 V and Inverted-V Curves
  • 4.33 Expression for Back EMF or Induced EMF Per Phase in a Synchronous Motor
  • 4.34 Power Flow in Synchronous Motor
  • 4.35 Power Developed by a Synchronous Motor
  • 4.36 Comparison Between Synchronous and Induction Motors
  • 4.37 Stepper Motor
  • 4.38 Brushless Direct Current (BLDC) Motor
  • Two Marks Questions and Answers
  • Review Questions
• 5. Measurement and Instrumentation viii Contents
  • 5.1 Introduction
  • 5.2 Essential Requirements of Measuring Instruments
  • 5.3 Elements of the Measuring Instruments
  • 5.4 Types of Electrical and Electronic Measuring Instruments
  • 5.5 Principles of Electrical Indicating Instruments
  • 5.6 Types of Indicating Instruments
  • 5.7 Moving-iron Instruments
  • 5.8 Moving-coil Instruments
  • 5.9 Electro Dynamometer Type
  • 5.10 Electrothermic Instruments
  • 5.11 Electrostatic Type Instrument
  • 5.12 Induction Type Instruments
  • 5.13 Rectifier Type Instruments
  • 5.14 Ammeter
  • 5.15 DC Voltmeter
  • 5.16 Digital Voltmeter (DVM)
  • 5.17 Ohmmeter
  • 5.18 Digital Multimeter
  • 5.19 Cathode Ray Oscilloscope
  • 5.20 Static and Dynamic Characteristics of Instruments
  • 5.21 Errors in Measurement
  • 5.22 Introduction to Transducer
  • 5.23 Classification of Transducers
  • 5.24 Resistive Transducer
  • 5.25 Inductive Transducer
  • 5.26 Capacitive Transducers
  • 5.27 Thermoelectric Transducer
  • 5.28 Piezoelectric Transducer
  • 5.29 Photoelectric Transducer
  • 5.30 Hall Effect Transducers
  • 5.31 Mechanical Tranducers
  • Two Mark Questions and Answers
  • Review Questions

x Preface

Chapter 5 concentrates on the type of electrical and electronic instruments, principles of electrical

instruments, multimeters, oscilloscopes, transducers and their classifications and applications.

ACKNOWLEDGEMENTS

The authors sincerely thank the management of SSN College of Engineering, Chennai for the constant

encouragement, and for providing necessary facilities for completing this project.

The authors are highly appreciative of the editorial and production team of McGraw Hill Education (India)

for their initiation and support to bring out this edition in a short span of time.

The authors would like to take this opportunity to thank the reviewers especially the colleagues V. Thiyaga-

rajan, U. Shajith Ali, Alagudheeraj S. Malathy and D. Umarani from EEE department, and M. Karthikeyan

from Velammal Engineering College, Chennai for their useful comments and suggestions.

The authors would also like to thank Mr. G. Muralikrishnan, Panimalar Engineering College, Chennai, for

his valuable feedback.

Finally, they thank their family members Mrs. Kalavathy Salivahanan, S. Santhosh Kanna & S. Subadesh

Kanna, Mrs. Rajalakshmi Rengaraj, R. Harivarshan and Master R. Devprasath, and Mr. S. Rajan Babu,

Mrs. Sumathi Babu, Mrs. G. R. Hemalakshmi Prakash & Mrs. R. Jeya Jeyaprakash for their patience and

constant inspiration during the preparation of this book.

Any constructive criticism, suggestions and corrections for further improvement of the book will be most

appreciated.

S. Salivahanan

R. Rengaraj

G. R. Venkatakrishnan

Publisher’s Note:

McGraw Hill Education (India) invites suggestions and comments, all of which can be sent to

[email protected] (kindly mention the title and author name in the subject line).

Piracy-related issues may also be reported.

AC Circuits and

Power Systems

CHAPTER

1.1 INTRODUCTION

Electrical power is generated, transmitted, distributed in sinusoidal form for the commercial, industrial and

domestic applications. In general, two types of electrical power can be generated: single-phase power and

poly-phase power. The main disadvantage of single-phase power supply is that it can carry only a reasonable

amount of power but poly-phase system is normally used to generate, transmit and distribute bulk electric

power. This chapter deals with the three-phase system, which is a type of poly-phase system. The generation

of three-phase electric power, the relationship between voltage and current, and their power measurements

are also discussed.

Further, the transmission and distribution of electric power, the necessity of protecting the power system

and operation of various protective devices like circuit breaker, fuse and relay are explained. Tariff refers

to the price of electrical energy that the consumer is charged for consumption. Tariff plays a major role

in maintaining a healthy relation between the supplier and consumer. Hence, due consideration has to be

given in fixing the tariff and the consumers must be charged with different tariffs, based on their usage. The

different objectives and characteristics of tariff, factors affecting the tariff, and different types of tariff are

discussed in this chapter. In an AC power system, power factor plays a major role in analysing the system

performance. If the power factor is low, heavy current will flow and damage the system. The causes of low

power factor, its consequences and the methods to improve the power factor are described in this chapter.

1.2 THREE-PHASE SUPPLY

In an electrical power system, there are two types of systems, namely: single-phase and poly-phase systems.

A single-phase system consists of two wires, where the current flows through one wire and returns through

another wire, when it is energized by two terminals. Generally, in most of the households and small industries

where the required capacity of a motor is not greater than 5 horsepower, single-phase systems are used. But

nowadays, a three-phase system, which is a type of poly-phase system, is used to generate, transmit and

distribute electrical energy.

In a three-phase system, three conductors can carry three alternating electrical quantities at the same

frequency. The electrical quantities in these three conductors reach the same peak amplitude at different

instances, as shown in Figure 1.1.

AC Circuits and Power Systems 3

1.3 BASICS OF A THREE-PHASE POWER SYSTEM

The colour codes of the wires used in a three-phase system vary from country to country. In India, Red (R),

Yellow (Y) and Blue (B) are the colour codes used in three-phase systems. The two different configura-

tions by which the three wires in a three-phase system are connected are: star (Y) connection and delta (D)

connection. The different types of three-phase power systems are: (i) three-phase, three-wire system and

(ii) three-phase, four-wire system. The fourth wire in a three-phase four-wire system is the neutral wire,

represented in black colour. It is known that the three-phase power system can be used as source and load.

As a source, a three-phase power system can be used as either three or four-wire star connection or

three-wire delta connection. Similarly, as a load, depending upon the application, the type of connection and

configuration of a three-phase power system varies. The different terms used in three-phase power systems

are described as follows:

● (^) Phase: A branch of the circuit in a three-phase system is known as a phase.

● (^) Line: The wire that connects the source and load is known as transmission line or line.

● (^) Neutral: The fourth wire in the three-phase system, where all the phases in a star connection are

connected together is known as neutral.

● (^) Phase voltage: The voltage measured between a line and neutral or the voltage across a particular

phase is called as phase voltage. It is represented as RB RN BN

V = V - V or simply (^) , , R Y B

V V V.

● (^) Line voltage or line-to-line voltage: The voltage measured between any two lines in a three-

phase power system is known as line voltage. It is represented as (^) , and RY YB BR

V V V and is given by

, – , , – RY R Y YB Y B

V = V V V = V V and – BR B R

V = V V respectively.

● (^) Line currents: The currents flowing through a particular line are called line currents, represented by

, R Y

I I and I^ B.

● (^) Phase current: The current flowing through a single-phase or a branch of the system is called as

phase current. It is represented as (^) , and RY YB BR

I I I and is given by^ I^ RY =^ I^ R -^ IY^ ,IYB^ =^ IY^ -^ IB and

BR B R

I = I - I respectively.

● (^) Load impedance: For a star-connected load, the impedance between the line and neutral is called

load or line impedance and for a delta-connected load, the impedance between two lines is called

load or phase impedance.

● (^) Phase sequence: The time order or the sequence in which the electrical quantity in the three-phase

system reach their respective maximum values is known as phase sequence. If the phase sequence of

a particular system is RYB, then it indicates that R phase reaches the maximum value of electrical

quantity at first and then followed by Y phase and B phase.

● (^) Balanced condition: The condition for having a balanced source or a balanced load is given below.

(i) Balanced source: A three-phase system is said to be a balanced source, if the phase voltage of each

phase has the same magnitude and frequency and the phase difference between the lines is 120°.

(ii) Balanced load: A three-phase system is said to be a balanced load if the impedance is same for all

the phases, either in star or delta connection.

● (^) Unbalanced condition: If the load impedance differs in one or more phases, then the three-phase

system is said to be an unbalanced load. This unbalanced condition leads to changes in line and phase

currents.

● (^) Three-phase source: If the three-phase system is used to generate a three-phase power supply, then

it is said to be a three-phase source.

● (^) Three-phase load: If the three-phase system uses the three-phase supply to perform certain functions,

then it is said to be a three-phase load.

4 Basic Electrical and Instrumentation Engineering

● (^) Power factor: The cosine of the angle between phase voltage and the phase current is known as power

factor. It can be lagging, leading or unity, depending upon the type of load connected to the system.

If the phase current lags behind the phase voltage, then it is a lagging power factor load. If the phase

current leads the phase voltage, then it is a leading power factor load. Similarly, if the phase current

is in phase with the phase voltage, then it is a unity power factor load.

● (^) Phasor diagram: The diagram that represents the line voltage, phase voltage, line current and phase

current of a three-phase source or a three-phase load is known as a phasor diagram. In a star-connected

three-phase system, phase voltage is taken as the reference; while, in a delta-connected three-phase

system, line voltage is taken as the reference.

The schematic diagrams of a three-phase star-connected power system with three wires and four wires

are shown in Figures 1.2 (a) and (b) respectively.

R

B

Y

VBN

V RN

V YN

R

B

Y

VBN

V YN

VRN

N

B

Y

N

R

VBN

V RN

VYN

N

B

Y

N

R

VRN

V BN

VYN

(a)

(b)

N

Figure 1.2 Schematic Diagram of a Star-connected Three-phase System

The schematic diagram of a three-phase delta-connected power system is shown in Figure 1.3.

R

VRY

R

B

Y

B Y

R

Y

B

VBR

VYB

VRB

VYB

VYR

Figure 1.3 Schematic Diagram of a Delta-connected Three-phase System

6 Basic Electrical and Instrumentation Engineering

Therefore, 0 RN YN BN

V + V + V = (1.4)

It is clear from Eqn. (1.4) that the phasor addition of all the phase voltages at any instant in a three-phase

balanced star-connected system is always zero. Similarly, if the instantaneous line voltages of the three-phase

system, when connected in delta connection, are added, we get 0 RY YB BR

V + V + V =.

1.5 ANALYSIS OF THE THREE-PHASE SYSTEM

The different three-phase systems for which the relationship between phase and line voltages, phase and

line currents, power, and phasor diagrams are discussed as follows:

1. Three-phase balanced star-connected source
2. Three-phase balanced delta-connected source
3. Three-phase balanced star-connected load
4. Three-phase balanced delta-connected load
5. Three-phase unbalanced delta-connected load
6. Three-phase unbalanced four-wire star-connected load
7. Three-phase unbalanced three-wire star-connected load

1.5.1 Three-Phase Balanced Star-Connected Source [AU April/May, 2015]

The circuit diagram for a three-phase balanced star-

connected source with phase sequence RYB is shown in

Figure 1.5.

In a balanced system, all the magnitudes of phase voltages,

line voltages, phase currents and line currents are equal,

which can be represented as:

ph

| | | | | | | | ; | | | | | | | | RN YN BN RY YB BR L

V = V = V = V V = V = V = V (1.5)

ph

| | | | | | | | ; | | | | | | | | R Y B L RY YB BR

I = I = I = I I = I = I = I (1.6)

Relationship Among Line and Phase Quantities

Current Relationship

Appling Kirchhoff’s current law at nodes R, Y and B

shown in Figure 1.5, we get:

; ; RY R YB Y BR B

I = I I = I I = I (1.7)

From Eqns. (1.6) and (1.7), we can conclude that, in a balanced star-connected three-phase source, phase

current is equal to the line current, as given by

ph L

I = I (1.8)

Voltage Relationship

It is known that, RY RN YN

V = V - V

R

B

N

Y

IR

IR

IB

VBR

VYB

I Y

I B

V RY

VRN

VYN

VBN

Figure 1.5 Circuit Diagram for a Three-phase

Balanced Star-connected Source

AC Circuits and Power Systems 7

Using the parallelogram law of addition and the vector diagram shown in Figure 1.6, we get:

2 2

| | | | | | 2 | || | cos 60 RY RN YN RN YN

V = V + V + V V ∞

Using Eqn. (1.5) in the above equation and solving, we get:

ph

| | 3 | | RY

V = V (1.9)

Similarly, we get:

ph ph

| | 3 | | and | | 3 | | YB BR

V = V V = V (1.10)

Therefore, using Eqns. (1.5), (1.9) and (1.10), we get the relation between the line and phase voltages, which is

ph

| | 3 | | L

V = V (1.11)

Hence, it can be concluded that in a star-connected balanced three-phase source, the line voltage is 3

times the phase voltage or that the phase voltage is

1

3

times the line voltage. It is to be noted that the angle

between the phase voltage and the line voltage is 30°.

Vector Diagram

The vector diagram for a three-phase balanced star-connected

source, by considering the phase voltage as reference, is shown

in Figure 1.6.

Power Relationship

The real power produced per phase in the system shown in Figure

1.5 is ph ph ph

P = | V || I | cosf.

Therefore, the total real power produced in the system is given

by

ph ph

P = 3 | V || I | cosf (1.12)

Using Eqns. (1.8) and (1.11), we get

| |

3 | | cos 3 | || | cos (W)

3

L

L L L

V

P = I f = V I f (1.13)

Similarly, the total reactive power, Q, and total apparent power,

S, produced in the system are given by:

3 | || | sin (VAR) L L

Q = V I f (1.14)

3 | || | (VA) L L

S = V I (1.15)

1.5.2 Three-Phase Balanced Delta-Connected Source [AU April/May, 2015]

The circuit diagram for a three-phase balanced delta-connected source with phase sequence RYB is shown

in Figure 1.7.

V BN

V BN

–V YN

V RY

–VRN V RN

VYN –VBN

V YB

120°

30°

120°

120°

Figure 1.6 Vector Diagram for a

Three-phase Balanced Star-

connected Source

AC Circuits and Power Systems 9

Vector Diagram

The vector diagram for a balanced delta-connected source, by

considering the phase currents as reference vector, is shown in

Figure 1.8.

Power Relationship

The real power produced per phase in the system shown in Figure

1.6 is ph ph ph

P = | V || I | cosf.

Therefore, the total real power produced in the system is given by

ph ph

P = 3 | V || I | cosf (1.21)

Using Eqns. (1.18) and (1.20), we get

| |

3 | | cos 3 | || | cos (W)

3

L

L L L

I

P = V f = V I f (1.22)

Similarly, the total reactive power, Q, and total apparent power, S,

produced in the system are given by:

3 | || | sin (VAR) L L

Q = V I f (1.23)

3 | || | (VA) L L

S = V I

(1.24)

1.5.3 Three-Phase Balanced Star-Connected Load [AU April/May, 2015]

The circuit diagram for a three-phase balanced star-connected load with phase sequence RYB is shown in

Figure 1.9.

I L 1

V RY

VBR

I L 2

IL 3

V YB

Y

V IY YN

Z

Z

Y

=^

ph

Z (^) B = Zph

V BN

IB

B

Z Z R

= ph

N

VRN

R

IR

Figure 1.9 Circuit Diagram for a Three-phase Balanced Star-connected Load

I B

IBR – IYB

• I RY

I RY

120°

120°

120°

30°

IY IYB – IBR IR

Figure 1.8 Phasor Diagram for a

Balanced Delta-connected

Source

10 Basic Electrical and Instrumentation Engineering

Relationship Among Phase Current, Phase Voltage and Load Impedance

Let Z R

, Z Y

and Z B

be the load impedances in R, Y and B phases respectively. But in a balanced load condi-

tion, all the load impedances are equal to the load impedance per phase, Z ph

, represented as:

Z R

= Z Y

= Z B

= Z ph

(1.25)

The current, voltage and power relationship between the line and phase quantities, explained in

Section 1.4.1, is applicable to the balanced three-phase star-connected load, i.e.,

and

ph ph

; | | 3 | | ; 3 | || | cos ; 3 | || | sin

3 | || |

L L L L L L

L L

I I V V P V I Q V I

S V I

= = = f = f

= (1.26)

The relation between phase current, phase voltage and load impedance per phase is given by:

ph

ph

ph

V

I

Z

=

Load Impedance

If the load is lagging, leading and unity power factor in nature, then the load impedance is given by

Z ph

= R ph

• jX ph

, Z ph

= R ph

• jX ph

and Z ph

= R ph

respectively.

Power Factor

The power factor of the given three-phase star-connected balanced load is cos f.

Phasor Diagram

The phasor diagram for a three-phase balanced star-connected load with lagging and leading power factor

load is shown in Figures 1.10 (a) and (b) respectively.

V BN

V BN

• VRN

IB

f

• V YN

f

120°

120°

120°

f

V RY

30°

V RN

• VBN

V YN

V YB

I Y

I R

(a)

V BR

V BN

• V RN

I B

• VYN

V RN

I R

f

f

f

120° 120°

120°

V YN

• VBN

I Y

V YB

V RY

30°

(b)

Figure 1.10 Phasor Diagram for a Three-phase Balanced Star-connected Load with (a) Lagging and (b) Lead-

ing Power Factor