List of Symbols/Abbrevations Xii
Content
Preface...... x
Acknowledgement...... xi
List of Symbols/Abbrevations...... xii
Chapter 1 : Introduction...... 1.1
1.1Basic Phenomena...... 1.1
1.2Ideal Elements...... 1.1
1.3Electric Circuit...... 1.1
1.4Units...... 1.2
1.5Definition of Various Terms...... 1.3
1.6Symbols used for Average, Rms and Maximum
Values...... 1.5
1.7Steady State and Transient Analysis...... 1.6
1.8Assumptions in Circuit Theory...... 1.6
Chapter 2: Basic Concepts of circuits...... 2.1
2.1Basic Elements of Circuits...... 2.1
2.2Nodes, Branches and Closed path...... 2.2
2.3Series, Parallel, Star and Delta Connections...... 2.4
2.3.1Series Connections...... 2.4
2.3.2Parallel Connections...... 2.5
2.3.3Delta Connections...... 2.7
2.4Open Circuit and Short Circuit...... 2.8
2.5Sign Conventions...... 2.9
2.6Ohm’s and Kirchoff’s Laws...... 2.10
2.6.1Ohm’s Law...... 2.10
2.6.2Kirchoff’s Current Law(KCL)...... 2.10
2.6.3Kirchoff’s Voltage Law(KVL)...... 2.11
2.7Voltage and Current Source...... 2.11
2.7.1 Ideal and Practical Source...... 2.11
2.7.2 Source Transformation...... 2.13
2.8Dependent Sources...... 2.13
2.9Power and Energy...... 2.14
2.10Resistance...... 2.15
2.10.1Resistance connected to DC source...... 2.15
2.10.2Current division in parallel connected
resistance...... 2.16
2.10.3Voltage division in parallel connected
resistance...... 2.16
2.11Network Topology...... 2.17
2.11.1Graph...... 2.17
2.11.2Tree, Link and Cotree...... 2.19
2.11.3Network Variables...... 2.21
2.11.4Solution of Network Variables...... 2.21
2.12Analysis of Series-Parallel Circuits...... 2.22
2.12.1 Single Loop Circuit...... 2.24
2.12.2 Single Node Pair Circuit...... 2.24
2.13Solved Problems...... 2.25
2.14Short Questions and Answers...... 2.31
2.15Exercises ...... 2.35
Chapter 3: Basic Concepts of AC circuits...... 3.1
3.1Introduction...... 3.1
3.2AC Voltage and Current Source...... 3.1
3.2.1 Source transformation...... 3.3
3.3Sinusoidal voltage...... 3.3
3.3.1Average value...... 3.5
3.3.2RMS value...... 3.6
3.3.3Form factor and Peak factor ……………………. 3.7
3.4Sinusoidal Current...... 3.7
3.5Inductance...... 3.8
3.5.1Voltage-current relation in an indutance...... 3.9
3.5.2Energy stored in an indutance………………...... 3.10
3.6Capacitance ...... 3.10
3.6.1Voltage-current relation in an capacitance...... 3.11
3.6.2Energy stored in an capacitance…………….. 3.12
3.7V-I Relation of R, L and C in Various Domains...... 3.12
3.8Sinusoidal V and I in Frequency Domain...... 3.15
3.8.1Phase and Phase Difference...... 3.15
3.8.2Phasor Representation of Sinusoidal Quantities.....3.17
3.8.3Phasor diagram of a circuit...... 3.18
3.9Power, Energy and Power Factor...... 3.20
3.10Resistance Connected to Sinusoidal Source...... 3.23
3.11Inductance Connected to Sinusoidal Source...... 3.25
3.12Capacitance Connected to Sinusoidal Source...... 3.28
3.13Impedance ...... 3.30
3.13.1Impedance Connected to Sinusoidal Source...... 3.31
3.14Conductance, Susceptance and Admittance...... 3.32
3.14.1Conductance...... 3.33
3.14.2Admittance...... 3.33
3.14.3Admittance Connected to Sinusoidal Source...... 3.34
3.15KVL, KCL and Ohm’s Law applied to AC Circuits...... 3.35
3.16Current and Voltage Division Rules for Impedance...... 3.36
3.16.1 Current Division in Paralllel Connected
Impedances...... 3.36
3.16.2 Voltage Division in Series Connected
Impedances...... 3.36
3.17Solved Problems...... 3.37
3.18Short Questions and Answers...... 3.60
3.19Exercises ...... 3.64
Chapter 4:Mesh analysis...... 4.1
4.1Introduction...... 4.1
4.2Mesh Analysis of Resistive Circuits Excited by
DC Sources...... 4.1
4.3Mesh Analysis of Reactive Circuits...... 4.20
4.4Mesh Analysis of Circuits Excited by Both Voltage
and Current Sources...... 4.26
4.5Mesh Analysis of Circuits Excited by Independent
and Dependent Sources...... 4.29
4.5.1Circuits with Dependent Voltage Source...... 4.29
4.5.2Circuits with Dependent Current Source...... 4.30
4.6Exercises...... 4.36
Chapter 5:Node analysis...... 5.1
5.1Introduction...... 5.1
5.2Node Analysis of Resistive Circuits Excited by
DC Sources...... 5.1
5.3Node Analysis of Reactive Circuits...... 5.14
5.4Node Analysis of Circuits Excited by both Voltage
and Current Sources...... 5.19
5.5Node Analysis of Circuits Excited by Independent
and Dependent Sources...... 5.28
5.5.1Circuits with Dependent Current Source...... 5.28
5.5.2Circuits with Dependent Voltage Source...... 5.29
5.6Exercises...... 5.34
Chapter 6:NETWORK REDUCTION...... 6.1
6.1Introduction...... 6.1
6.2Resistances in Series and Parallel ...... 6.1
6.2.1Equivalent of Series Connected Resistances...... 6.1
6.2.2Voltage Division in Series Connected
Resistances...... 6.2
6.2.3Equivalent of Parallel Connected Resistances...... 6.3
6.2.4Voltage Division in Parallel Connected
Resistances...... 6.4
6.3Resistances in Star and Delta...... 6.5
6.3.1Delta to Star Transformation...... 6.6
6.3.2Star to Delta Transformation...... 6.9
6.4Source Transformation...... 6.13
6.5Voltage Sources in Series and Parallel ...... 6.14
6.5.1 Series Connection of Voltage Sources...... 6.14
6.5.2Parallel Connection of Voltage Sources...... 6.15
6.6Current Sources in Series and Parallel ...... 6.17
6.6.1 Series Connection of Current Sources...... 6.17
6.6.2Parallel Connection of Current Sources...... 6.18
6.7Inductances in Series and Parallel ...... 6.19
6.7.1Equivalent of Series Connected Inductances...... 6.19
6.7.2Equivalent of Parallel Connected Inductances...... 6.21
6.8Capacitances in Series and Parallel ...... 6.22
6.8.1Equivalent of Series Connected Capacitances...... 6.22
6.8.2Equivalent of Parallel Connected Capacitances...... 6.24
6.9Impedances in Series and Parallel ...... 6.25
6.9.1Equivalent of Series Connected Impedances...... 6.25
6.9.2Voltage Division in Series Connected
Impedances...... 6.26
6.9.3Equivalent of Parallel Connected Impedances...... 6.27
6.9.4Current Division in Parallel Connected
Impedances...... 6.28
6.9.5Reactances in Series and Parallel...... 6.29
6.10Impedances in Star and Delta...... 6.29
6.10.1Delta to Star Transformation...... 6.30
6.10.2Star to Delta Transformation...... 6.30
6.11Conductances in Series and Parallel ...... 6.31
6.11.1Equivalent of Series Connected Conductances...... 6.31
6.11.2Equivalent of Parallel Connected Conductances.....6.32
6.12Admittances in Series and Parallel ...... 6.33
6.12.1Equivalent of Series Connected Admittances...... 6.33
6.12.2Equivalent of Parallel Connected Admittances...... 6.35
6.13Solved Problems...... 6.36
6.14Short Questions and Answers...... 6.44
6.15Exercises ...... 6.49
Chapter 7 :Theorems in circuit Analysis...... 7.1
7.1Superposition Theorem...... 7.1
7.2Thevenin’s and Norton’s Theorems...... 7.20
7.3Maximum Power Transfer Theorem...... 7.48
7.4Reciprocity Theorem...... 7.71
7.5Short Questions and Answers...... 7.82
7.6Exercises...... 7.87
Chapter 8 :Series and parallel resonance...... 8.1
8.1Series Resonance...... 8.1
8.1.1Quality factor of series RLC circuit ...... 8.3
8.1.2Bandwidth of series RLC circuit ...... 8.5
8.1.3Selectivity of series RLC circuit ...... 8.9
8.1.4Voltage across L & C at resonance in series
RLC circuit ...... 8.10
8.1.5Solved problems in series resssonance...... 8.11
8.2Parallel Resonance...... 8.15
8.2.1Resonant frequency of parallel RLC circuit ...... 8.16
8.2.2Characteristics of parallel RLC circuit ...... 8.21
8.2.3Quality factor of parallel RLC circuit ...... 8.23
8.2.4Bandwidth of parallel RLC circuit ...... 8.25
8.2.5Current through L & C at resonance in parallel
RLC circuit ...... 8.31
8.2.6Solved problems in parallel resonance...... 8.32
8.3Short Questions And Answers...... 8.39
8.4Exercises...... 8.44
Chapter 9 :Coupled circuits...... 9.1
9.1Introduction...... 9.1
9.2Self Inductance and Mutual Inductance...... 9.1
9.2.1Self Inductance...... 9.1
9.2.2Mutual Inductance...... 9.2
9.2.3Coefficient of Coupling...... 9.4
9.3Analysis of Coupled Coils...... 9.5
9.3.1Dot convention for coupled coils...... 9.6
9.3.2Expression for self and mutual induced
emf in various domains...... 9.9
9.3.3Writing mesh equations for coupled coils...... 9.10
9.3.4Electrical equivalent of magnetic
coupling...... 9.11
9.3.5Representation of mutual induced emf
by dependent voltage sources...... 9.14
9.3.6Writing mesh equations for circuits with
electrical connection & magnetic coupling...... 9.16
9.4Series and Parallel Connections of Coupled Coils...... 9.18
9.5Tuned Coupled Circuits...... 9.24
9.5.1Single tuned coupled circuits...... 9.24
9.5.2Double tuned coupled circuits...... 9.28
9.6Solved Problems...... 9.32
9.7Short Questions and Answers...... 9.57
9.8Exercises...... 9.60
Chapter 10 : Transients...... 10.1
10.1Introduction...... 10.1
10.2Transient Response...... 10.1
10.2.1First and Second Order Circuits...... 10.2
10.3Transient Analysis using Laplace Transform...... 10.3
10.3.1Some Standard Voltage Signals...... 10.3
10.3.2s-Domain Representation of R,L,C
Parameters...... 10.5
10.3.3Solving Initial and Final Conditions
Using Laplace Transform...... 10.9
10.4Transient in RL Circuit ...... 10.10
10.4.1Source Free Reponse of RL Circuit...... 10.10
10.4.2Step Response of RL Circuit ...... 10.11
10.4.3RL Transient with Initial Current Io...... 10.16
10.5Transient in RC Circuit ...... 10.19
10.5.1Source Free Reponse of RC Circuit...... 10.19
10.5.2Step Response of RC Circuit ...... 10.21
10.5.3RC Transient with Initial Voltage Vo...... 10.25
10.6Transient in RLC Circuit ...... 10.29
10.6.1Source Free Response of RLC Circuit...... 10.29
10.6.2Step Response of RLC Circuit...... 10.30
10.6.3s-Domain current & voltage equation of
RLC circuit...... 10.36
10.6.4Initial conditions in RLC Circuit...... 10.36
10.6.5Final conditions in RLC Circuit...... 10.37
10.7Transient in Circuits Excited by AC Source...... 10.39
10.7.1RL circuit excited by AC source...... 10.39
10.7.2RC circuit excited by AC source...... 10.41
10.7.3RLC circuit excited by AC source...... 10.43
10.8Solved Problems in RL Transient...... 10.45
10.9Solved Problems in RC Transient...... 10.61
10.10Solved Problems in RLC Transient...... 10.78
10.11Short Questions and Answers...... 10.90
10.12Exercises...... 10.92
Chapter 11 : Three phase circuits...... 11.1
11.1Introduction...... 11.1
11.2Three Phase Sources...... 11.1
11.3Representation of Three Phase Emfs...... 11.2
11.4Three Phase Star Connected Source...... 11.4
11.4.1Star Connected Source - Three Wire
System...... 11.4
11.4.2Star Connected Source - Four Wire
System...... 11.7
11.5Three Phase Delta Connected Source...... 11.8
11.6Three Phase Loads...... 11.12
11.6.1Choice of Reference Phasor in Analysis
of Three Phase Circuits...... 11.12
11.7Analysis of Balanced Loads...... 11.13
11.7.1Four Wire Star Connected Balanced Load...... 11.13
11.7.2Three Wire Star Connected Balanced Load...... 11.15
11.7.3Delta Connected Balanced Load...... 11.16
11.7.4Power consumed by three equal impedance
in star and delta...... 11.17
11.8Analysis of Unbalanced Loads...... 11.18
11.8.1Four Wire Star Connected Unbalanced Load...... 11.18
11.8.2Three Wire Star Connected Unbalanced Load...... 11.20
11.8.3Neutral shift in Star Connected Load...... 11.21
11.8.4Delta Connected Unbalanced Load...... 11.22
11.9Two Wattmeter Method of Power Measurement...... 11.23
11.9.1Power Measurement in Balanced Load...... 11.24
11.9.2Relation between Power Factor and Wattmeter
Reading...... 11.26
11.10Solved Problems...... 11.28
11.11Short Questions and Answers...... 11.63
11.12Exercises...... 11.65
Appendix 1 Laplace Transform...... A.1
Appendix 2 Calculations Using Complex Mode Of Calculator.....A.5
Index ...... I.1