Basic Electrical Engineering_A. Mittle and v. N. Mittle

7/24/2019 Basic Electrical Engineering_A. Mittle and v. N. Mittle

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Scilab Textbook Companion for

Basic Electrical Engineering

by A. Mittle and V. N. Mittle1

Created byIdris Manaqibwala

Electrical TechnologyCivil Engineering

VNIT NagpurCollege Teacher

Prof. V. B. BorghateCross-Checked byBhavani Jalkrish

August 28, 2014

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the Textbook Companion Projectsection at the website http://scilab.in


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Book Description

Title: Basic Electrical Engineering

Author: A. Mittle and V. N. Mittle

Publisher: Tata McGraw Hill

Edition: 2

Year: 2005

ISBN: 9780070593572

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Scilab numbering policy used in this document and the relation to theabove book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

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Contents

List of Scilab Codes 5

1 DC Circuits 13

2 Electrostatics 22

3 Electromagnetism 26

4 Magnetic Circuit 29

5 Electromagnetic Induction 41

6 Fundamentals of Alternating Current 52

7 AC Series Circuit 68

8 AC Parallel Circuit 80

9 Three Phase Systems 97

10 Measuring Instruments 107

13 Temperature Rise and Ventilation in Electrical Machines 111

14 Single Phase Transformers 113

15 Three Phase Transformers 127

16 Electromechanical Energy Conversion 130

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17 Fundamentals of DC Machines 132

18 DC Generators 140

19 DC Motors 150

20 Testing of DC Machine 160

21 Three Phase Alternators 167

22 Synchronous Motors 176

23 Three Phase Induction Motor 185

24 Single Phase Induction Motor 204

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List of Scilab Codes

Exa 1.1 Example on Ohms Law . . . . . . . . . . . . . . . . . 13Exa 1.2 Example on Ohms Law . . . . . . . . . . . . . . . . . 13Exa 1.3 Example on Ohms Law . . . . . . . . . . . . . . . . . 14Exa 1.4 Example on Kirchhoffs Law . . . . . . . . . . . . . . . 14Exa 1.5 Example on Kirchhoffs Law . . . . . . . . . . . . . . . 15Exa 1.6 Example on Kirchhoffs Law . . . . . . . . . . . . . . . 15Exa 1.7 Example on Kirchhoffs Law . . . . . . . . . . . . . . . 16Exa 1.8 Example on Superposition Theorem . . . . . . . . . . 16Exa 1.9 Example on Superposition Theorem . . . . . . . . . . 17Exa 1.10 Example on Thevenin Theorem . . . . . . . . . . . . . 17Exa 1.11 Example on Norton Theorem . . . . . . . . . . . . . . 18Exa 1.12 Example on Nodal Analysis . . . . . . . . . . . . . . . 18Exa 1.13 Example on Maximum Power Transfer Theorem . . . 19

Exa 1.14 Example on Delta to Star and Star to Delta Transfor-mation . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Exa 1.16 Example on Delta to Star and Star to Delta Transfor-mation . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Exa 2.1 Example on Coulombs Law . . . . . . . . . . . . . . . 22Exa 2.2 Example on Electric Intensity . . . . . . . . . . . . . 22Exa 2.3 Example on Electric Potential. . . . . . . . . . . . . . 23Exa 2.4 Example on charging and discharging of capacitor . . 24Exa 2.5 Example on charging and discharging of capacitor . . 24Exa 2.6 Example on charging and discharging of capacitor . . 25Exa 3.2 Example on Field Strength and Flux Density . . . . . 26

Exa 3.3 Example on Field Strength and Flux Density . . . . . 26Exa 3.4 Example of Force on on Current Carrying Conductor . 27Exa 3.5 Example of Force on on Current Carrying Conductor . 27Exa 4.1 Example on Series Magnetic Circuit . . . . . . . . . . 29

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Exa 4.2 Example on Series Magnetic Circuit . . . . . . . . . . 30

Exa 4.3 Example on Series Magnetic Circuit . . . . . . . . . . 30Exa 4.4 Example on Series Magnetic Circuit . . . . . . . . . . 31Exa 4.5 Example on Series Magnetic Circuit . . . . . . . . . . 32Exa 4.6 Example on Series Magnetic Circuit . . . . . . . . . . 33Exa 4.7 Example on Series Magnetic Circuit . . . . . . . . . . 33Exa 4.8 Example on Series Magnetic Circuit . . . . . . . . . . 34Exa 4.9 Example on Series Magnetic Circuit . . . . . . . . . . 35Exa 4.10 Example on Series Magnetic Circuit . . . . . . . . . . 36Exa 4.11 Example on Series Magnetic Circuit . . . . . . . . . . 37Exa 4.12 Example on Series Parallel Magnetic Circuit. . . . . . 38Exa 4.13 Example on Series Parallel Magnetic Circuit. . . . . . 39

Exa 5.1 Example on Induced EMF. . . . . . . . . . . . . . . . 41Exa 5.2 Example on Induced EMF. . . . . . . . . . . . . . . . 41Exa 5.3 Example on Induced EMF. . . . . . . . . . . . . . . . 42Exa 5.4 Example on Induced EMF. . . . . . . . . . . . . . . . 42Exa 5.5 Example on Induced EMF. . . . . . . . . . . . . . . . 43Exa 5.6 Example on Induced EMF. . . . . . . . . . . . . . . . 44Exa 5.7 Example on Induced EMF. . . . . . . . . . . . . . . . 44Exa 5.8 Example on Induced EMF. . . . . . . . . . . . . . . . 45Exa 5.9 Example on Induced EMF. . . . . . . . . . . . . . . . 45Exa 5.10 Example on Induced EMF. . . . . . . . . . . . . . . . 46

Exa 5.11 Example on Induced EMF. . . . . . . . . . . . . . . . 46Exa 5.12 Example on Growth and Decay of Current in InductiveCircuits . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Exa 5.13 Example on Growth and Decay of Current in InductiveCircuits . . . . . . . . . . . . . . . . . . . . . . . . . . 47



Exa 5.16 Example on Energy Stored in Magnetic Field . . . . . 49Exa 5.17 Example on Energy Stored in Magnetic Field . . . . . 49

Exa 5.18 Example on Energy Stored in Magnetic Field . . . . . 50Exa 6.1 Example on AC Wave Shapes . . . . . . . . . . . . . . 52Exa 6.2 Example on AC Wave Shapes . . . . . . . . . . . . . . 54Exa 6.3 Example on AC Wave Shapes . . . . . . . . . . . . . . 54Exa 6.4 Example on AC Wave Shapes . . . . . . . . . . . . . . 55

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Exa 6.5 Example on AC Wave Shapes . . . . . . . . . . . . . . 56

Exa 6.6 Example on AC Wave Shapes . . . . . . . . . . . . . . 56Exa 6.7 Example on AC Wave Shapes . . . . . . . . . . . . . . 60Exa 6.8 Example on AC Wave Shapes . . . . . . . . . . . . . . 61Exa 6.9 Example on AC Wave Shapes . . . . . . . . . . . . . . 64Exa 6.10 Example on AC Wave Shapes . . . . . . . . . . . . . . 64Exa 6.11 Example on Phase Difference . . . . . . . . . . . . . . 66Exa 6.13 Example on Simple AC Circuits . . . . . . . . . . . . 66Exa 6.14 Example on Simple AC Circuits . . . . . . . . . . . . 67Exa 7.1 Example on AC Series Circuit . . . . . . . . . . . . . 68Exa 7.2 Example on AC Series Circuit . . . . . . . . . . . . . 68Exa 7.3 Example on AC Series Circuit . . . . . . . . . . . . . 69

Exa 7.4 Example on AC Series Circuit . . . . . . . . . . . . . 70Exa 7.5 Example on AC Series Circuit . . . . . . . . . . . . . 71Exa 7.6 Example on AC Series Circuit . . . . . . . . . . . . . 71Exa 7.7 Example on AC Series Circuit . . . . . . . . . . . . . 73Exa 7.8 Example on AC Series Circuit . . . . . . . . . . . . . 73Exa 7.9 Example on AC Series Circuit . . . . . . . . . . . . . 74Exa 7.10 Example on AC Series Circuit . . . . . . . . . . . . . 75Exa 7.11 Example on AC Series Circuit . . . . . . . . . . . . . 76Exa 7.12 Example on AC Series Circuit . . . . . . . . . . . . . 76Exa 7.13 Example on AC Series Circuit . . . . . . . . . . . . . 77

Exa 7.14 Example on AC Series Circuit . . . . . . . . . . . . . 78Exa 7.15 Example on AC Series Circuit . . . . . . . . . . . . . 79Exa 8.1 Example on Phasor Method. . . . . . . . . . . . . . . 80Exa 8.2 Example on Phasor Method. . . . . . . . . . . . . . . 81Exa 8.3 Example on Phasor Method. . . . . . . . . . . . . . . 83Exa 8.4 Example on Phasor Method. . . . . . . . . . . . . . . 84Exa 8.5 Example on Admittance Method . . . . . . . . . . . . 86Exa 8.6 Example on Symbolic Method . . . . . . . . . . . . . 87Exa 8.7 Example on Symbolic Method . . . . . . . . . . . . . 88Exa 8.8 Example on Symbolic Method . . . . . . . . . . . . . 89Exa 8.9 Example on Symbolic Method . . . . . . . . . . . . . 90

Exa 8.10 Example on Series Parallel Circuit . . . . . . . . . . . 91Exa 8.11 Example on AC Network Theorems . . . . . . . . . . 92Exa 8.12 Example on Resonance in Parallel Circuits. . . . . . . 93Exa 8.13 Example on Resonance in Parallel Circuits. . . . . . . 95Exa 9.1 Example on Three Phase Circuits . . . . . . . . . . . 97

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Exa 9.2 Example on Three Phase Circuits . . . . . . . . . . . 98

Exa 9.3 Example on Three Phase Circuits . . . . . . . . . . . 99Exa 9.4 Example on Three Phase Circuits . . . . . . . . . . . 100Exa 9.5 Example on Three Phase Circuits . . . . . . . . . . . 101Exa 9.6 Example on Three Phase Circuits . . . . . . . . . . . 101Exa 9.7 Example on Three Phase Circuits . . . . . . . . . . . 102Exa 9.8 Example on Power Measurement . . . . . . . . . . . . 103Exa 9.9 Example on Power Measurement . . . . . . . . . . . . 103Exa 9.10 Example on Power Measurement . . . . . . . . . . . . 104Exa 9.11 Example on Power Measurement . . . . . . . . . . . . 105Exa 9.12 Example on Power Measurement . . . . . . . . . . . . 105Exa 10.1 Example on Moving Coil Instruments . . . . . . . . . 107

Exa 10.2 Example on Moving Coil Instruments . . . . . . . . . 107Exa 10.3 Example on Moving Coil Instruments . . . . . . . . . 108Exa 10.4 Example on Moving Coil Instruments . . . . . . . . . 109Exa 10.5 Example on Moving Coil Instruments . . . . . . . . . 109Exa 10.6 Example on Moving Coil Instruments . . . . . . . . . 110Exa 13.1 Example on Heating and Cooling of Electrical Machines 111Exa 13.2 Example on Heating and Cooling of Electrical Machines 112Exa 14.1 Example on EMF Equation . . . . . . . . . . . . . . . 113Exa 14.2 Example on EMF Equation . . . . . . . . . . . . . . . 113Exa 14.3 Example on Equivalent Circuit . . . . . . . . . . . . . 114

Exa 14.4 Example on Equivalent Circuit . . . . . . . . . . . . . 115Exa 14.5 Example on Regulation and Efficiency . . . . . . . . . 116Exa 14.6 Example on Regulation and Efficiency . . . . . . . . . 116Exa 14.7 Example on Regulation and Efiiciency . . . . . . . . . 117Exa 14.8 Example on Regulation and Efficiency . . . . . . . . . 118Exa 14.9 Example on Regulation and Efficiency . . . . . . . . . 119Exa 14.10 Example on Regulation and Efficiency . . . . . . . . . 120Exa 14.11 Example on Regulation and Efficiency . . . . . . . . . 120Exa 14.12 Example on Regulation and Efficiency . . . . . . . . . 121Exa 14.13 Example on Regulation and Efficiency . . . . . . . . . 121Exa 14.14 Example on Testing of Transformer. . . . . . . . . . . 122

Exa 14.15 Example on Testing of Transformer. . . . . . . . . . . 123Exa 14.16 Example on Testing of Transformer. . . . . . . . . . . 124Exa 14.17 Example on Parallel Operation . . . . . . . . . . . . . 124Exa 14.18 Example on Parallel Operation . . . . . . . . . . . . . 125Exa 15.1 Example on three phase transformer . . . . . . . . . . 127

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Exa 15.2 Example on three phase transformer . . . . . . . . . . 128

Exa 15.3 Example on three phase transformer . . . . . . . . . . 128Exa 15.4 Example on three phase transformer . . . . . . . . . . 129Exa 16.2 Example on Electromechanical Energy Conversion De-

vices. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Exa 16.3 Example on Electromechanical Energy Conversion De-

vices. . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Exa 17.1 Example on DC Winding . . . . . . . . . . . . . . . . 132Exa 17.2 Example on DC Winding . . . . . . . . . . . . . . . . 132Exa 17.3 Example on EMF Equation . . . . . . . . . . . . . . . 133Exa 17.4 Example on EMF Equation . . . . . . . . . . . . . . . 133Exa 17.5 Example on EMF Equation . . . . . . . . . . . . . . . 134

Exa 17.6 Example on EMF Equation . . . . . . . . . . . . . . . 134Exa 17.7 Example on Types of DC Machines. . . . . . . . . . . 135Exa 17.8 Example on Types of DC Machines. . . . . . . . . . . 135Exa 17.9 Example on Types of DC Machines. . . . . . . . . . . 136Exa 17.10 Example on Types of DC Machines. . . . . . . . . . . 136Exa 17.11 Example on Types of DC Machines. . . . . . . . . . . 137Exa 17.12 Example on Types of DC Machines. . . . . . . . . . . 137Exa 17.13 Example on Types of DC Machines. . . . . . . . . . . 138Exa 17.14 Example on Types of DC Machines. . . . . . . . . . . 139Exa 18.1 Example on Magnetization Characteristics. . . . . . . 140

Exa 18.2 Example on Magnetization Characteristics. . . . . . . 142Exa 18.3 Example on Magnetization Characteristics. . . . . . . 143Exa 18.4 Example on Magnetization Characteristics. . . . . . . 145Exa 18.5 Example on Parallel Operation . . . . . . . . . . . . . 147Exa 18.6 Example on Parallel Operation . . . . . . . . . . . . . 148Exa 18.7 Example on Parallel Operation . . . . . . . . . . . . . 149Exa 19.1 Example on Torque and Speed . . . . . . . . . . . . . 150Exa 19.2 Example on Torque and Speed . . . . . . . . . . . . . 151Exa 19.3 Example on Torque and Speed . . . . . . . . . . . . . 151Exa 19.4 Example on Torque and Speed . . . . . . . . . . . . . 152Exa 19.5 Example on Torque and Speed . . . . . . . . . . . . . 153

Exa 19.6 Example on Torque and Speed . . . . . . . . . . . . . 154Exa 19.7 Example on Torque and Speed . . . . . . . . . . . . . 155Exa 19.8 Example on Speed Control of DC Motors . . . . . . . 155Exa 19.9 Example on Speed Control of DC Motors . . . . . . . 156Exa 19.10 Example on Speed Control of DC Motors . . . . . . . 157

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Exa 19.11 Example on Speed Control of DC Motors . . . . . . . 157

Exa 19.12 Example on Speed Control of DC Motors . . . . . . . 158Exa 19.13 Example on Speed Control of DC Motors . . . . . . . 159Exa 20.1 Example on losses in DC Machine . . . . . . . . . . . 160Exa 20.2 Example on losses in DC Machine . . . . . . . . . . . 160Exa 20.3 Example on losses in DC Machine . . . . . . . . . . . 161Exa 20.4 Example on losses in DC Machine . . . . . . . . . . . 162Exa 20.5 Example on losses in DC Machine . . . . . . . . . . . 163Exa 20.6 Example on losses in DC Machine . . . . . . . . . . . 164Exa 20.7 Example on losses in DC Machine . . . . . . . . . . . 165Exa 20.8 Example on losses in DC Machine . . . . . . . . . . . 166Exa 21.1 Example on emf Equation . . . . . . . . . . . . . . . . 167

Exa 21.2 Example on emf Equation . . . . . . . . . . . . . . . . 168Exa 21.3 Example on emf Equation . . . . . . . . . . . . . . . . 168Exa 21.4 Example on emf Equation . . . . . . . . . . . . . . . . 169Exa 21.5 Example on emf Equation . . . . . . . . . . . . . . . . 170Exa 21.6 Example on Regulation . . . . . . . . . . . . . . . . . 171Exa 21.7 Example on emf Equation . . . . . . . . . . . . . . . . 172Exa 21.8 Example on Regulation . . . . . . . . . . . . . . . . . 173Exa 21.9 Example on Regulation . . . . . . . . . . . . . . . . . 174Exa 21.10 Example on Regulation . . . . . . . . . . . . . . . . . 174Exa 22.1 Example on Phasor Diagram and Power angle Charac-

teristics . . . . . . . . . . . . . . . . . . . . . . . . . . 176Exa 22.2 Example on Phasor Diagram and Power angle Charac-teristics . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Exa 22.3 Example on Phasor Diagram and Power angle Charac-teristics . . . . . . . . . . . . . . . . . . . . . . . . . . 178





Exa 22.8 Example on Variation of Excitation . . . . . . . . . . 183Exa 23.1 Example on Slip and Rotor Frequency . . . . . . . . . 185Exa 23.2 Example on Slip and Rotor Frequency . . . . . . . . . 185

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Exa 23.3 Example on Slip and Rotor Frequency . . . . . . . . . 187

Exa 23.4 Example on Equivalent Circuit . . . . . . . . . . . . . 188Exa 23.5 Example on Equivalent Circuit . . . . . . . . . . . . . 188Exa 23.6 Example on Equivalent Circuit . . . . . . . . . . . . . 189Exa 23.7 Example on Equivalent Circuit . . . . . . . . . . . . . 191Exa 23.8 Example on Losses in Induction Motor . . . . . . . . . 193Exa 23.9 Example on Losses in Induction Motor . . . . . . . . . 193Exa 23.10 Example on Losses in Induction Motor . . . . . . . . . 194Exa 23.11 Example on Losses in Induction Motor . . . . . . . . . 194Exa 23.12 Example on Losses in Induction Motor . . . . . . . . . 195Exa 23.13 Example on Torque . . . . . . . . . . . . . . . . . . . 196Exa 23.14 Example on Torque . . . . . . . . . . . . . . . . . . . 197

Exa 23.15 Example on Torque . . . . . . . . . . . . . . . . . . . 198Exa 23.16 Example on Torque . . . . . . . . . . . . . . . . . . . 199Exa 23.17 No load and Block Rotor Test. . . . . . . . . . . . . . 200Exa 23.18 Example on Circle Diagram . . . . . . . . . . . . . . . 201Exa 23.19 Example on starting . . . . . . . . . . . . . . . . . . . 202Exa 23.20 Example on starting . . . . . . . . . . . . . . . . . . . 202Exa 24.1 Example on Equivalent Circuit . . . . . . . . . . . . . 204Exa 24.2 Example on Equivalent Circuit . . . . . . . . . . . . . 205Exa 24.3 Example on Equivalent Circuit . . . . . . . . . . . . . 206Exa 24.4 Example on No Load and Block Rotor Test . . . . . . 208

Exa 24.5 Example on No Load and Block Rotor Test . . . . . . 209

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List of Figures

4.1 Example on Series Magnetic Circuit. . . . . . . . . . . . . . 344.2 Example on Series Magnetic Circuit. . . . . . . . . . . . . . 37

6.1 Example on AC Wave Shapes . . . . . . . . . . . . . . . . . 536.2 Example on AC Wave Shapes . . . . . . . . . . . . . . . . . 576.3 Example on AC Wave Shapes . . . . . . . . . . . . . . . . . 606.4 Example on AC Wave Shapes . . . . . . . . . . . . . . . . . 65

18.1 Example on Magnetization Characteristics . . . . . . . . . . 14118.2 Example on Magnetization Characteristics . . . . . . . . . . 14218.3 Example on Magnetization Characteristics . . . . . . . . . . 14418.4 Example on Magnetization Characteristics . . . . . . . . . . 146

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Chapter 1

DC Circuits

Scilab code Exa 1.1 Example on Ohms Law

1

2 / / By KCL , I 1 + I 2 = 2 . 253 I 1 = 1 0 / ( 2 + 8 )

4 I 2 = 2 . 2 5 - I 1

5 r = ( 1 0 - 5 * I 2 ) / I 2

6 mprintf ( r =%d ohm , c u r r e n t i n br anc h ABC=%d A and

c u r r e n t i n br anc h ADC=%f A , r , I1 , I2 )


1

2 // i 1 , i 2 , i 3 be t he c u r r e n t s i n t he b ra nc he s CD, EFand GH r e s p e c t i v e l y

3 // i 1+i2+i 3 =1.5

4 i 2 = ( 2 0 - 1 . 5 * 1 0 ) / 1 55 i 3 = ( 2 0 - 1 . 5 * 1 0 ) / 1 5

6 i 1 = 1 . 5 - i 2 - i 3

7 r = ( 2 0 - 1 . 5 * 1 0 ) / i 1

8 mprintf ( r=%f ohm , r )

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1

2 // p o i n t s A, E , F ,G a r e a t t he same p o t e n t i a l3 R a b = 2 0

4 R e b = 5 0

5 R 1 = R a b * R e b / ( R a b + R e b ) // e q u i v a l e n t r e s i s t a n c e o f Raband Reb

6 R b c = 2 57 R 2 = R 1 + R b c // e q u i v a l e n t r e s i s t a n c e o f R1 and Rbc8 R f c = 5 0

9 R 3 = R f c * R 2 / ( R f c + R 2 ) // e q u i v al e n t r e s i s t a n c e o f R2a nd R fc

10 R c d = 3 0

11 R 4 = R 3 + R c d // e q u i v a l e n t r e s i s t a n c e o f R3 and Rcd12 R = R 4 * 5 0 / ( 5 0 + R 4 ) // e q u i v a l e n t r e s i s t a n c e b et we en A

a n d D13 i = 2 0 0 / R //Ohm s Law14 mprintf ( C u r r en t dra wn by c i r c u i t =%f A , i )

Scilab code Exa 1.4 Example on Kirchhoffs Law

1

2 // r e f e r F i g . 1 . 10 i n t he t ex tb oo k3 // ap pl y i ng KCL, I1+ I2 = 20; I2+I3=304 // ap pl y i ng KVL5

// f o r mesh ABGHA, 0.1I2 + 20R1=1086 // f o r mesh BCFGB, 0. 3I2 +20R130R2=07 // f o r mesh CDEFC, 0. 2I2 +30R2=1148 a = [ - 0. 1 20 0 ;0 .3 2 0 - 30 ;0 .2 0 3 0]

9 b = [ 1 0 8 ; 0 ; 1 1 4 ]

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10 x = inv ( a ) * b

11 I 2 = x ( 1 , 1 )12 R 1 = x ( 2 , 1 )

13 R 2 = x ( 3 , 1 )

14 I 1 = 2 0 - I 2

15 I 3 = 3 0 + I 2

16 mprintf ( R1=%f ohm , R2=%f ohm , I1=%f A, I2=%f A, I3=%f A , R1 , R2 , I1 , I2 , I3 )


1

2 // r e f e r F i g . 1 . 1 1 i n t he t ex tb oo k3 // ap pl y i ng KVL ov e r l o op s ABEFA and BCDEB, I2 = 3. 5

I 1 ; 2 I1+ 7 I2=104 a = [ 3. 5 - 1; - 2 7 ]

5 b = [ 0 ; 1 0 ]

6 i = inv ( a ) * b

7 I 1 = i ( 1 , 1 )

8 I 2 = i ( 2 , 1 )

9 I = I 2 - I 110 mprintf ( C u r re nt t hr o ug h 8 ohm r e s i s t a n c e =%f A f ro m

E t o B , I )


1

2 // r e f e r F i g . 1 . 1 2 i n t he t ex tb oo k

3 // A ppl y i n g KVL4 // f o r mesh AHGBA, 23 i 1 + 2 0 i 2 + 3 i 4= 05 // f o r mesh GFCBG, 20i 143 i 2 + 2 0 i 3 + 3 i 4= 06 // f o r mesh FEDCF, 20i 243 i 3 + 3 i 4= 07 // f o r mesh ABCDJIA, 3i 1 +3 i 2 + 3 i 39 i4+50=0

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8 a = [-23 20 0 3;20 -43 20 3;0 20 -43 3;3 3 3 -9]

9 b = [ 0 ; 0 ; 0 ; - 5 0 ]10 i = inv ( a ) * b

11 i 1 = i ( 1 , 1 )

12 i 2 = i ( 2 , 1 )

13 i 3 = i ( 3 , 1 )

14 i 4 = i ( 4 , 1 )

15 V 1 = 3 * ( i 4 - i 1 )

16 V 2 = 3 * ( i 4 - i 2 )

17 V 3 = 3 * ( i 4 - i 3 )

18 mprintf ( V o l t a g e a c r o s s b r an c h AB=%f V , V o l t a g ea c r o s s b r a nc h BC=%f V, V o l t a g e a c r o s s b r a nc h CD=

%f V , V1 , V2 , V3 )


1

2 // r e f e r F i g . 1 . 1 3 i n t he t ex tb oo k3 / / by a p p l y i n g KVL4 // f o r mesh ABCDA, 7. 45 i 1 3. 25i 2 =10

5 // f o r mesh EFBAE , 8. 55 i 2 5.3i 3 3. 25i 1 =106 // f o r mesh HGBFEAH, 11 .3 i 3 5.3i 2 =807 a = [ 7 .4 5 - 3. 25 0 ; - 3. 25 8 .5 5 - 5. 3; 0 - 5. 3 1 1. 3]

8 b = [ 1 0 ; 1 0 ; 8 0 ]

9 i = inv ( a ) * b

10 i 1 = i ( 1 , 1 )

11 i 2 = i ( 2 , 1 )

12 i 3 = i ( 3 , 1 )

13 mprintf ( C ur re n t i n 6 ohm r e s i s t o r =%f A, c u r re n t i n3 ohm r e s i s t o r =%f A , i3 , i2 - i 1)

Scilab code Exa 1.8 Example on Superposition Theorem

16


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1

2 / / u s i n g S u p e r p o s i t i o n Theorem3 / / c o n s i d e r E1 a l o n e4 E 1 = 1 . 5

5 R 1 = ( 1 + 1 ) * 2 / ( 1 + 1 + 2 ) + 2 // t o t a l r e s i s t a n c e6 I 1 = E 1 / R 1 / / c u r r e n t s u p p l i e d7 i 1 = I 1 / 2 // c u r r e n t i n b ra nc h AB f ro m B t o A8 / / c o n s i d e r E2 a l o n e9 E 2 = 1 . 1

10 R 2 = ( 1 + 1 ) * 2 / ( 1 + 1 + 2 ) + 1 + 1 // t o t a l r e s i s t a n c e11 I 2 = E 2 / R 2 / / c u r r e n t s u p p l i e d12 i 2 = I 2 / 2 // c u r r e n t i n b ra nc h AB f ro m B t o A

13 mprintf ( C u r re nt t hr o ug h 2 ohm r e s i s t o r =%f A , i 1+ i2)

Scilab code Exa 1.9 Example on Superposition Theorem

1

2 // r e f e r F i g . 1 . 2 0 i n t he t ex tb oo k3 // ap pl y i ng KVL

4 / / f o r m es h BAEFB , 4I1 +2 I2 =1.55 // f o r mesh BACDB, 2I1 +4 I2 =1.16 a = [4 2 ;2 4]

7 b = [ 1 . 5 ; 1 . 1 ]

8 i = inv ( a ) * b

9 I 1 = i ( 1 , 1 )

10 I 2 = i ( 2 , 1 )

11 mprintf ( C u r re nt t hr o ug h 2 ohm r e s i s t o r =%f A f ro m Bt o A , I1 + I2 )

Scilab code Exa 1.10 Example on Thevenin Theorem

1

17


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2 // r e f e r F ig . 1 . 2 2 ( a ) i n t he t ex tb o ok

3 / / r e s i s t a n c e b et we en A and B i s rem oved4 / / I 1 be c u r r e n t i n b ra nc h CD5 // ap pl y i ng KCL6 //100 I 1 i s t he c u r r en t i n b r a nc h AF7 / / I 150 i s t he c u r r e nt i n br a nc h DE8 //70 I 1 i s t h e c u r r e n t i n br a n c h FE9 // ap pl y i ng KVL f o r mesh CDEFC , we ge t ,

10 I 1 = 5 6

11 V = . 1 * I 1 + . 1 5 * ( I 1 - 5 0 ) / / t h e v en i n s v o l t a g e12 r = ( . 1 + . 1 5 ) * ( . 1 + . 1 5 ) / ( . 2 5 + . 2 5 ) // t he v e ni n s

e q u i v a l e n t r e s i s t a n c e

13 I = V / ( r + . 0 5 )14 mprintf ( C u rr en t f l o w i n g i n t he b ra nc h AB o f 0 . 0 5

ohm r e s i s t a n c e i s %f A , I )

Scilab code Exa 1.11 Example on Norton Theorem

1

2 //by N or ton s T he or em

3 I = 2 * 1 0 // t o t a l c u r r e n t p ro du ce d by c u r r e nt s o u r ce4 r = 2 * 2 / ( 2 + 2 ) // r e s u l t a n t r e s i s t a n c e o f c u r r e n t s o u r c e5 I n = 2 0 * r / ( r + 1 ) / / n o r t on c u r r e n t6 R n = 1 + r // n or to n r e s i s t a n c e7 I = I n * R n / ( R n + 8 )

8 mprintf ( C u rr e n t t h r o ug h t he l oa d r e s i s t a n c e o f 8ohm=%f A f r om A t o B , I )

Scilab code Exa 1.12 Example on Nodal Analysis

1

2 // c i r c u i t ha s 4 nodes , v iz , A, B , C and D3 / / node D i s t ak en a s r e f e r e n c e node

18


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4 / / v o l t a g e s a t A , B a nd C be Va , Vb and Vc

r e s p e c t i v e l y5 // ap pl y i ng KCL6 / / a t node A, 7VaVbVc=257 / / a t n od e B, 4Va+19Vb10Vc=08 / / a t n od e C, 4Va10Vb+19Vc=409 a = [7 -1 -1; -4 19 - 10; - 4 -10 1 9]

10 b = [ 2 5 ; 0 ; - 4 0 ]

11 v = inv ( a ) * b

12 V a = v ( 1 , 1 )

13 V b = v ( 2 , 1 )

14 V c = v ( 3 , 1 )

15 I = ( V a - V c ) / 516 mprintf ( C u r r en t i n 5 ohm AC b r an c h=%f A f ro m A t o C

, I )17 // e r r o r i n t e xt bo o k a ns we r

Scilab code Exa 1.13 Example on Maximum Power Transfer Theorem

1

2 V = 3 * 2 0 / ( 2 + 3 ) / / t h e v en i n s v o l t a g e3 r = 1 + 2 * 3 / ( 2 + 3 ) // t he ve ni n s e q u i v a l e n t r e s i s t a n c e4 R = r

5 P m a x = V ^ 2 / ( 4 * r )

6 mprintf ( Max p ower t r a n s f e r r e d t o t he l oa d i s %f Wwhen l o ad r e s i s t a n c e i s %f ohm , P m a x , R )

Scilab code Exa 1.14 Example on Delta to Star and Star to Delta Trans-

formation

1

2 // i n n er d e l t a DEF i s t ra ns f o r m ed t o e q u i v a l e n t s t a rc o nn e ct i on h av in g r e s i s t a n c e s Ra , Rb , Rc

19


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22/212

12 I = I 3 + I 4

13 mprintf ( By S u p e r p o s i t i o n Theorem , c u r r e n t t h r ou g ht h e 2 ohm r e s i s t a n c e i s %f A from A t o B\n , I )14 //by T he v eni n s T he or em15 // ap pl y i ng KCL16 // f o r mesh CDHIC , 15i 1 +12 i 2= 217 // f o r mesh DEGHD, 12i 1 +17 i 2= 418 a = [ 15 1 2; 12 1 7]

19 b = [ 2 ; 4 ]

20 i = inv ( a ) * b

21 i 1 = i ( 1 , 1 )

22 i 2 = i ( 2 , 1 )

23 V a b = 4 - 3 * i 2 - i 224 R 1 = ( 1 + 2 ) * 1 2 / ( 1 + 2 + 1 2 ) //R1 i s e q ui v a l e n t r e s i s t a n c e

o f Rcd , R ci , Rdh25 R = ( 1 + R 1 ) * ( 3 + 1 ) / ( 1 + R 1 + 3 + 1 ) / / t h e v en i n s e q u i v a l e n t

r e s i s t a n c e26 I = V a b / ( R + 2 )

27 mprintf ( By T h ev e ni n Theorem , c u r r e n t t h r o u g h 2 ohmr e s i s t a n c e i s %f A from A t o B\n , I )

28 / / b y M ax we ll Mesh A n a l y s i s29 // ap pl y i ng KVL30

// f o r mesh CDEHC, 15 I112 I2=231 // f o r mesh DABED, 12 I1+ 15 I2+ 2 I3=032 // f o r mesh AFGBA, 2I2 +6 I3=433 a = [1 5 -12 0; -12 15 2;0 2 6]

34 b = [ 2 ; 0 ; 4 ]

35 i = inv ( a ) * b

36 I 1 = i ( 1 , 1 )

37 I 2 = i ( 2 , 1 )

38 I 3 = i ( 3 , 1 )

39 mprintf ( By M ax we ll Mesh A n a l y s i s , c u r r e n t t h r ou g h 2ohm r e s i s t a n c e i s %f A from A t o B , I2 + I3 )

21


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Chapter 2

Electrostatics

Scilab code Exa 2.1 Example on Coulombs Law

1

2 e p s i l o n = 8 . 8 5 4 D - 1 2

3 r = sqrt ( . 1 ^ 2 + . 1 ^ 2 ) / / d i s t a n c e b /w A and C4 F c a = ( 2 D - 6 ) * ( 4 D - 6 ) / ( 4 * % p i * e p s i l o n * r ^ 2 ) / / f r o m A t o C5 F c b = ( 4 D - 6 ) * ( 2 D - 6 ) / ( 4 * % p i * e p s i l o n * . 1 ^ 2 ) / / f r o m C t o B6 F c d = ( 4 D - 6 ) * ( 4 D - 6 ) / ( 4 * % p i * e p s i l o n * . 1 ^ 2 ) / / f r o m C t o D

7 / / Fr ha s h o r i z o n t a l and v e r t i c a l compone nt s a s Frxand Fry r e s p e c t i v e l y

8 F r x = F c d - F c a * cos ( 4 5 * % p i / 1 8 0 )

9 F r y = F c b - F c a * sin ( 4 5 * % p i / 1 8 0 )

10 Fr = sqrt ( F r x ^ 2 + F r y ^ 2 )

11 mprintf ( R e s u l ta n t f o r c e a c t i n g on c h ar g e a t C=%f N, F r )

12 // e r r o r i n t e xt bo o k a ns we r

Scilab code Exa 2.2 Example on Electric Intensity

1

22


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2 e p s i l o n = 8 . 8 5 4 D - 1 2

3 E 1 = ( 4 D - 8 ) / ( 4 * % p i * e p s i l o n * . 0 5 ^ 2 ) / / f i e l d i n t e n s i t y d uet o c ha rg e a t A, d i r e c t i o n i s from D t o A4 r = sqrt ( 2 * . 0 5 ^ 2 ) / / d i s t a n c e b /w B a nd D5 E 2 = ( 4 D - 8 ) / ( 4 * % p i * e p s i l o n * r ^ 2 ) / / f i e l d i n t e n s i t y d ue

t o c ha rg e a t B , d i r e c t i o n i s from B t o D a lo ngd i a g o n a l BD

6 E 3 = ( 8 D - 8 ) / ( 4 * % p i * e p s i l o n * . 0 5 ^ 2 ) / / f i e l d i n t e n s i t y d uet o c ha rg e a t C , d i r e c t i o n i s from D t o C

7 / / Er ha s h o r i z o n t a l and v e r t i c a l compone nt s a s Erxand Ery r e s p e c t i v e l y

8 E r x = E 3 - E 2 * cos ( 4 5 * % p i / 1 8 0 )

9 E r y = - E 1 + E 2 * sin ( 4 5 * % p i / 1 8 0 )10 Er = sqrt ( E r x ^ 2 + E r y ^ 2 )

11 t h e t a = a t a n d ( E r y / E r x )

12 mprintf ( R e s u l ta n t i n t e n s i t y on c h ar g e a t C=%f 1 0 4N/C a t a n g l e %f d e g r e e s , E r / 10 ^4 , - t h e t a )

Scilab code Exa 2.3 Example on Electric Potential

12 e p s i l o n = 8 . 8 5 4 D - 1 2

3 A B = . 0 5

4 B C = . 0 7

5 AC = sqrt ( . 0 5 ^ 2 + . 0 7 ^ 2 )

6 V 1 = 2 D - 1 0 / ( 4 * % p i * e p s i l o n * . 0 5 ) // p o t e n t i a l a t A due t oc ha rg e a t B

7 V 2 = - 8 D - 1 0 / ( 4 * % p i * e p s i l o n * A C ) // p o t e n t i a l a t A due t oc ha rg e a t C

8 V 3 = 4 D - 1 0 / ( 4 * % p i * e p s i l o n * . 0 7 ) // p o t e n t i a l a t A due t o

c ha rg e a t D9 V = V 1 + V 2 + V 310 mprintf ( P o t e n t i a l a t A due t o c h ar g es a t B , C and D

=%f V, V )

23


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Scilab code Exa 2.4 Example on charging and discharging of capacitor

1

2 C = 3 0 D - 6

3 R = 5 0 0

4 T = C * R

5 mprintf ( Time c o n s t a n t T=%f s e c \n , T )6 / / at t =0 s ec , v o l t a ge a c r o s s c a p a c i t o r i s z er o7 V = 1 0 0 // a p l i e d v o l t a g e8 I = V / R //Ohm s Law9 mprintf ( I n i t i a l cu rr en t=%f A\n , I )

10 t = . 0 5

11 Q = C * V

12 q = Q * ( 1 - exp ( - t / T ) )

13 mprintf ( Charge on t h e c a p ac i t or a f t e r 0 . 0 5 s e c i s%f C\n , q )

14 i 1 = I * exp ( - t / T )

15 mprintf ( C h a r g i n g c u r r e n t a f t e r 0 . 0 5 s e c i s %f A\n ,i1 )

16 t = . 0 1 517 i 2 = I * exp ( - t / T )

18 mprintf ( C h a r g i n g c u r r e n t a f t e r 0 . 0 1 5 s e c i s %f A\n, i 2 )

19 V = i 1 * R

20 mprintf ( V ol ta ge a c r o s s 500 ohm r e s i s t o r a f t e r 0 . 0 5s e c i s %f V , V )

21 // a ns we rs v ar y fro m t he t ex tb o ok due t o ro und o f f e r r o r


1

24


26/212

2 C = 1 0 0 D - 6

3 V = 2 0 04 Q = C * V

5 C t = 1 0 0 D - 6 + 5 0 D - 6 // t o t a l c a p a c i t a nc e6 V t = Q / C t

7 mprintf ( P . D. a c r o s s t h e c o mb i n at i on =%f V\n , V t )8 E E 1 = 1 0 0 D - 6 * V ^ 2 / 2

9 mprintf ( E l e c t r o s t a t i c e ne rg y b e f o r e c a p a c i t o r s a rec on ne ct ed i n p a r a l l e l =%f J \n , E E1 )

10 E E 2 = C t * V t ^ 2 / 2

11 mprintf ( E l e c t r o s t a t i c e ne rg y a f t e r c a p a c i t o r s a rec on n ec te d i n p a r a l l e l =%f J , EE2 )


1

2 C 1 = 1 0 0 D - 6 // c a p a c i t a nc e o f f i r s t c a p a c i t o r whi ch i st o be c ha rg ed

3 V = 2 0 0 // v o l t a g e a c r o s s C14 Q = C 1 * V

5 / / L et Q1 , Q2 , Q3 , Q4 b e t he c h a r ge s on r e s p e c t i v ec a p a c i t o r s a f t e r c on n e ct i o n

6 Q 2 = 4 0 0 0 D - 6

7 Q 3 = 5 0 0 0 D - 6

8 Q 4 = 6 0 0 0 D - 6

9 Q 1 = Q - ( Q 2 + Q 3 + Q 4 )

10 C 2 = C 1 * ( Q 2 / Q 1 )

11 C 3 = C 1 * ( Q 3 / Q 1 )

12 C 4 = C 1 * ( Q 4 / Q 1 )

13 mprintf ( T hree c a p a c i t o r s h ave c a p a c i t a n c e s %d

mi cr oF , %d mi c r oF and %d mi c r oF\n , C 2 *1 0^ 6 , C 3* 1 0 ^ 6 , C 4 * 1 0 ^ 6 )14 V t = Q 1 / C 1

15 mprintf ( V o l t a ge a c r o s s t h e c o mb i na t io n =%f V , V t )

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Chapter 3

Electromagnetism

Scilab code Exa 3.2 Example on Field Strength and Flux Density

1

2 m u _ n o t = 4 D - 7 * % p i

3 N = 1 5 0 // no . o f t ur ns o f c o i l4 I =4 // c u r r e nt c a r r i e d by c o i l5 l = . 3 // l e ng t h o f s o l e n o i d i n mt rs6 B c = m u _ n o t * N * I / l

7 mprintf ( F lux d e n s i t y a t c e n t r e =%f 10 3 Wb/m2 ,B c * 1 0 ^ 3 )

Scilab code Exa 3.3 Example on Field Strength and Flux Density

1

2 m u _ n o t = 4 D - 7 * % p i

3 // c a l c u l a t i n g f l ux d e n s i t y a t c e n t r e o f c o i l B=

mu not I /(2R)4 I = 5 0

5 R = 4 D - 2

6 B = m u _ n o t * I / ( 2 * R )

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7 mprintf ( Fl ux d e n si t y a t c e n tr e o f c o i l =%f 10 6 Wb/

m2( Te sl a ) \n , B * 1 0^ 6)8 / / c a l c u l a t i n g f l u x d e n s i t y p e r p e nd i c u l a r t o p la ne o f c o i l a t a d i s t a n ce o f 10 cm from i t

9 z = 1 0 D - 2

10 B = m u _ n o t * I * R ^ 2 / ( 2 * ( R ^ 2 + z ^ 2 ) ^ 1 . 5 )

11 mprintf ( Fl ux d e n s i t y p e r p e nd i c u l a r t o p la ne o f c o i la t a d i s t a n ce o f 10 cm f rom i t =%f 106 Wb/m 2 (

T e s l a ) , B * 1 0^ 6 )

Scilab code Exa 3.4 Example of Force on on Current Carrying Conductor

1

2

3 m u _ n o t = 4 D - 7 * % p i

4 I 1 = 3 0 // c u r r e nt i n w i re A5 I 2 = 3 0 // c u r r e nt i n w i re B6 R = 1 0 D - 2 // d i s t a n c e b /w 2 w i r e s7 F = m u _ n o t * I 1 * I 2 / ( 2 * % p i * R )

8 mprintf ( F or ce p er m et r e l e ng t h i s %d10 4 N / m i n

b ot h c a s e s ( i ) a nd ( i i ) . However i n c a s e ( i ) , i t i sa t t r a c t i v e and i n c as e ( i i ) , i t i s r e p u l s i v e , F

*10^4)

Scilab code Exa 3.5 Example of Force on on Current Carrying Conductor

1

2 B = . 0 6 // f l u x d e n s i t y3 I = 4 0 D - 3 // c u r re n t i n c o i l4 l = 4 D - 2 // l en gt h o f c o i l s i d e5 F = B * I * l

6 N = 5 0 // no . o f t u r ns

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7 mprintf ( F or ce a c t i n g on e ac h c o i l s i d e=%f 10 3 N ,

F * N * 1 0 ^ 3 )

28


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Chapter 4

Magnetic Circuit

Scilab code Exa 4.1 Example on Series Magnetic Circuit

1

2

3 m u _ n o t = 4 D - 7 * % p i

4 a = ( 3 D - 2 ) ^ 2 / / c r o s ss e c t i o n a l a re a5 L a = ( 2 0 - 1 . 5 - 1 . 5 ) * 1 D - 2 // l e n g t h o f f l u x pat h i n p ar t A6 m u _ r = 1 0 0 0 // r e l a t i v e p e r m e ab i l i t y f o r p ar t A

7 S a = L a / ( m u _ n o t * m u _ r * a )8 mprintf ( R e l u c t a n c e o f p a r t A=%f 104AT/Wb\n , Sa

/10^4)

9 L b = ( 1 7 + 8 . 5 + 8 . 5 ) * 1 D - 2 // l e n g t h o f f l u x pat h i n p ar t B10 m u _ r = 1 2 0 0 // r e l a t i v e p e r m e ab i l i t y f o r p ar t B11 S b = L b / ( m u _ n o t * m u _ r * a )

12 mprintf ( R e l u c t a n c e o f p a r t B=%f 104AT/Wb\n , Sb/10^4)

13 L g = ( 2 + 2 ) * 1 D - 3 // l e n g t h o f f l u x pa th i n a i r gap14 S g = L g / ( m u _ n o t * a )

15 mprintf ( R e l uc t an c e o f 2 a i r g ap s=%f 1 0 4 AT/Wb\n ,S g / 1 0 ^ 4 )16 S = S a + S b + S g

17 mprintf ( T ot al r e l u c t a n c e o f m ag ne ti c c i r c u i t =%f 10 4 AT/Wb\n , S / 1 0^ 4)

29


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18 N = 1 0 0 0 // no . o f t ur ns on e a c h c o i l

19 I =1 // c u r r e n t i n c o i l20 m m f = 2 * N * I21 mprintf ( mmf=%d AT\n , m mf )22 f l u x = m m f / S

23 mprintf ( F lux i n m ag ne ti c c i r c u i t =%f 104 Wb\n ,f l u x * 1 0 ^ 4 )

24 f l u x _ d e n s i t y = f l u x / a

25 mprintf ( F l ux d e n s i t y =%f T e s l a , f l u x _d e n si t y )


1

2

3 B g = . 7 // f l u x d e ns i t y i n a i r gap4 L g = 3 D - 3 // l e ng t h o f a i r gap5 A T g = . 7 9 6 * B g * L g * 1 D + 6

6 B s = B g // f l u x d e n si t y i n i r o n path7 H = 6 6 0 // a mpere t u rn s c o r r es p o n d i ng t o Bs fro m BH

c u rv e ( F ig . 4 . 2 ) o f t e xt b o o k

8 L i = 4 0 D - 2 // l e n g t h o f f l u x pa th i n i r on p o rt i on9 A T s = H * L i

10 AT = round ( A T g ) + round ( A T s )

11 mprintf ( T o ta l ampere t u rn s t o be p r ov i de d on t heel ec tr om ag ne t=%d AT , A T )

12 / / a ns we r v ar y fr om t he t ex t bo o k due t o ro un d o f f e r r o r


1

2 m u _ n o t = 4 D - 7 * % p i

3 N = 7 0 0 // no . o f t ur ns on s t e e l r i ng

30


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33/212

10 I = A T / N

11 mprintf ( C u rr en t i n t he c o i l =%f A\n ,I )12 L g = 2 D - 3 // l e ng t h o f a i r gap13 L i = L - L g // l e ng t h o f mean f l u x pat h i n r i n g14 m u = B / H

15 B g = A T / ( L i / m u + . 7 9 6 * L g * 1 D + 6 )

16 f l u x = B g * A

17 mprintf ( M a g n e t ic f l u x p r o d uc e d=%f 10 4 Wb\n ,flux* 1 D + 4 )

18 / / c a l c u l a t i n g v al u e o f c u r r e n t which w i l l p ro du cet he same f l u x a s i n ( i )

19 A T i = H * L i

20 A T g = . 7 9 6 * B * L g * 1 D + 621 A T = A T i + A T g

22 I = A T / N

23 mprintf ( C u rr e n t i n t he c o i l whi ch w i l l g i ve t hesa me f l u x a s i n ( i )=%f A ,I )


12 m u _ n o t = 4 D - 7 * % p i

3 N = 4 0 0 // number o f t u r ns on t he c o i l wound on i r o nr i n g

4 I = 1 . 2 // c u r r e n t t hr ou gh t he c o i l5 A T = N * I

6 l =1 // mean f l u x pat h i n r i n g i n mt rs7 H = A T / l

8 B = 1 . 1 5 / / f l u x D e ns i t y9 m u _ r = B / ( H * m u _ n o t )

10 mprintf ( R el p e r m e a b i l i t y o f i r o n r i n g mu r=%d ,round ( m u _ r ) )11 // e r r o r i n t e xt bo o k a ns we r

32


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1

2 m u _ n o t = 4 D - 7 * % p i

3 L i = 5 0 d - 2 // l e n g t h o f f l u x pa th i n i r on4 m u _ r = 1 3 0 0 // r e l a t i v e p e r m ea b i l i t y5 a = 1 2 D - 4 // c r o s s s e c t i o n a l a re a6 S i = L i / ( m u _ n o t * m u _ r * a )

7 mprintf ( R el uc ta nc e o f i r o n p ar t o f m ag n et i c c i r c u i t=%f10 3 AT/Wb\n , S i / 1 0 ^ 3 )

8 L g = . 4 D - 2 // l e n g t h o f f l u x pa th i n a i r gap9 S g = L g / ( m u _ n o t * a )

10 mprintf ( R el uc ta nc e o f a i r gap o f m a gn et i c c i r c u i t =%f10 3 AT/Wb\n , S g / 1 0 ^ 3 )

11 S = S i + S g

12 mprintf ( T ot al r e l u c t a n c e o f m ag ne ti c c i r c u i t =%f 10 3 AT/Wb\n , S / 1 0 ^ 3 )

13 N = 4 0 0 + 4 0 0 // t o t a l no . o f t u rn s14 I =1 // c u r r e nt t hr ou gh e ac h c o i l

15 m m f = N * I16 f l u x = m m f / S

17 mprintf ( T o t a l f l u x =%f m i ll i Wb \n , f l ux * 1 0 ^ 3 )18 B = f l u x / a

19 mprintf ( F l u x d e n s i t y i n a i r g ap=%f Wb/m 2 , B )20 // a ns we rs v ar y fro m t he t ex tb o ok due t o ro und o f f

e r r o r


1

2 m u _ n o t = 4 D - 7 * % p i

3 N = 3 0 0 // no . o f t ur ns i n c o i l

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Figure 4.1: Example on Series Magnetic Circuit

4 I = . 7 // c u r r e n t t hr ou gh c o i l5 A T = N * I6 L = 6 0 D - 2 // l e ng t h o f r i n g7 L g = 2 D - 3 // l e ng t h o f a i r gap8 L i = L - L g // l e n g t h o f f l u x pat h i n r i ng9 m u _ r = 3 0 0 // r e l p e r m e a b i l i t y o f i r on

10 B = A T / ( L i / ( m u _ n o t * m u _ r ) + . 7 9 6 * L g * 1 D + 6 )

11 mprintf ( Flux de n s it y=%f Wb/m2 , B )


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1

2 m u _ n o t = 4 D - 7 * % p i3 p h i = . 0 0 0 6 / / f l u x4 A = 5 . 5 D - 4 / / c r o s ss e c t i o n a l a re a o f r i n g5 B = p h i / A

6 h =[0 200 400 5 00 600 800 1 00 0]

7 b = [0 .4 .8 1 1. 09 1 .1 7 1 .1 9]

8 plot2d ( h , b )

9 xtitle ( BH c ur ve f o r e xa mp le 4 . 8 , H ( a m p er e t u r n sp e r m e tr e ) , B(Wb/m 2 ) )

10 H = 6 0 0 / / c o r r e s p o n d i n g t o B f ro m BH c u r v e11 L = 2 7 0 D - 2 // l e ng t h o f r i n g

12 L g = 4 . 5 D - 3 // l e ng t h o f a i r gap13 L i = L - L g // l e n g t h o f f l u x pat h i n i r on p o rt i o n o f r i ng14 A T i = H * L i

15 A T g = . 7 9 6 * B * L g * 1 D + 6

16 AT = round ( A T i ) + round ( A T g )

17 mprintf ( T o t a l a m pe re t u r n s =%d , A T )18 // e r r o r i n t e xt bo o k a ns we r


1

2 m u _ n o t = 4 D - 7 * % p i

3 f l u x = 1 . 1 D - 3

4 A = 4 * 4 * 1 D - 4 / / c r o s ss e c t i o n a l a re a5 B = f l u x / A

6 m u _ r = 2 0 0 0 // r e l p e r m e a b i l i t y7 H = B / ( m u _ n o t * m u _ r )

8 / / c a l c u l a t i n g ampere t u rn s r e q u i r e d f o r p o ti o n C

9 l = . 2 5 / / l e n g t h o f mean f l u x p at h10 A T c = H * l11 / / c a l c u l a t i n g ampere t u rn s r e q u i r e d f o r p o ti o n D12 l = . 3 // l e n g t h o f mean f l u x p at h13 A T d = H * l

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14 / / c a l c u l a t i n g ampere t u rn s r e q u i r e d f o r a i r gap

15 A T g = . 7 9 6 * B * . 0 0 2 * 1 0 ^ 616 AT = round ( A T c ) + round ( A T d ) + round ( 2 * A T g )

17 mprintf ( T o t a l a mp er e t u r n s r e q u i r e d =%d , A T )18 / / a ns we r v ar y fr om t he t ex t bo o k due t o ro un d o f f

e r r o r


12 m u _ n o t = 4 D - 7 * % p i

3 f l u x = . 0 1 8

4 // c o n s i d e r p a rt A5 a = 2 0 5 D - 4 // c r o s s s e c t i o n a l a re a6 B a = f l u x / a

7 H = 7 6 0 // c o r r es p o n d i ng t o Ba a s o b ta i n ed fro m F ig .4 . 2 i n t he t ex tb oo k

8 l = ( 3 8 - . 2 5 ) * 1 D - 2 // l e ng t h o f mean f l u x pat h i n i r o np o rt i o n o f p ar t A

9 A T i = H * l

10 A T g = . 7 9 6 * B a * 2 . 5 D - 3 * 1 0 ^ 611 A T a = A T i + A T g

12 // c o n s i d e r p a rt B13 a = 2 5 5 D - 4

14 B b = f l u x / a

15 H = 6 7 0 // c o r r e s p o n d i n g t o Bb a s o b t a i n ed f ro m F ig .4 . 2 i n t he t ex tb oo k

16 l = . 2 5 // l e ng t h o f mean f l u x pat h i n i r o n p o r ti o n o f p a r t B

17 A T b = H * l

18 AT = round ( A T a ) + round ( A T b )19 mprintf ( T o ta l ampere t u rn s r e q u i r e d f o r c om pl et em a g n e t i c c i r c u i t =%d , A T )

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12 a = 5 D - 4 / / c r o s ss e c t i o n a l a re a

13 B _ o l = p h i _ o l / a14 H = 1 2 0 0 // c o rr e sp o nd i ng t o B o l from F i g 4 . 2 i n t het e x t b o o k

15 l = . 3 5 // l e n g t h o f mean f l u x p at h16 A T _ o l = H * l

17 A T = A T _ c c + A T _ o l

18 N = 4 0 0

19 mprintf ( C u rr en t r e q u i r e d i n t he c o i l =%f A , AT / N)

Scilab code Exa 4.13 Example on Series Parallel Magnetic Circuit

1

2 m u _ n o t = 4 D - 7 * % p i

3 p h i _ c c = 1 . 2 D - 3 // f l u x i n c e n t r a l c or e4 p h i _ o l = p h i _ c c / 2 // f l u x i n e ac h o u te r l imb5 // c o n s i d e r c e n t r a l c o re6 a = 9 D - 4 / / c r o s ss e c t i o n a l a re a7 B _ c c = p h i _ c c / a // f l u x d e n s i t y8 H = 1 6 0 0 // c o rr e sp o nd i ng t o B c c from F ig 4 . 2 i n t he

t e x t b o o k9 l = ( 1 5 - . 2 ) * 1 D - 2 // l e ng t h o f mean f l u x path o f c a s t

s t e e l10 A T _ c c = H * l

11 A T g = . 7 9 6 * B _ c c * 2 D - 3 * 1 0 ^ 6

12 // c o n s i d e r o u t er l im b13 a = 5 D - 2 / / c r o s ss e c t i o n a l a re a14 B _ o l = p h i _ o l / a

15 H = 1 2 0 0 // c o rr e sp o nd i ng t o B o l from F i g 4 . 2 i n t het e x t b o o k

16 l = . 3 5 // l e n g t h o f mean f l u x p at h17 A T _ o l = H * l18 A T = A T _ c c + A T g + A T _ o l

19 N = 4 0 0

20 mprintf ( E x c i t in g c u r r e nt i n t he c o i l =%f A , A T / N )

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Chapter 5

Electromagnetic Induction

Scilab code Exa 5.1 Example on Induced EMF

1

2 N = 1 0 0 0 // no . o f t ur ns i n t h e c o i l3 d p h i = - 2 * 9 0 0 D - 6 // c ha ng e i n f l u x i n Wb4 d t = . 2 // t im e i n s e c i n whi ch c h ang e t a ke s p l a ce5 e m f = - N * d p h i / d t

6 mprintf ( A v er ag e emf i n d u ce d i n t h e c o i l =%d V , round

( e m f ) )


1

2 l = 8 0 D - 2 // l e n g t h o f c o n du c t or3 B = 1 . 2 / / f l u x d e n s i t y o f u n if o rm m a gn e ti c f i e l d4 v = 3 0 // v e l o c i t y o f c o nd u ct o r i n m/ s5 // when t h e d i r e c t i o n o f mot io n i s p e r pe n d i cu l a r t o

f i e l d6 e = B * l * v

7 mprintf ( emf i n du c ed i n t h e c o n du c to r when t h e

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10 mprintf ( R e l a t i v e p e r m e a b i l i t y o f m et al=%f \n , m u _ r )

11 A = % p i * 2 . 5 D - 2 ^ 2 / 4 // c r o s s s e c t i o n a l a re a o f r i n g12 p h i = B * A13 L = N * p h i / I

14 mprintf ( S e l f i n du c t an c e o f c o i l =%f H\n ,L )15 / / s o l v i n g p a r t ( i i i )16 d p h i = . 0 8 * p h i - p h i // c ha ng e i n f l u x17 d t = . 0 0 1 5 // t i me t ak en f o r c ha ng e18 e = - N * d p h i / d t

19 mprintf ( emf i nd uc e d i n t h e c o i l when v al ue o f f l u xf a l l s t o 8 p e rc e n t i t s v a l i u e i n 0 . 00 1 5 s e c=%f V,e )


1

2 m u _ n o t = 4 D - 7 * % p i

3 H = 3 5 0 0 // a mpere t u r ns p er m et re o f f l u x p at h l e n g t h4 l = % p i * 4 0 D - 2 // l e ng t h o f mean f l u x path i n r i n g5 A T = H * l

6 N = 4 4 0 // no . o f t ur ns on c o i l7 I = A T / N // e x c i t i n g c u r r e nt8 mprintf ( E x c i t i n g c u r r e n t =%d A\n , round ( I ) )9 B = . 9 // f l u x d e n s i t y

10 A = 1 5 D - 4 / / c r o s ss e c t i o n a l a re a o f r i n g11 p h i = B * A

12 L = N * p h i / I

13 mprintf ( S e l f i n d uc t an c e o f c o i l =%f H\n ,L )14 / / s o l v i n g p a r t ( i i i )15 l = ( l - 1 / 1 0 ^ 2 ) // l e n g t h o f mean f l u x pat h i n s t e e l r i ng

16 A T i = H * l // ampere t u rn s r e q u i r e d f o r i r o n p o r ti o n17 A T g = . 7 9 6 * B * 1 D - 2 * 1 D + 6 // ampere t ur n s f o r a i r gap18 A T = A T i + A T g

19 I = A T / N

20 mprintf ( When an a i r gap 1 cm l on g i s c ut i n t he

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r in g , e x c i t i n g c u r r e nt I=%f A and s e l f i n d uc t an c e

o f c o i l =%f H\n , I , N * p h i / I )


1

2 N = 8 0 0 // no . o f t u rn s3 d I = 1 0 - 5 // c ha ng e i n c u r r en t4 d B = 1 . 2 - . 8 // c o r r es p o n d i ng c ha ng e i n f l u x d e n s i t y

5 A = 1 5 D - 4 // c r o s s s e c t i o n a l a re a6 L = A * N * d B / d I7 mprintf ( S e l f i n d u c t a n ce o f c o i l , L=%f H\n ,L )8 d i = 5 - 1 0 // c ha ng e i n c u r r en t9 d t = . 0 4 // t i me t ak en f o r c ha ng e

10 e = - L * d i / d t

11 mprintf ( I n d u ce d emf when t h e c u r r e n t f a l l su n i fo r m ly from 10 A t o 5 A i n 0 . 0 4 s e c=%d V ,round ( e ) )


1

2 m u _ n o t = 4 D - 7 * % p i

3 N = 1 2 0 0 // no . o f t ur ns i n t h e c o i l on s o l e n o i d4 l = 8 0 D - 2 // l e ng t h o f s o l e n o i d5 A = % p i / 4 * ( 5 D - 2 ) ^ 2 / / c r o s ss e c t i o n a l a re a6 L = N * ( m u _ n o t * N * A / l )

7 mprintf ( S e l f i n d u c t a n c e =%f mH\n , L * 1 0 0 0 )

8 // c a l c u l a t i n g i nd uc ed emf 9 d i = - 5 - 5

10 d t = . 0 3

11 e = - L * d i / d t

12 mprintf ( Induc e d e mf=%f V ,e )

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8 e = - M * 2 0 0

9 mprintf ( emf i nd uc ed i n s e a r ch c o i l =%f V ,e )


1

2 m u _ n o t = 4 D - 7 * % p i

3 N = 8 0 0 // no . o f t ur ns f o r e a c h s o l e n o i d4 l = 9 0 D - 2 // l e ng t h o f e a ch s o l e n o i d

5 A x = % p i * ( 3 D - 2 ) ^ 2 / 4 / / c r o s ss e c t i o n a l a re a o f s o l e n o i dX6 A y = % p i * ( 6 D - 2 ) ^ 2 / 4 / / c r o s ss e c t i o n a l a re a o f s o l e n o i d

Y7 M = N * N * m u _ n o t * A x / l

8 mprintf ( M ut ua l i n d u c t a n c e o f a r r a n g em e n t=%f mH\n,1000*M)

9 // c a l c u l a t i n g c o up l i ng co e f f i c i e n t10 L x = N * m u _ n o t * N * A x / l

11 L y = N * m u _ n o t * N * A y / l

12 k = M / sqrt ( L x * L y )

13 mprintf ( C o u p l i ng co e f f i c i e n t =%f ,k )


1

2 m u _ n o t = 4 D - 7 * % p i

3 N b = 5 0 0 // no . o f t ur ns i n c o i l B4 l = 1 2 0 D - 2 // mean l e n g t h o f f l u x pa th i n i r on c i r c u i t

5 N a = 5 0 // no . o f t ur ns i n c o i l A6 m u _ r = 2 0 0 0 // r e l a t i v e p e r m e ab i l i t y o f i r on7 A = 8 0 * 1 0 ^ - 4 / / c r o s ss e c t i o n a l a re a8 M = N b * m u _ n o t * m u _ r * N a * A / ( l )

9 mprintf ( M u tu al i n d u c t a n c e M=%f H\n ,M )

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10 d i = 1 2

11 d t = . 0 1 512 e = - M * d i / d t

13 mprintf ( Emf i n d u ce d i n c o i l B=%f V ,e )

Scilab code Exa 5.12 Example on Growth and Decay of Current in In-ductive Circuits

1

2 V = 1 1 0 // a p p l i e d v o l t a g e3 L = . 5 // i n du c t a nc e o f c o i l4 r = V / L

5 mprintf ( R at e o f c h an g e o f c u r r e n t =%d A/ s \n ,r )6 R =8 // r e s i s t a n c e o f c o i l7 I = V / R

8 mprintf ( F i n a l s t e a d y c u r r e n t =%f A\n ,I )9 T = L / R

10 mprintf ( Time c o n s t a n t =%f s e c\n ,T )11 / / s o l v i n g p a r t ( i v )12 t = - log ( . 5 ) * T

13 mprintf ( Time t ak e n f o r t h e c u r r e n t t o r i s e t o h a l f i t s f i n a l v a lu e=%f s e c ,t )


1

2 / / c a l c u l a t i n g t i m e i t w i l l t a k e c ur r e nt t o r ea ch . 8

o f i t s f i n a l s t e a dy v a lu e3 L =5 / / i n d u c t a nc e o f w in di n g4 R = 5 0 // r e s i s t a n c e o f w in di ng5 T = L / R

6 V = 1 1 0 // a p p l i e d v o l t a g e

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7 I = V / R // f i n a l s te ad y c u r r e nt

8 i = . 8 * I9 t = - T * log ( 1 - i / I )

10 mprintf ( C u rr e n t g row s t o . 8 t im es i t s f i n a l s te ad yv a l ue , %f s e c a f t e r t he s wi tc h i s c l o se d\n ,t )

11 / / c a l c u l a t i n g t i m e i t w i l l t a k e f o r t h e c ur r e nt t or e a c h . 9 o f i t s f i n a l s t e a d y v a l u e

12 i = . 9 * I

13 t = - T * log ( 1 - i / I )

14 mprintf ( Time t ak en f o r t he c u r r e n t t o grow t o . 9t i m e i t s f i n a l s t e a d y v a l ue i s %f s e c\n ,t )

15 // c a l c u l a t i n g a v er a ge emf i nd uc ed

16 e = - L * ( - 2 . 2 / . 0 5 )17 mprintf ( e mf i nd uc e d=%d V\n , round ( e ) )


1

2 // c a l c u l a t i n g i nd uc ta nc e and r e s i s t a n c e o f t h e r e l ay

3 T = . 0 0 4 // t im e c o ns t a n t whi ch i s t i me t ak en f o r t hec ur re nt t o r i s e t o . 63 2 o f i t s f i n a l s t e a d y v a l u e

4 I = . 3 5 / . 6 3 2 // f i n a l s te ad y v al ue5 V = 2 0 0 // a p p l i e d v o l t a g e6 R = V / I

7 L = T * R

8 mprintf ( R e s i s t a nc e o f r e l a y c i r c u i t =%f ohm\n In du ct an ce o f r e l a y c i r c u i t =%f H\n , R , L )

9 // c a l c u l a t i n g i n i t i a l r a t e o f r i s e o f c u r r e n t10 r = V / L

11 mprintf ( I n i t i a l r a t e o f r i s e o f c u r r e n t=%f A/ s ,r )

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Scilab code Exa 5.15 Example on Growth and Decay of Current in In-

ductive Circuits

1

2 R = . 5 + 4 0 + 1 5 // t o t a l r e s i s t a n c e3 L =1 // t o t a l i n d uc t an c e4 T = L / R

5 V = 1 2 // emf o f b a t t er y6 I = V / R // f i n a l s te ad y c ur r e nt i n t h e c i r c u i t7 i = . 0 4 // c ur r e nt a t t i m e t a f t e r c l o s i n g t h e c i r c u i t8 t = - T * log ( 1 - i / I )

9 mprintf ( The r e l a y w i l l b eg in t o o pe r a t e %f s e c

a f t e r t h e r e l a y c i r c u i t i s c l o s e d\n ,t )

Scilab code Exa 5.16 Example on Energy Stored in Magnetic Field

1

2 m u _ n o t = 4 * % p i * 1 D - 7

3 // c a l c u l a t i n g i n d uc t an c e4 N = 4 0 0 0 / / number o f t u r n s

5 I =2 // c u r r e nt f l o w i n g i n t he s o l e n o i d6 d = 8 D - 2 // d i am e te r o f s o l e n o i d7 A s = % p i / 4 * d ^ 2

8 l = 8 0 D - 2 // l e ng t h o f s o l e n o i d i n mtr s9 p h i = m u _ n o t * N * I * A s / l

10 L = N * p h i / I

11 mprintf ( I n d u c t a n c e = % f H\n ,L )12 // c a l c u l a t i n g e ne rg y s t o r e d i n t he m ag ne ti c f i e l d13 E = L * I ^ 2 / 2

14 mprintf ( E n er gy s t o r e d i n t h e m a g ne t i c f i e l d =%f J ,E)


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1

2 m u _ n o t = 4 D - 7 * % p i3 // c a l c u l a t i n g e x c i t i n g c u r r e n t4 B = 1 . 2 // f l u x d e n s i t y5 m u _ r = 5 0 0 // r e l p e r m e a b i l i t y f o r i r on6 H = B / ( m u _ n o t * m u _ r )

7 D = 1 0 D - 2 / / mean d i a m e t e r8 l = % p i * D // l e n g t h o f f l u x pat h i n t he r i ng9 A T = H * l

10 N = 3 0 0 // number o f t u rn s on t he r i n g11 I = A T / N

12 mprintf ( E x c i t i n g c u r r e n t =%d A\n , round ( I ) )

13 // c a l c u l a t i n g i n d uc t an c e14 A s = 8 D - 4 / / c r o s ss e c t i o n a l a re a15 p h i = B * A s

16 L = N * p h i / I

17 mprintf ( I n d u c t a n c e = % f H\n ,L )18 // c a l c u l a t i n g e ne rg y s t o r e d19 E = L * I ^ 2 / 2

20 mprintf ( E n e rg y s t o r e d =%f J \n ,E )21 // c o n s i d e r t he c a se i n which an a i r gap o f 2 mm i n

t he r i n g i s made22 l i = l - 2 D - 3

// l e n g th o f f l u x pat h i n i r on p o rt i o n23 l g = 2 D - 3 // l e ng t h o f a i r gap24 A T i = H * l i // ampere t ur n s f o r i r o n p o r ti o n25 A T g = . 7 9 6 * B * l g * 1 0 ^ 6 // ampere t ur n s f o r a i r gap26 A T = A T i + A T g

27 I = A T / N

28 mprintf ( When t h e r e i s an a i r gap o f 2mm in t he r i n g\ n E x c i t i n g c u r r e n t=%f A\n ,I )

29 L = N * p h i / I

30 mprintf ( Ind uc t an c e =%f mH\n , L * 1 0 0 0 )31 E = L * I ^ 2 / 2

32 mprintf ( E n e rg y s t o r e d =%f J \n ,E )

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1

2 m u _ n o t = 4 D - 7 * % p i

3 // c a l c u l a t i n g p u l l on t he a rm at u re4 m u _ r = 3 0 0 // r e l p e r m e a b i l i t y o f i r on5 A T = 2 0 0 0 // t o t a l a mp ere t u r n s6 l i = 5 0 D - 2 // l e n g th o f i r o n pa th7 l g = 1 . 5 D - 3 // l e ng t h o f a i r gap8 B = A T / ( l i / ( m u _ n o t * m u _ r ) + . 7 9 6 * l g * 1 0 ^ 6 )

9 A = 3 D - 4 // a r ea o f e ac h p o l e s ho e10 x = B ^ 2 * A / ( 2 * m u _ n o t ) // p u l l on t he a rm at ur e a t e ac h

p o l e11 p = 2 * x

12 mprintf ( T o ta l p u l l due t o b ot h t he p o l e s=%f N\n ,p )13 // c o n s i d e r i n g t he gap c l o s e s t o . 2 mm14 l g = . 2 * 1 D - 3

15 B = A T / ( l i / ( m u _ n o t * m u _ r ) + . 7 9 6 * l g * 1 0 ^ 6 )

16 x = B ^ 2 * A / ( 2 * m u _ n o t )

17 p = 2 * x

18 mprintf ( When t h e gap c l o s e s t o . 2 mm, t o t a l f o r c en ee de d due t o bot h t he p ol es , t o p u l l t he

arm atu re away=%f N,p )

19 / / a ns we r v ar y fr om t he t ex t bo o k due t o ro un d o f f e r r o r

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Figure 6.1: Example on AC Wave Shapes

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Scilab code Exa 6.2 Example on AC Wave Shapes

1

2

3 // i=Imaxs i n (2%p if t )4 I m a x = 1 0 0 //max v a lu e o f c u r r e nt5 f = 2 5 // f r e q u e n cy i n Hz6 // c a l c u l a t i n g t im e a f t e r whi ch c u r re n t becomes 20 A7 i = 2 0

8 t = asin ( i / I m a x ) / ( 2 * % p i * f )

9 mprintf ( Time a f t e r w hi ch c u r r e n t b ec om es 2 0 A=%f s e c\n ,t )

10 // c a l c u l a t i n g t im e a f t e r whi ch c u r re n t becomes 50 A11 i = 5 0

12 t = asin ( i / I m a x ) / ( 2 * % p i * f )

13 mprintf ( Time a f t e r w hi ch c u r r e n t b ec om es 5 0 A=%f s e c\n ,t )

14 / / c a l c u l a t i n g t im e a f t e r whi ch c u r r e n t beco mes 10 0 A15 i = 1 0 0

16 t = asin ( i / I m a x ) / ( 2 * % p i * f )17 mprintf ( Time a f t e r w hi ch c u r r e n t b ec om es 1 00 A=%f

s e c\n ,t )


1

2 // c a l c u l a t i n g i n s t an t an e o u s v o l t a ge a t . 0 0 5 s e c

a f t e r t h e wave p a ss e s t h r o ug h z e r o i n p o s i t i v ed i r e c t i o n

3 f = 5 0 / / f r e q u e n c y4 E m a x = 3 5 0 //max v a lu e o f v o l t a g e5 t = . 0 0 5

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6 e 1 = E m a x * sin ( 2 * % p i * f * t )

7 mprintf ( V ol ta ge a t . 0 0 5 s e c a f t e r t he wave p a ss e st hr ou gh z e ro i n p o s i t i v e d i r e c t i o n =%d V\n , e 1 )8 // c a l c u l a t i n g i n s t an t an e o u s v o l t a ge a t . 0 0 8 s e c

a f t e r t he wave p a s se s t hr ou gh z e ro i n n e g at i v ed i r e c t i o n

9 t = . 0 0 8

10 e 2 = - E m a x * sin ( 2 * % p i * f * t )

11 mprintf ( V ol ta ge a t . 0 0 8 s e c a f t e r t he wave p a ss e st hr ou gh z e r o i n n e g a t i v e d i r e c t i o n =%f V , e 2 )


1

2 //e = 100s i n (1 0 0 %pi t )3 // c a l c u l a t i n g r a t e o f c ha ng e o f v o l t a g e a t t =. 0025

s e c4 t = . 0 0 2 5

5 r 1 = 1 0 0 0 0 * % p i * cos ( 1 0 0 * % p i * t )

6 mprintf ( Rate o f c h an ge o f v o l t a g e a t . 0 02 5 s e c=%f V

/ se c\n , r 1 )7 // c a l c u l a t i n g r a t e o f c ha ng e o f v o l t a g e a t t =. 005

s e c8 t = . 0 0 5

9 r 2 = 1 0 0 0 0 * % p i * cos ( 1 0 0 * % p i * t )

10 mprintf ( Rate o f c ha ng e o f v o l t a g e a t . 0 0 5 s e c=%d V/s e c\n , r 2 )

11 // c a l c u l a t i n g r a te o f c ha n g e o f v o l t a ge a t t =.01 s e c12 t = . 0 1

13 r 3 = 1 0 0 0 0 * % p i * cos ( 1 0 0 * % p i * t )

14 mprintf ( Rate o f c ha ng e o f v o l t a g e a t . 0 1 s e c=%f V/s e c\n , r 3 )15 // e r r o r i n t e xt bo o k a ns we r i n f i r s t and l a s t c a s e

55


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1

2

3 / / c a l c u l a t i n g g r e a t e s t r a te o f c ha n ge o f c u rr e n t4 // i =50s i n ( 1 0 0%p i t )5 mprintf ( G r e a t e st r a t e o f c ha ng e o f c u r r e n t=%f A/ s e c

\n,50*100*%pi )6 / / c a l c u l a t i n g a v e ra g e v a lu e o f c u r re n t7 f = 5 0 // f r e q u e n cy o f t h e wave8 T = 1 / f

9 I m e a n = 1 / . 0 1 * i n t e g r a t e ( 50s i n ( 1 0 0 %pi t ) , t ,0,T/2)10 mprintf ( A ve ra ge v a l ue o f t he g i ve n c u r r e n t=%f A\n ,

I m e a n )

11 I r m s = sqrt ( i n t e g r a t e ( ( 5 0s i n ( t h e t a ) ) 2 , t h e t a ,0,2*% p i ) / ( 2 * % p i ) )

12 mprintf ( RMS v a l u e o f c u r r e n t =%f A\n , I r m s )13 / / c a l c u l a t i n g t im e i n t e r v a l b et we en a maximum v a l u e

and n ex t z e r o v a lu e

14 t = ( % p i / 2 ) / ( 1 0 0 * % p i )15 mprintf ( Time i n t e r v a l b et we en a maximum v a l u e a nd

t h e n ex t z er o v al ue i s %f s e c t o %f s e c , t , 2 * t )16 / / v al ue o f g r e a t e s t r a t e o f c h a ng e o f c u r r e n t i s

g i v en wrong i n t he t e xt bo o k due t o a pp r ox im a ti on


1

2 i = linspace ( 0 , 0 , 2 )

3 t = linspace ( 0 , 1 , 2 )

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57


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4 plot2d ( t , i )

5 for j = 0 : 36 i = linspace ( 4 0 + 2 0 * j , 4 0 + 2 0 * j , 2 )

7 t = linspace ( j + 1 , j + 2 , 2 )

8 plot2d ( t , i )

9 if j = = 0 then

10 t = linspace ( j + 1 , j + 1 , 2 )

11 i = linspace ( 0 , 4 0 , 2 )

12 plot2d ( t , i )

13 else

14 t = linspace ( j + 1 , j + 1 , 2 )

15 i = linspace (40+20*(j-1) ,40+20*j,2)

16 plot2d ( t , i )17 end

18 end

19 for j = 1 : 3

20 i = linspace ( 1 0 0 - 2 0 * j , 1 0 0 - 2 0 * j , 2 )

21 t = linspace ( j + 4 , j + 5 , 2 )

22 plot2d ( t , i )

23 i = linspace (100-20*(j-1) ,100-20*j,2)

24 t = linspace ( j + 4 , j + 4 , 2 )

25 plot2d ( t , i )

26 end

27 i = linspace ( 4 0 , 0 , 2 )

28 t = linspace ( 8 , 8 , 2 )

29 plot2d ( t , i )

30 i = linspace ( 0 , 0 , 2 )

31 t = linspace ( 8 , 9 , 2 )

32 plot2d ( t , i )

33 for j = 0 : 3

34 i = linspace ( - ( 4 0 + 2 0 * j ) , - ( 4 0 + 2 0 * j ) , 2 )

35 t = linspace ( j + 9 , j + 1 0 , 2 )

36 plot2d ( t , i )

37 if j = = 0 then38 t = linspace ( j + 9 , j + 9 , 2 )

39 i = linspace ( 0 , - 4 0 , 2 )

40 plot2d ( t , i )

41 else

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42 t = linspace ( j + 9 , j + 9 , 2 )

43 i = linspace ( - 4 0 - 2 0* ( j - 1 ) , - 4 0 - 20 * j , 2 )44 plot2d ( t , i )

45 end

46 end

47 for j = 1 : 3

48 i = linspace ( - ( 1 0 0 - 2 0 * j ) , - ( 1 0 0 - 2 0 * j ) , 2 )

49 t = linspace ( j + 1 2 , j + 1 3 , 2 )

50 plot2d ( t , i )

51 i = linspace ( - 1 0 0 + 20 * ( j - 1 ) , - 1 0 0 + 20 * j , 2 )

52 t = linspace ( j + 1 2 , j + 1 2 , 2 )

53 plot2d ( t , i )

54 end55 i = linspace ( 0 , - 4 0 , 2 )

56 t = linspace ( 1 6 , 1 6 , 2 )

57 plot2d ( t , i )

58 xtitle ( P e r i o d i c c u r r e nt wave f o r ex am pl e 6 . 6 , t i m ei n s e c on d s , c u r r e n t )

59

60 / / c a l c u l a t i n g a v e ra g e v a lu e f o r t h i s wave s ha pe61 I a v g = ( 0 + 4 0 + 6 0 + 8 0 + 1 0 0 + 8 0 + 6 0 + 4 0 ) / 8

62 mprintf ( A v e ra ge v a lu e o f c u r re n t o f g i ve n wave

shape=%f A\n, I a v g )

63 // c a l c u l a t i n g RMS v a lu e f o r t he g i v en wave s ha pe64 I r m s = sqrt ( ( 0 ^ 2 + 4 0 ^ 2 + 6 0 ^ 2 + 8 0 ^ 2 + 1 0 0 ^ 2 + 8 0 ^ 2 + 6 0 ^ 2 + 4 0 ^ 2 )

/8)

65 mprintf ( RMS v a l u e o f c u r r e n t o f g i v e n wave s h a pe=%f A\n , I r m s )

66 // c a l c u l a t i n g form f a c t o r67 x = I r m s / I a v g

68 mprintf ( Form f a c t o r o f g i v e n wave f or m=%f \n ,x )69 // c a l c u l a t i n g peak f a c t o r70 I m a x = 1 0 0 / /maximum v a l u e o f c u r r e n t wa ve

71 y = I m a x / I r m s72 mprintf ( Peak f a c t o r o f g i v e n wave=%f \n ,y )73 // c a l c u l a t i n g a v er a ge and RMS v a lu e o f c u r r e nt

c o n s i d e r i n g t he wave t o be s i n u s o i d a l h av in g peakv al ue o f 100 A

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74 I a v g = i n t e g r a t e ( 100 / %pis i n ( t h e t a ) , t h e t a , 0 , % p i )75 mprintf ( A v er ag e v a l u e o f s i n e wave=%f A\n , I a v g )76 I r m s = sqrt ( i n t e g r a t e ( (10 0s i n ( th et a ) ) 2/ %pi , t h e t a

, 0 , % p i ) )

77 mprintf ( RMS v a l u e o f s i n e w av e=%f A , I r m s )


1

2 t h e t a = linspace (0,2*%pi ,100)

3 i = 1 0 + 1 0 * sin ( t h e t a ) // e x p r e s s i o n f o r t he r e s u l t a n t

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wave

4 plot2d ( t h e t a , i )5 xtitle ( Wave s h ap e f o r e xa mp le 6 . 7 , t h e t a , c u r r e n t )

6

7 / / c a l c u l a t i n g a v e ra g e v a lu e o f t he r e s u l t a n t wave8 I a v g = i n t e g r a t e ( 10+10s i n ( t h e t a ) , t h e t a , 0 , 2 * % p i )

/ ( 2 * % p i )

9 mprintf ( A v e ra ge v a lu e o f t he r e s u l t a n t c u r r e nt wave=%d A\n , I a v g )

10 // c a l c u l a t i n g RMS v a lu e o f c u r r e nt o f t he r e s u l t a n twave

11 I r m s = sqrt ( i n t e g r a t e ( ( 1 0+ 1 0s i n ( t h e t a ) ) 2 , t h e t a , 0 , 2 * % p i ) / ( 2 * % p i ) )

12 mprintf ( RMS v a l u e o f t h e r e s u l t a n t c u r r e n t wave=%f A , I r m s )


1

2 t h e t a = linspace (0,2*%pi ,100)3 i = 5 0 * sin ( t h e t a )

4 xset ( window ,0)5 plot2d ( t h e t a , i )

6 xtitle ( C u r r en t wave s h ap e f o r e xa mp le 6.8>( a ) , t h e t a , c u r r e n t )

7

8 xset ( window ,1)9 t h e t a = linspace (0, %pi ,100)

10 i = 5 0 * sin ( t h e t a )

11 plot2d ( t h e t a , i )12 t h e t a = linspace (%pi ,2*%pi ,100)

13 i = - 5 0 * sin ( t h e t a )

14 plot2d ( t h e t a , i )

15 xtitle ( C u r r en t wave s h ap e f o r e xa mp le 6.8>( b ) ,

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t h e t a , c u r r e n t )

1617 xset ( window ,2)18 t h e t a = linspace ( 0 , 0 , 2 )

19 i = linspace ( 0 , 5 0 , 2 )


21 t h e t a = linspace ( 0 , % p i , 2 )

22 i = linspace ( 5 0 , 5 0 , 2 )


24 t h e t a = linspace ( % p i , % p i , 2 )

25 i = linspace ( 5 0 , - 5 0 , 2 )


27 t h e t a = linspace ( % p i , 2 * % p i , 2 )28 i = linspace ( - 5 0 , - 5 0 , 2 )


30 i = linspace ( - 5 0 , 0 , 2 )

31 t h e t a = linspace ( 2 * % p i , 2 * % p i , 2 )


33 xtitle ( C u r r en t wave s h ap e f o r e xa mp le 6.8>( c ) , t h e t a , c u r r e n t )

34

35 xset ( window ,3)36 t h e t a = linspace ( 0 , % p i / 2 , 2 )

37 i = linspace ( 0 , 5 0 , 2 )


39 t h e t a = linspace ( % p i / 2 , % p i , 2 )

40 i = linspace ( 5 0 , 0 , 2 )


42 t h e t a = linspace ( % p i , 3 * % p i / 2 , 2 )

43 i = linspace ( 0 , - 5 0 , 2 )


45 t h e t a = linspace ( 3 * % p i / 2 , 2 * % p i , 2 )

46 i = linspace ( - 5 0 , 0 , 2 )

47 plot2d ( t h e t a , i )48 xtitle ( C u r r en t wave s h ap e f o r e xa mp le 6.8>( d ) ,

t h e t a , c u r r e n t )49

50 / / c o n s i d e r wave s ha pe ( a )

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51 mprintf ( Fo r w ave s ha pe ( a ) \nAs t he n e g a t i v e and

p o s i t i v e p a rt s o f t he wave a re e q u a l , r e a d i ng o f moving c o i l ammeter i s z e r o\n )52 I r m s = sqrt ( i n t e g r a t e ( (5 0s i n ( t h e t a ) ) 2 , t h e t a ,0,2*

% p i ) / ( 2 * % p i ) )

53 mprintf ( R e a d in g o f m ov in g i r o n a mm et er=%f A\n , I r m s)

54

55 / / c o n s i d e r wave s ha pe ( b )56 I a v g = i n t e g r a t e ( 5 0s i n ( t h e t a ) , t h e t a , 0 , % p i ) / % p i57 mprintf ( Fo r wave s ha pe ( b ) \ n R ea d in g o n t h e m ov in g

c o i l a mm et er=%f A\n , I a v g )

58 I r m s = sqrt ( i n t e g r a t e ( (5 0s i n ( t h e t a ) ) 2 , t h e t a ,0,2*% p i ) / ( 2 * % p i ) )

59 mprintf ( R e a d i n g o n m ov in g i r o n a mm et er=%f A\n , I r m s)

60

61 / / c o n s i d e r c a s e ( c )62 mprintf ( F o r wa ve s h a p e ( c ) \ n Av er ag e v a l u e o v er o ne

c om pl et e p e ri o d i s c l e a r l y z e r o . Thus r e ad i ng onmoving c o i l ammeter i s z e r o . As t he v a lu e o f c u r r e nt r em ai ns c o ns t a n t a t 50 A d u ri ng v a r i o u s

i n t e r v a l s , RMS v a lu e w i l l be 50 A o n ly . Hence ,r e a d i n g on m ov in g i r o n ammeter =50 A\n )63

64 / / c o n s i d e r c a s e ( d )65 I a v g = ( 0 + 1 0 + 2 0 + 3 0 + 4 0 + 5 0 + + 4 0 + 3 0 + 2 0 + 1 0 + 0 + ( - 1 0 ) + ( - 2 0 )

+ ( - 3 0 ) + ( - 4 0 ) + ( - 5 0 ) + ( - 4 0 ) + ( - 3 0 ) + ( - 2 0 ) + ( - 1 0 ) + 0 ) / 2 0

66 mprintf ( Fo r wave s ha pe ( d ) \ n Re ad in g on m ov in g c o i lammeter=%d\n , I a v g )

67 I r m s = sqrt

( ( 0 ^ 2 + 1 0 ^ 2 + 2 0 ^ 2 + 3 0 ^ 2 + 4 0 ^ 2 + 5 0 ^ 2 + 4 0 ^ 2 + 3 0 ^ 2 + 2 0 ^ 2 + 1 0 ^ 2 + 0 ^ 2 + ( - 1 0 )

^ 2 + ( - 2 0 ) ^ 2 + ( - 3 0 ) ^ 2 + ( - 4 0 ) ^ 2 + ( - 5 0 ) ^ 2 + ( - 4 0 ) ^ 2 + ( - 3 0 )

^ 2 + ( - 2 0 ) ^ 2 + ( - 1 0 ) ^ 2 + 0 ^ 2 ) / 2 0 )68 mprintf ( R e a d i n g o n m ov in g i r o n a mm et er=%f A\n , I r m s

)

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1

2 / / l e t u s a s su me V=1 V , T=1 s e c3 // e=V t /T4 V =1

5 T =1

6 E r m s = sqrt ( i n t e g r a t e ( (V t / T ) 2 , t ,0 , T ) / T)7 mprintf ( RMS v a l u e o f v o l t a g e i s %f t i m e s maximum

v o l t a g e\n , E r m s / V )8 E m e a n = i n t e g r a t e ( V t/T , t , 0 , T ) / T9 k = E r m s / E m e a n

10 mprintf ( Form f a c t o r o f t h i s wave=%f ,k )


1

2 / / t h e g r ap h i s drawn c o n s i d e r i n g R=%pi3 R = % p i

4 t h e t a = linspace (-%pi ,%pi ,100)

5 V = sqrt ( R ^ 2 - t h e t a ^ 2 )

6 plot2d ( t h e t a , V )

7 xtitle ( Wave s h ap e f o r e xa mp le 6 . 1 0 , t h e t a , V o l t a g e )

8 t h e t a = linspace (%pi ,3*%pi ,100)

9 V = - sqrt (R^2-(theta -2*%pi)^2)10 plot2d ( t h e t a , V )

11

12 V r m s = sqrt ( i n t e g r a t e ( (R2x 2 ) / ( 2R) , x , - R , R ) )

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13 mprintf ( RMS v a l u e o f s uc h a wave s ha pe w i l l be %f

o f i t s maximum v o l t a g e , V r m s / R )

Scilab code Exa 6.11 Example on Phase Difference

1

2 / / c o n s i d e r p a r t ( i )3 p h i = % p i / 1 2

4 mprintf ( Fo r p a r t ( i ) \ n Vo lt ag e l e a d s t he c u r re n t

wa ve by %d d e g r e e s \n , round ( p h i * 1 8 0 / % p i ) )5 f = 3 7 7 . 1 6 / ( 2 * % p i )6 mprintf ( F r e q u en c y o f t h e wa ve s h a p e=%d Hz\n ,f )7 / / c o n s i d e r p a r t ( i i )8 p h i = % p i / 3

9 mprintf ( F or p a r t ( i i ) \ n Vo lt ag e l e a d s t he c u r r e nt by% d d e g r e e s\n , round ( p h i * 1 8 0 / % p i ) )

10 mprintf ( F r e q u en c y o f t h e wa ve s h a p e=om eg a / ( 2p i ) \n)

11 / / c o n s i d e r p a r t ( i i i )12 p h i = 0 - ( - % p i / 2 )

13 mprintf ( F or p a r t ( i i i ) \ n Vo lt ag e l e a d s t he c u r r e n twa ve by %d d e g r e e s \n , round ( p h i * 1 8 0 / % p i ) )

14 mprintf ( F r e q u en c y o f t h e wa ve s h a p e=om eg a / p i \n )15 / / c o n s i d e r p a r t ( i v )16 mprintf ( Fo r p a r t ( i v ) \ n Cu rr en t wave l a g s t h e

v o l t a g e by an a n g l e =a l p h a+a t an ( x /R) and t h ef r e qu e n cy o f t h i s wave s ha pe i s omega / ( 2p i ) )

Scilab code Exa 6.13 Example on Simple AC Circuits

1

2 V = 2 3 0 // a p p l i e d v o l t a g e3 L = 6 0 D - 3 // i nd u ct an c e o f c o i l

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4 f = 5 0 / / f r e q u e n c y o f s u p pl y

5 X l = 2 * % p i * f * L6 I = 2 3 0 / X l

7 // i f f r e qu e n cy i s r ed uc ed t o 20 Hz8 X l = 2 * % p i * 2 0 * L

9 I 1 = V / X l

10 mprintf ( C ur re n t t hr ou gh t he c o i l i f f r eq u en c y i sr e d u c e d t o 2 0 Hz=%f A\n , I 1 )

11 // i f f r eq u en c y i s i n c r e a se d t o 60 Hz12 X l = 2 * % p i * 6 0 * L

13 I 2 = V / X l

14 mprintf ( C ur re n t t hr ou gh t he c o i l i f f r eq u en c y i s

i n c r e a s e d t o 6 0 Hz=%f A\n , I 2 )15 // i f f r eq u en c y i s i n c r e a se d t o 100 Hz16 X l = 2 * % p i * 1 0 0 * L

17 I 3 = V / X l

18 mprintf ( C ur re n t t hr ou gh t he c o i l i f f r eq u en c y i si n c r e a s e d t o 1 00 Hz=%f A\n , I 3 )

Scilab code Exa 6.14 Example on Simple AC Circuits

1

2 // c a l c u l a t i n g r e a c ta n ce o f c a p ac i t o r3 C = 1 0 0 D - 6

4 X c = 1 / ( 2 * % p i * 5 0 * C )

5 mprintf ( C a p a c i t i v e r e a c t a n c e , X c=%f ohm\n , X c )6 // c a l c u l a t i n g RMS v a lu e o f c u r r e nt7 V = 2 0 0

8 I r m s = V / X c

9 mprintf ( RMS v a l u e o f c u r r e n t =%f A\n , I r m s )

10 // c a l c u l a t i n g max c u r r e nt11 I m a x = I r m s * sqrt (2)12 mprintf ( Maximum c u r r e n t=%f A , I m a x )

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Chapter 7

AC Series Circuit

Scilab code Exa 7.1 Example on AC Series Circuit

1

2 / / c a l c u l a t i n g c u rr e n t f l ow i n g i n t h e c i r c u i t3 L = 0 . 1 / / i n d u c t a n c e4 f = 5 0 / / f r e q u e n c y5 X l = 2 * % p i * f * L

6 R = 1 5 // t o t a l r e s i s t a n c e i n t h e c i r c u i t

7 Z = sqrt ( R ^ 2 + X l ^ 2 )8 V = 2 3 0 // v o l t a g e a p p l i e d t o s e r i e s c i r c u i t9 I = V / Z

10 mprintf ( C ur re n t f l o w i n g i n t he c i r c u i t =%f A\n ,I )11 // c a l c u l a t i n g power f a c t o r12 p f = R / Z

13 mprintf ( Power f a c t o r o f t he c i r c u i t i s %f ( l a g g i n g ) \n V ol t ag e a c r o s s r e a c t o r =%f V\ n Vo lt ag e a c r o s sr e s i s t o r =%f V , p f , I * X l , I * R )

Scilab code Exa 7.2 Example on AC Series Circuit

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1

2 V 1 = 2 0 0 // v o l t a g e a p p l i e d t o noni n d u c t i v e l oa d3 I 1 = 2 0 // c u r r e nt f l o w i n g t hr ou gh t he l o ad4 R = V 1 / I 1

5 V = 2 3 0 // a p pl i ed v o l t a ge t o s e r i e s c on ne c t i o n o f R andL

6 I = I 1

7 Z = V / I

8 Xl = sqrt ( Z ^ 2 - R ^ 2 )

9 L = X l / ( 2 * % p i * 5 0 )

10 p h i = a t a n d ( X l / R )

11 mprintf ( I n d u ct a nc e o f t he r e a c t o r =%f H, p

Documents

Basic Electrical Engineering_A. Mittle and v. N. Mittle