toaz.info-basic-electrical-and-electronics-engineering-by-s-k-bhattacharya-pr_0bc4dcd75ad871e52fb39d20c354072d.pdf

 Basic Electrical Engineering A01_BHAT0000_01_FM.indd 1 3/8/11 1:56 PM  This page is intentionally left blank. A01_BHAT0000_01_FM.indd 2 3/8/11 1:56...

 Basic Electrical Engineering A01_BHAT0000_01_FM.indd 1 3/8/11 1:56 PM  This page is intentionally left blank. A01_BHAT0000_01_FM.indd 2 3/8/11 1:56 PM  Basic Electrical Engineering S. K. Bhattacharya Delhi Chennai Chandigarh A01_BHAT0000_01_FM.indd 3 3/8/11 1:56 PM  Copyright © 2011 Dorling Kindersley (India) Pvt. Ltd Licensees of Pearson Education in South Asia No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s prior written consent. This eBook may or may not include all assets that were part of the print version. The publisher reserves the right to remove any material present in this eBook at any time. ISBN 9788131754566 eISBN 9789332501126 Head Office: A-8(A), Sector 62, Knowledge Boulevard, 7th Floor, NOIDA 201 309, India Registered Office: 11 Local Shopping Centre, Panchsheel Park, New Delhi 110 017, India A01_BHAT0000_01_FM.indd 4 3/8/11 7:30 PM  Dedicated to my wife, Sumita, without whose patience and encouragement this work could not have been completed. A01_BHAT0000_01_FM.indd 5 3/8/11 1:56 PM  This page is intentionally left blank. A01_BHAT0000_01_FM.indd 6 3/8/11 1:56 PM  Contents Preface xxi About the Author xxiii 1. Basic Concepts, Laws, and Principles 1 1.1 Introduction 1 1.2 Atomic Structure and Electric Charge 2 1.3 Conductors, Insulators, and Semiconductors 2 1.4 Electric Field and Magnetic Field 4 1.5 Electric Current, Resistance, Potential, and Potential Difference 4 1.5.1 Electric Current 4 1.5.2 Resistance 5 1.5.3 Potential and Potential Difference 5 1.6 Ohm’s Law 5 1.7 The Effect of Temperature on Resistance 6 1.8 Work, Power, and Energy 8 1.8.1 Work 8 1.8.2 Power 9 1.8.3 Energy 9 1.8.4 Units of Work, Power, and Energy 10 1.9 Electromagnetism and Electromagnetic Induction 16 1.9.1 Introduction 16 1.9.2 Magnetic Field Around a Current-carrying Conductor 17 1.9.3 Magnetic Field Around a Coil 17 1.9.4 A Current-carrying Conductor Placed in a Magnetic Field 19 1.9.5 A Current-carrying Coil Placed in a Magnetic Field 20 1.10 Laws of Electromagnetic Induction 21 1.11 Induced EMF in a Coil Rotating in a Magnetic Field 22 1.12 EMF Induced in a Conductor 23 1.13 Dynamically Induced EMF and Statically Induced EMF 24 1.14 Self-induced EMF and Mutually Induced EMF 25 1.15 Self-inductance of a Coil 25 1.16 Mutual Inductance 28 A01_BHAT0000_01_FM.indd 7 3/8/11 1:56 PM  viii Contents 1.17 Inductance of Coils Connected in Series Having a Common Core 30 1.18 Energy Stored in a Magnetic Field 32 1.19 Electrical Circuit Elements 36 1.19.1 Resistors 36 1.19.2 Inductors 36 1.19.3 Capacitors 37 1.20 Energy Stored in a Capacitor 38 1.21 Capacitor in Parallel and in Series 39 1.22 Review Questions 40 2. DC Networks and Network Theorems 44 2.1 Introduction 44 2.2 DC Network Terminologies, Voltage, and Current Sources 45 2.2.1 Network Terminologies 45 2.2.2 Voltage and Current Sources 46 2.2.3 Source Transformation 48 2.3 Series–Parallel Circuits 50 2.3.1 Series Circuits 50 2.3.2 Parallel Circuits 50 2.3.3 Series–Parallel Circuits 51 2.4 Voltage and Current Divider Rules 52 2.4.1 Voltage Divider Rule 52 2.4.2 Current Divider Rule 53 2.5 Kirchhoff’s Laws 56 2.5.1 Kirchhoff’s Current Law 56 2.5.2 Kirchhoff’s Voltage Law 56 2.5.3 Solution of Simultaneous Equations Using Cramer’s Rule 57 2.5.4 Method of Evaluating Determinant 58 2.6 Maxwell’s Mesh Current Method 61 2.7 Nodal Voltage Method (Nodal Analysis) 64 2.8 Network Theorems 66 2.8.1 Superposition Theorem 66 2.8.2 Thevenin’s Theorem 78 2.8.3 Norton’s Theorem 91 2.8.4 Millman’s Theorem 101 2.8.5 Maximum Power Transfer Theorem 102 2.9 Star–Delta Transformation 112 2.9.1 Transforming Relations for Delta to Star 113 2.9.2 Transforming Relations for Star to Delta 114 A01_BHAT0000_01_FM.indd 8 3/8/11 1:56 PM  Contents ix 2.10 DC Transients 132 2.10.1 Introduction 132 2.10.2 Transient in R–L Circuit 133 2.10.3 Transient in R–C Circuit 137 2.11 Review Questions 142 3. AC Fundamentals and Single-phase Circuits 152 3.1 AC Fundamentals 152 3.1.1 Introduction 152 3.1.2 Generation of Alternating Voltage in an Elementary Generator 154 3.1.3 Concept of Frequency, Cycle, Time Period, Instantaneous Value, Average Value, and Maximum Value 155 3.1.4 Sinusoidal and Non-sinusoidal Wave Forms 156 3.1.5 Concept of Average Value and Root Mean Square (RMS) Value of an Alternating Quantity 157 3.1.6 Analytical Method of Calculation of RMS Value, Average Value, and Form Factor 160 3.1.7 RMS and Average Values of Half-wave-rectified Alternating Quantity 161 3.1.8 Concept of Phase and Phase Difference 162 3.2 Single-phase AC Circuits 168 3.2.1 Behaviour of R, L, and C in AC Circuits 168 3.2.2 L–R Series Circuit 175 3.2.3 Apparent Power, Real Power, and Reactive Power 177 3.2.4 Power in an AC Circuit 177 3.2.5 R–C Series Circuit 179 3.2.6 R–L–C Series Circuit 181 3.2.7 AC Parallel Circuits 184 3.2.8 AC Series—Parallel Circuits 211 3.3 Resonance in AC Circuits 218 3.3.1 Resonance in AC Series Circuit 218 3.3.2 Resonance in AC Parallel Circuits 229 3.4 Review Questions 236 4. Three-phase System 243 4.1 Introduction 243 4.2 Advantages of Three-phase Systems 244 4.3 Generation of Three-phase Voltages 244 4.4 Terms Used in Three-phase Systems and Circuits 247 4.5 Three-phase Winding Connections 248 4.5.1 Star Connection 248 4.5.2 Delta Connection 249 A01_BHAT0000_01_FM.indd 9 3/8/11 1:56 PM  x Contents 4.5.3 Relationship of Line and Phase Voltages, and Currents in a Star-connected System 249 4.5.4 Relationship of Line and Phase Voltages and Currents in a Delta-connected System 251 4.6 Active and Reactive Power 252 4.7 Comparison Between Star Connection and Delta Connection 253 4.8 Measurement of Power in Three-phase Circuits 261 4.8.1 One-Wattmeter Method 261 4.8.2 Two-Wattmeter Method 262 4.8.3 Three-Wattmeter Method 265 4.9 Review Questions 269 5. Electromagnetism and Magnetic Circuits 272 5.1 Magnets and Magnetic Fields 272 5.1.1 Field Around a Current-carrying Conductor 273 5.1.2 Magnetic Flux Density 274 5.1.3 Magnetic Field Strength 275 5.1.4 Permeability 276 5.1.5 Relative Permeability 277 5.2 Magnetic Field Due to Current-carrying Conductor Laws of Electromagnetism 277 5.2.1 Ampere’s Circuital Law 278 5.2.2 Biot-Savart Law 278 5.2.3 Application of Biot-Savart Law 279 5.3 Magnetization Curve of a Magnetic Material 283 5.4 Hysteresis Loss and Eddy Current Loss in Magnetic Materials 283 5.4.1 Hysteresis Loss 284 5.4.2 Eddy Current Loss 285 5.5 Magnetic Circuits 285 5.6 Comparison Between Magnetic and Electric Circuits 289 5.7 Magnetic Leakage and Fringing 290 5.8 Series and Parallel Magnetic Circuits 291 5.9 Attractive Force or the Lifting Power of Electromagnets 292 5.10 Review Questions 305 6. Transformers 309 6.1 Introduction 309 6.2 Applications of Transformers 310 6.3 Basic Principle and Constructional Details 311 6.3.1 Basic Principle 312 6.3.2 Constructional Details 313 A01_BHAT0000_01_FM.indd 10 3/8/11 1:56 PM  Contents xi 6.4 Core-type and Shell-type Transformers 315 6.4.1 Power Transformers and Distribution Transformers 316 6.5 Emf Equation 316 6.6 Transformer on No-load 318 6.7 Transformer on Load 319 6.8 Transformer Circuit Parameters and Equivalent Circuit 321 6.9 Phasor Diagram of a Transformer 324 6.10 Concept of Voltage Regulation 325 6.11 Concept of an Ideal Transformer 326 6.12 Transformer Tests 327 6.12.1 Open-circuit Test or No-load Test 327 6.12.2 Short-circuit Test 328 6.13 Efficiency of a Transformer 330 6.14 Condition for Maximum Efficiency 330 6.15 All-day Efficiency 332 6.16 Calculation of Regulation of a Transformer 332 6.17 Factors Affecting Losses in a Transformer 333 6.18 Solved Numerical Problems 334 6.19 Review Questions 349 7. DC Machines 354 7.1 Introduction and Principle of Working 354 7.1.1 Nature of Load Current When Output is Taken out Through Brush and Slip-ring Arrangement 355 7.1.2 Nature of Load Current When Output is Taken Through Brush and Commutator Arrangement 357 7.1.3 Function of Brush and Commutators in Motoring Action 358 7.2 Constructional Details 359 7.2.1 The Field System 359 7.2.2 The Armature 359 7.2.3 Armature Winding 361 7.2.4 Types of Armature Winding 361 7.3 EMF Equation of a DC Machine 363 7.3.1 Induced EMF is Equated to Flux Cut Per Second 364 7.4 Types of DC Machines 364 7.5 Characteristics of DC Generators 365 7.5.1 No-load Characteristics 365 7.5.2 Load Characteristics 366 7.6 Applications of DC Generators 368 7.7 Operation of a dc Machine As a Motor 368 7.7.1 Working Principle of a DC Motor 368 A01_BHAT0000_01_FM.indd 11 3/8/11 1:56 PM  xii Contents 7.7.2 Changing the Direction of Rotation 369 7.7.3 Energy Conversion Equation 369 7.8 Torque Equation 370 7.9 Starting a DC Motor 370 7.10 Speed Control of DC Motors 371 7.10.1 Voltage Control Method 372 7.10.2 Field Control Method 372 7.10.3 Armature Control Method 372 7.11 Starter for a DC Motor 372 7.11.1 Three-point Starter 372 7.11.2 Four-point Starter 374 7.12 Types and Characteristics of DC Motors 374 7.12.1 Characteristics of DC Shunt Motors 374 7.12.2 Characteristics of DC Series Motors 375 7.12.3 Characteristics of DC Compound Motors 376 7.13 Losses and Efficiency 377 7.13.1 Losses in a DC Machine 377 7.13.2 Efficiency of DC Machine 378 7.13.3 Condition for Maximum Efficiency 379 7.14 Applications of DC Machines 381 7.14.1 DC Generators 381 7.14.2 DC Motors 381 7.14.3 DC Series Motors 381 7.14.4 DC Compound Motors 381 7.15 Solved Numerical Problems 381 7.16 Review Questions 389 8. Three-phase Induction Motors 393 8.1 Introduction 393 8.2 Constructional Details 394 8.3 Windings and Pole Formation 396 8.4 Production of Rotating Magnetic Field 398 8.5 Principle of Working 399 8.6 Rotor-induced EMF, Rotor Frequency, Rotor Current 401 8.7 Losses in Induction Motors 403 8.8 Power Flow Diagram 403 8.9 Torque Equation 404 8.10 Starting Torque 406 8.11 Condition for Maximum Torque 406 8.12 Torque–Slip Characteristic 408 8.13 Variation of Torque–Slip Characteristic With Change in Rotor–Circuit Resistance 409 A01_BHAT0000_01_FM.indd 12 3/8/11 1:56 PM  Contents xiii 8.14 Starting of Induction Motors 411 8.14.1 Direct-on-Line Starting 412 8.14.2 Manual Star–Delta Starter 413 8.15 Speed Control of Induction Motors 415 8.16 Determination of Efficiency 417 8.16.1 No-load Test 418 8.16.2 Blocked-rotor Test 419 8.17 Applications of Induction Motors 419 8.18 Solved Numerical Problems 419 8.19 Review Questions 426 9. Single-phase Motors 430 9.1 Introduction to Single-phase Induction Motors 430 9.2 Constructional Details 430 9.3 Double Revolving Field Theory and Principle of Working of Single-phase Induction Motors 431 9.4 Torque–Speed Characteristic 433 9.5 Split–Phase Induction Motors 435 9.6 Shaded Pole Induction Motor 437 9.7 Single-phase AC Series Motors 438 9.8 Operation of a Series Motor on DC and AC (Universal Motors) 439 9.9 Single-phase Synchronous Motors 440 9.9.1 Reluctance Motors 440 9.9.2 Hysteresis Motors 441 9.10 Stepper Motors 441 9.11 Review Questions 442 10. Synchronous Machines 445 10.1 Introduction 445 10.2 Constructional Details of Synchronous Machines 446 10.3 Advantages of Stationary Armature and Rotating Field 447 10.4 Use of Laminated Sheets for the Stator and the Rotor 448 10.5 Armature Windings 448 10.6 Concept of Coil Span, Mechanical, and Electrical Degrees 449 10.7 Types of Windings 450 10.8 Induced EMF in a Synchronous Machine 451 10.8.1 EMF Equation 452 10.8.2 Distribution Factor 453 10.8.3 Pitch Factor 454 A01_BHAT0000_01_FM.indd 13 3/8/11 1:56 PM  xiv Contents 10.9 Open-circuit or No-load Characteristic 457 10.10 Synchronous Generator on Load 458 10.11 Synchronous Impedance and Voltage Drop Due to Synchronous Impedance 458 10.12 Voltage Regulation of a Synchronous Generator 460 10.13 Determination of Voltage Regulation by the Synchronous Impedance Method 461 10.14 Synchronous Generators Connected in Parallel to Supply a Common Load 464 10.14.1 Advantages of Parallel Operation 464 10.14.2 Parallel Connection of Alternators 464 10.14.3 Conditions for Parallel Connection and Synchronization 465 10.14.4 Load Sharing 465 10.15 Synchronous Motor 467 10.15.1 Introduction 467 10.15.2 Principle of Working of a Synchronous Motor 467 10.15.3 Effect of Change of Excitation of a Synchronous Motor 468 10.15.4 Application of Synchronous Motors 470 10.16 Review Questions 470 11. Measurement and Measuring Instruments 474 11.1 Introduction 474 11.2 Analog and Digital Instruments 476 11.3 Passive and Active Instruments 477 11.4 Static Characteristics of Instruments 477 11.4.1 Accuracy 477 11.4.2 Precision 478 11.4.3 Sensitivity and Resolution 478 11.4.4 Error, Threshold, and Loading Effect 480 11.5 Linear and Non-linear Systems 480 11.6 Dynamic Characteristics of Instruments 481 11.7 Classification of the Instrument System 481 11.7.1 Active and Passive Instruments 481 11.7.2 Analog and Digital Instruments 481 11.7.3 Indicating, Recording, and Integrating Instruments 482 11.7.4 Deflection- and Null-type Instruments 482 11.8 Measurement Error 483 11.9 Indicating-type Instruments 488 11.9.1 Permanent Magnet Moving Coil Instruments 488 11.9.2 Use of Shunts and Multipliers 492 11.9.3 Moving Iron Instruments 494 11.9.4 Dynamometer-type moving coil Instruments 496 A01_BHAT0000_01_FM.indd 14 3/8/11 1:56 PM  Contents xv 11.10 Measurement of Power 497 11.10.1 Power in dc and ac Circuits 497 11.10.2 Measurement of Power in Single-phase ac Circuit 498 11.10.3 Sources of Error in measurement using Dynamometer-type Wattmeters 500 11.11 Measurement of Energy 502 11.11.1 Introduction 502 11.11.2 Constructional details and working principle of Single-phase Induction-type Energy Meter 503 11.12 Instrument Transformers 505 11.12.1 Current Transformers 507 11.12.2 Potential Transformers 510 11.13 Megger and Measurement of Insulation Resistance 510 11.14 Multimeter and Measurement of Resistance 510 11.15 Review Questions 514 12. Transducers 518 12.1 Introduction 518 12.2 Classification of Transducers 518 12.3 Characteristics of a Transducer 520 12.4 Linear Variable Differential Transformer 520 12.5 Capacitive Transducers 522 12.6 Inductive Transducers 524 12.7 Potentiometric Transducer 525 12.8 Strain Gauge Transducer 527 12.9 Thermistors 528 12.10 Thermocouples 529 12.11 Hall Effect Transducers 531 12.12 Piezoelectric Transducer 532 12.13 Photoelectric Transducer 534 12.14 Selection of Transducers 534 12.15 Review Questions 536 13. Power Systems 538 13.1 Introduction 538 13.2 Generation of Electricity 539 13.3 Sources of Energy for Electricity Generation 539 13.4 Thermal Power Generation from Fossil-fuel 540 13.4.1 Coal-fired Thermal Power Stations 540 13.4.2 Gas-fired Thermal Power Stations 541 13.4.3 Oil- and Diesel-oil-fired Thermal Power Stations 542 13.5 Hydroelectric Power-generating Stations 542 A01_BHAT0000_01_FM.indd 15 3/8/11 1:56 PM  xvi Contents 13.6 Nuclear Power-generating Stations 544 13.7 Non-conventional or Alternative Generating Stations 546 13.7.1 Solar Electricity Generation 546 13.7.2 Wind Energy to Produce Electricity 547 13.7.3 Electricity from Biomass 547 13.7.4 Mini/Micro Hydel Power Generation 548 13.7.5 Electricity from Tidal Energy 548 13.7.6 Electricity from Ocean Energy 548 13.7.7 Electricity from Geothermal Energy 548 13.8 Transmission and Distribution of Electricity 549 13.8.1 AC Versus DC Transmission 550 13.8.2 Distribution System 550 13.8.3 Overhead Versus Underground Distribution Systems 550 13.8.4 Connection Schemes of Distribution System 551 13.9 Domestic Wiring 553 13.9.1 Service Connection 553 13.9.2 Service Mains 554 13.9.3 Distribution Board for Single-phase Installation 554 13.9.4 Neutral and Earth Wire 554 13.9.5 Earthing 555 13.9.6 System of Wiring 557 13.9.7 System of Connection of Lights, Fans and Other Electrical Loads 558 13.10 Circuit Protective Devices and Safety Precautions 560 13.10.1 Safety Precautions in Using Electricity 561 13.11 Efficient Use of Electricity   561 13.12 Review Questions 561 14. Semiconductor Devices 564 14.1 Introduction 564 14.2 Review of Atomic Theory 565 14.3 Binding Forces Between Atoms in Semiconductor Materials 566 14.4 Extrinsic Semiconductors 567 14.4.1 n-Type Semiconductor Material 567 14.4.2 P-Type Semiconductor Material 568 14.4.3 The p–n Junction 569 14.4.4 Biasing of p–n Junction 571 14.5 Semiconductor Diodes 573 14.5.1 Volt-ampere Characteristic of a Diode 574 14.5.2 An Ideal Diode 574 14.5.3 Diode Parameters and Diode Ratings 576 A01_BHAT0000_01_FM.indd 16 3/8/11 1:56 PM  Contents xvii 14.6 Zener Diode 577 14.6.1 Zener Diode As Voltage Regulator 578 14.6.2 Zener Diode As a Reference Voltage 578 14.7 Bipolar Junction Transistors 579 14.7.1 Working of a n–p–n Transistor 580 14.7.2 Working of a p–n–p Transistor 581 14.7.3 Transistor Configurations 583 14.7.4 Transistor As an Amplifier 585 14.7.5 Transistor As a Switch 587 14.8 Field Effect Transistors 588 14.8.1 Junction Field Effect Transistors 589 14.8.2 FET Applications 590 14.9 MOSFET 591 14.9.1 The Enhancement MOSFET (EMOSFET) 592 14.9.2 The Depletion MOSFET 593 14.9.3 Static Characteristics of MOSFET 594 14.9.4 Applications of MOSFET 594 14.10 Silicon-controlled Rectifier 595 14.10.1 Characteristics of SCR 595 14.10.2 Two-transistor Analogy of an SCR 597 14.10.3 Applications of SCR 598 14.11 DIAC 600 14.12 TRIAC 600 14.13 Optoelectronic Devices 602 14.13.1 Light-dependent Resistor 603 14.13.2 Light-emitting Diodes 604 14.13.3 Seven Segment Displays 605 14.13.4 Liquid Crystal Displays 606 14.13.5 Photodiodes 606 14.13.6 Photovoltaic Cells or Solar Cells 607 14.13.7 Phototransistors 607 14.13.8 Photo-darlington 609 14.13.9 Optocouplers 609 14.14 Review Questions 610 15. R  ectifiers and Other Diode Circuits 614 15.1 Rectifiers 614 15.1.1 Introduction 614 15.1.2 Half-wave Rectifier 614 15.1.3 Analysis of Half-wave Rectifier 615 15.1.4 Full-wave Rectifier 620 15.1.5 Full-wave Bridge Rectifier 621 A01_BHAT0000_01_FM.indd 17 3/8/11 1:56 PM  xviii Contents 15.1.6 Analysis of Full-wave Rectifiers 622 15.1.7 Comparison of Half-wave and Full-wave Rectifiers 624 15.2 Filters 627 15.3 Applications of Diodes in Clipping and Clamping Circuits 629 15.3.1 Negative and Positive Series Clippers 629 15.3.2 Shunt Clippers 630 15.3.3 Biased Clippers 631 15.3.4 Clamping Circuits 631 15.4 Review Questions 633 16. Digital Electronics 635 16.1 Introduction 635 16.2 Number Systems 636 16.2.1 Decimal Number System 636 16.2.2 Binary Number System 637 16.2.3 Conversion of Binary to Decimal 637 16.2.4 Conversion of Decimal to Binary 638 16.2.5 Binary Addition 640 16.2.6 Binary Subtraction 641 16.2.7 Binary Multiplication 642 16.3 Octal Number System 642 16.4 Hexadecimal Number System 643 16.4.1 Application of Binary Numbers in Computers 644 16.5 Logic Gates 644 16.5.1 NOT Gate 645 16.5.2 OR Gate 646 16.5.3 AND Gate 646 16.5.4 NAND Gate 647 16.5.5 NOR Gate 647 16.6 Boolean Algebra 648 16.6.1 Boolean Expressions 648 16.7 De Morgan’s Theorem 650 16.8 Combinational Circuits 651 16.9 Simplification of Boolean Expressions Using De Morgan’s Theorem 657 16.10 Universal Gates 658 16.10.1 Use of NAND Gate to Form the Three Basic Gates 658 16.10.2 Use of NOR Gate to Form the Three Basic Gates 659 16.11 Flip-flops 659 16.11.1 RS Flip-flop 659 16.11.2 Gated or Clocked RS Flip-flop 661 A01_BHAT0000_01_FM.indd 18 3/8/11 1:56 PM  Contents xix 16.11.3 JK Flip-flop 662 16.11.4 D Flip-flops 662 16.11.5 T Flip-flops (Toggle Flip-flop) 663 16.11.6 Master–Slave JK Flip-flop 663 16.11.7 Counters and Shift Registers 663 16.11.8 Arithmetic Circuits 664 16.11.9 Memory Function or Data Storage 664 16.11.10 Digital Systems 664 16.12 Review Questions 665 17. Integrated Circuits 668 17.1 Introduction 668 17.2 Fabrication of Monolithic ICs 669 17.3 Hybrid Integrated Circuits 670 17.4 Linear and Digital ICs 670 17.5 Operational Amplifiers 671 17.6 Op-amp Applications 673 17.6.1 Op-amp As a Summing Amplifier 674 17.6.2 Op-amp As a Differential Amplifier (Subtractor) 675 17.6.3 Op-amp As a Derivative Amplifier 676 17.6.4 Op-amp As an Integrator 676 17.6.5 Other Applications of Op-amps 677 17.7 The 555 Timer Integrated Circuit 677 17.7.1 Three Operating Modes of IC 555 678 17.7.2 Pin Configuration of IC 555 678 17.7.3 Functional Block Diagram of IC 555 679 17.7.4 Monostable Application of IC 555 680 17.7.5 Astable Application of IC 555 682 17.7.6 An IC 555 Timer Astable Oscillator Circuit 683 17.8 IC Voltage Regulators or Regulator ICs 684 17.9 Digital Integrated Circuits 686 17.10 Review Questions 694 Index 697 A01_BHAT0000_01_FM.indd 19 3/8/11 1:56 PM  This page is intentionally left blank. A01_BHAT0000_01_FM.indd 20 3/8/11 1:56 PM  Preface This comprehensive book on basic electrical engineering has been prepared by consulting the syllabus of all the Indian universities. The content of the book covers almost all the topics of basic electrical engi- neering, ranging from circuits to machines to measurements to power systems. An introduction to basic electronics has also been provided so as to prepare the students for an in-depth study later. The chapters have been developed using the basic principles of learning and motivation. Easy explanation of topics, plenty of examples and illustrations, practice problems and multiple choice questions with answers, and short answer type review questions are the principal features of this book. This book has been developed on the basis of my long experience in teaching the subject to first year B.Tech. students at a number of different engineering colleges. My experience as a technical teacher/ trainer has helped me to prepare the text in a way that is suitable for students of the first year of B.Tech. The manuscript of this book was reviewed by experienced teachers of various engineering colleges all over India. Their suggestions were incorporated while preparing the final manuscript. Although a number of books are available on this subject, the user friendliness of this book will definitely make it popular among students and teachers alike. I am thankful to the publisher, Pearson Education, for bringing out this book on time and in such a presentable form. PowerPoint slides have also been prepared to illustrate the key concepts. These slides can be used for presentation in the classroom by the teachers and can also be studied individually by the students. Additional study material on certain topics and solutions to all the numerical questions given at the end of each chapter are available on the publisher’s Web site. S. K. BHATTACHARYA A01_BHAT0000_01_FM.indd 21 3/8/11 1:56 PM  This page is intentionally left blank. A01_BHAT0000_01_FM.indd 22 3/8/11 1:56 PM  About the Author Dr S. K. Bhattacharya is currently the principal of SUS Women’s Engineering College, Mohali. Formerly, he was the principal of Technical Teachers’ Training Institute, Chandigarh; Director of National Institute of Technical Teachers’ Training and Research (NITTTR), Kolkata; and Director of Hindustan Institute of Technology, Greater Noida. Dr Bhattacharya graduated in electrical engineering from Jadavpur University, obtained his M.Tech. degree from Calcutta University and his Ph.D. from Birla Institute of Technology and Sci- ence, Pilani. As a senior fellow of MHRD, Government of India, he attended the technical teacher’s training programme at the Bengal Engineering College, Shibpur. On Dutch Government’s fellowship programme, he attended a one-year teacher training programme at the Netherlands and the UK, and six months’ fellowship programme of British Council on educational technology at Sheffield, UK. Dr Bhattacharya has visited many institutions in India and in countries like the UK, the Netherlands, Australia, Japan, Korea, Philippines, Malaysia, etc. He is a fellow of the Institution of Engineers and the Institution of Electronics and Telecommunication Engineers. A large number of popular books, technical papers, non-print type teaching and learning materials have been published by Dr Bhattacharya. A01_BHAT0000_01_FM.indd 23 3/8/11 1:56 PM  1 Basic Concepts, Laws, and Principles TOPICS DISCUSSED  The need to study electrical and electron-  Effect of temperature on resistance ics engineering  Electromagnetism and electromagnetic  Behaviour of materials as conductors, induction semiconductors, and insulators  Laws of electromagnetic induction  Concept of current, resistance, potential,  Dynamically and statically induced EMF and potential difference  Self and mutual inductance  Differences between electric field and mag-  Electrical circuit elements netic field  Ohm’s law 1.1 introduction We see applications of electricity all around us. We observe the presence of electricity in nature. It is indeed amazing as well as interesting to know how mankind has been able to put electricity for its use. All electronic and electrical products operate on electricity. Be it your computer system, cell phones, home entertainment system, lighting, heating, and air-conditioning systems—all are exam- ples of applications of electricity. Application of electricity is limitless and often extends beyond our imagination. Electrical energy has been accepted as the form of energy which is clean and easy to transmit from one place to the other. All other forms of energy available in nature are, therefore, transformed into electrical energy and then transmitted to places where electricity is to be used for doing some work. Electrical engineering, therefore, has become a discipline, a branch of study which deals with genera- tion, transmission, distribution, and utilization of electricity. M01_BHAT0000_01_C01.indd 1 3/3/11 11:35 AM  2 Basic Electrical Engineering Electronics engineering is an offshoot of electrical engineering, which deals with the theory and use of electronic devices in which electrons are transported through vacuum, gas, or semiconductors. The motion of electrons in electronic devices like diodes, transistors, thyristors, etc. are controlled by electric fields. Modern computers and digital communication systems are advances of electronics. Introduction of very large scale integrated (VLSI) circuits has led to the miniaturization of all electronic systems. Electrical and electronic engineering are, therefore, very exciting fields of study. A person who is unaware of the contribution of these fields of engineering and the basic concepts underlying the advance- ment, will only have to blame himself or herself for not taking any initiative in knowing the unknown. In this chapter, we will introduce some basic concepts, laws, and principles which the students might have studied in physics. However, since these form the basis of understanding of the other chapters in this book, it will be good to study them again. 1.2 Atomic Structure and Electric Charge Several theories have been developed to explain the nature of electricity. The modern electron theory of matter, propounded by scientists Sir Earnest Rutherford and Niel Bohr considers every matter as electri- cal in nature. According to this atomic theory, every element is made up of atoms which are neutral in nature. The atom contains particles of electricity called electrons and protons. The number of electrons in an atom is equal to the number of protons. The nucleus of an atom contains protons and neutrons. The neutrons carry no charge. The protons carry positive charge. The electrons revolve round the nucleus in elliptical orbits like the planets around the sun. The electrons carry negative charge. Since there are equal number of protons and electrons in an atom, an atom is basically neutral in nature. If from a body consisting of neutral atoms, some electrons are removed, there will be a deficit of electrons in the body, and the body will attain positive charge. If neutral atoms of a body are supplied some extra electrons, the body will attain negative charge. Thus, we can say that the deficit or excess of electrons in a body is called charge. Charge of an electron is very small. Coulomb is the unit of charge. The charge of an electron is only 1.602 × 10-19 Coulomb (C). Thus, we can say that the number of electrons per Coulomb is the reciprocal of 1.602 × 10-19 which equals approx. 6.28 × 1018 electrons. Therefore, charge of 6.28 × 1018 electrons is equal to 1C. When we say that a body has a positive charge of 1C, it is understood that the body has a deficit of 6.28 × 1018 electrons. Any charge is an example of static electricity because the electrons or protons are not in motion. You must have seen the effect of charged particles when you comb your hair with a plastic comb, the comb attracts some of your hair. The work of combing causes friction, producing charge of extra electrons and excess protons causing attraction. Charge in motion is called electric current. Any charge has the potential of doing work, i.e., of mov- ing another charge either by attraction or by repulsion. A charge is the result of separating electrons and protons. The charge of electrons or protons has potential because it likes to return back the work that was done to produce it. 1.3 Conductors, Insulators, and Semiconductors The electrons in an atom revolve in different orbits or shells. The shells are named as K, L, M, N, etc. The number of electrons that should be in a filled inner shell is given by 2n2 where n is shell number M01_BHAT0000_01_C01.indd 2 3/3/11 11:35 AM  Basic Concepts, Laws, and Principles 3 1, 2, 3, 4, etc. starting from the nearest one, i.e., first shell to the nucleus. If n = 1, the first shell will contain two electrons. If n = 2, the second shell will contain eight electrons. This way, the number of electrons in the shells are 2, 8, 18, 32, etc. The filled outermost shell should always contain a maxi- mum number of eight electrons. The outermost shell of an atom may have less than eight electrons. As for example, copper has an atomic number of 29. This means, copper atom has 29 protons and 29 electrons. The protons are concentrated in the nucleus while the electrons are distributed in the K, L, M, and N shells as 2, 8, 18, and 1 electrons, respectively. The outermost shell of a copper atom has one electron only whereas this shell could have 8 electrons. The position occupied by an electron in an orbit signifies its energy. There exists a force of attraction between the orbiting electron and the nucleus due to the opposite charge the of electron and the proton. The electrons in the inner orbits are closely bound to the nucleus than the electrons of the outer or out- ermost orbit. If the electron is far away from the nucleus, the force of attraction is weak, and hence the electrons of outermost orbit are often called free electrons. For example, a copper atom has only one atom in the last orbit which otherwise could have eight electrons. In a copper wire consisting of large number of copper atoms, the atoms are held close together. The outermost electrons of atoms in the copper wire are not sure about which atom they belong to. They can move easily from one atom to the other in a random fashion. Such electrons which can move easily from one atom to the other in a random fashion are called free electrons. It is the movement of free electrons in a material like copper that constitutes flow of current. Here, of course, the net current flow will be zero as the movement of the free electrons is in random directions. When we apply a potential, which is nothing but a force, it will direct the flow of electrons in a particular direction, i.e., from a point of higher potential towards a point of lower potential. Thus, current flow is established between two points when there exists a potential difference between the points. When in a material the electrons can move freely from one atom to another atom, the material is called a conductor. Silver, copper, gold, and aluminium are good conductors of electricity. In general, all metals are good conductors of electricity. Although silver is the best conductor of electricity, the sec- ond best conductor, i.e., copper, is mostly used as conductor because of the cost factor. In electrical and electronic engineering fields, the purpose of using a conductor as carrier of electricity is to allow electric current to flow with the minimum of resistances, i.e., the minimum of opposition. In a material where the outermost orbit of the atoms is completely filled, the material is called an insu- lator. Insulators like glass, rubber, mica, plastic, paper, air, etc. do not conduct electricity very easily. In the atoms of these materials, the electrons tend to stay in their own orbits. However, insulators can store electricity and can prevent flow of current through them. Insulating materials are used as dielectric in capacitors to store electric charge, i.e., electricity. Carbon, silicon, and germanium having atomic numbers of 6, 14, and 32, respectively, are called semi conducting material. The number of electrons in the outermost orbit of their atoms is four instead of the maximum of eight. Thus, in the outermost orbit of a semiconductor material, there are four vacant positions for electrons. These vacant positions are called holes. In a material, the atoms are so close together that the electrons in the outermost orbit or shell behave as if they were orbiting in the outermost shells of two adjacent atoms producing a binding force between the atoms. In a semiconductor material the atoms forming a bonding, called covalent bonding, share their electrons in the outermost orbit, and thereby attain a stable state. The condition is like an insulator having all the eight positions in the outer- most orbit filled by eight electrons. However, in semiconducting materials, with increase in temperature it is possible for some of the electrons to gain sufficient energy to break the covalent bonds and become free electrons, and cause the flow of current. M01_BHAT0000_01_C01.indd 3 3/3/11 11:35 AM  4 Basic Electrical Engineering 1.4 Electric Field and Magnetic Field When charges are separated, a space is created where forces are exerted on the charges. An elec- tric field is such a space. Depending upon the polarity of the charges, the force is either attractive or repulsive. Therefore, we can say that static charges generate an electric field. An electric field influences the space surrounding it. Electric field strength is determined in terms of the force exerted on charges. A capacitor is a reservoir of charge. The two parallel plates of a capacitor, when connected to a voltage source, establishes an electric field between the plates. The positive termi- nal, or pole of the voltage source will draw electrons from plate 1 whereas the negative pole will push extra electrons on to plate 2. Voltage across the capacitor will rise. The capacitor gets charged equal to the voltage of the source. The capacitance of a capacitor is a measure of its ability to store charge. The capacitance of a capacitor is increased by the presence of a dielectric material between the two plates of the capacitor. A current-carrying conductor or a coil produces magnetic field around it. The strength of the mag- netic field produced depends on the magnitude of the current flowing through the conductor or the coil. There is presence of magnetic field around permanent magnets as well. A magnet is a body which attracts iron, nickel, and cobalt. Permanent magnets retain their magnetic properties. Electromagnets are made from coils through which current is allowed to flow. Their mag- netic properties will be present as long as current flows through the coil. The space within which forces are exerted by a magnet is called a magnetic field. It is the area of influence of the magnet. 1.5 Electric Current, Resistance, Potential, and Potential Difference 1.5.1 Electric Current In any conducting material, the flow of electrons forms what is called current. Electrons have negative charge. Charge on an electron is very small. For this reason charge is expressed in terms of Coulomb. Charge of one Coulomb is equal to a charge of 6.28 × 1018 electrons. The excess or deficit of electrons in a body is called charge. Thus, electrical current is expressed as a flow of negative charge, i.e., electrons. Any substance like copper, aluminum, silver, etc. which has a large number of free electrons (i.e., loosly bound electrons in the outermost orbit of its atom) will permit the flow of electrons when electrical pres- sure in the form of EMF (electromotive force, i.e., voltage) is applied. Since these materials conduct electricity, they are called conductors. They easily allow electric cur- rent to flow through them. The strength of current will depend upon the flow of charge per unit time. This is expressed as Q Current, I = (1.1) t where charge Q is measured in Coulomb and time, t in seconds. The unit of current, therefore, is Coulomb per second, when 1 C of charge flows in 1 s; the magnitude of current is called ampere, named after André-Marie Ampere. Thus, 1 ampere of current is equivalent to the flow of charge of 1 Coulomb per second. In earlier years, current was assumed to flow from positive to negative terminals. This convention is used even now although it is known that current is due to the movement of electrons from the negative to the positive terminal. M01_BHAT0000_01_C01.indd 4 3/3/11 11:35 AM  Basic Concepts, Laws, and Principles 5 1.5.2 Resistance Electrical resistance is the hindrance or opposition to the flow of electrons in a given material. It is measured in unit called ohm. Since current is the flow of electrons, resistance is the opposition offered by a material, to the flow of free electrons. Resistance, R, is directly proportional to the length of the material, and inversely proportional to the area of the cross section of the material, through which current flows. The resistance offered by conducting materials like copper and aluminum is low whereas resistance offered by some other conduct- ing materials like nicrome, tungsten, etc. is very high. All these materials are called conducting materials. However, the values of resistivity of these materials are different. The resistance, R of a material is expressed as  R =ρ (1.2) A where r is the resistivity, l is the length and A is the cross-sectional area of the conducting material. The resistivity, r is also called the specific resistance of the material. The most conducting material, silver has the lowest value of resistivity, i.e., 0.016 × 10–6 ohm-m. After silver, copper is most conducting. The resistivity or specific resistance of copper is somewhat more than that of silver, i.e., 0.018 × 10–6 ohm-m. That is to say, copper is less conducting than silver. We will see a little later why and how the value of resistance changes with temperature. 1.5.3 Potential and Potential Difference EMF produces a force or pressure that causes the free electrons in a body to move in a particular direction. The unit of EMF is volt. EMF is also called electric potential. When a body is charged (i.e., either defficiency of electrons or excess of electrons is created), an amount of work is done. This work done is stored in the body in the form of potential energy. Such a charged body is capable of doing work by attracting or repelling other charges. The ability of a charged body to do work in attracting or repelling charges is called its potential or electrical potential. Work done to charge a body to 1 C is the measure of its potential expressed in volts: Work done in Joules Volt = (1.3) Charge in Coulombs When work done is 1 joule and charge moved is 1 C, the potential is called 1 volt. If we say that a point has a potential of 6 volts, it means that 6 Joules of work has been done in moving 1 C of charge to that point. In other words, we can say that every Coulomb of charge at that point has an energy of 6 Joules. The potential difference of two points indicates the difference of charged condition of these points. Suppose point A has a potential of 6 volts, and point B has a potential of 3 volts. When the points A and B are joined together by a conducting wire, electrons will flow from point B to point A. We say that current flows from point A towards point B. The direction of current flow is taken from higher potential to lower potential while the flow of electrons are actually in the opposite direction. The flow of current from higher potential to lower potential is similar to the flow of water from a higher level to a lower level. 1.6 Ohm’s Law George Simon Ohm found that the voltage, V between two terminals of a current-carrying conductor is directly proportional to the current, I flowing through it. The proportionality constant, R is the resistance of the conductor. Thus, according to Ohm’s law V V = IR Or, l = (1.4) R This relation will hold good provided the temperature and other physical conditions do not change. M01_BHAT0000_01_C01.indd 5 3/3/11 11:35 AM  6 Basic Electrical Engineering I V R=3 R=2 R=1 slope = 1 R slope = R 0 V I (a) (b) Figure 1.1 (a) Shows linear relationship between V and I; (b) V–I characteristics for different values of R Ohm’s law is not applicable to nonlinear devices like Zener diode, voltage regulators, etc. Ohm’s law is expressed graphically on V and I-axies as a straight line passing through the origin as shown in Fig. 1.1 (a). The relationship between V and I have been shown for different values of R in Fig. 1.1 (b). Here in V = RI, R indicates the slope of the line. The more the value of R is, the more will be the slope of the line as shown in Fig. 1.1 (b). 1.7 The Effect of Temperature on Resistance Resistance of pure metals like copper, aluminum, etc. increases with increase in temperature. The varia- tion of resistance with change in temperature has been shown as a linear relationship in Fig. 1.2. The change in resistance due to change in temperature is found to be directly proportional to the ini- tial resistance, i.e., Rt – R0 ∝ R0. Resistance (Rt – R0) also varies directly as the temperature rise and this change also depends upon the nature of the material. Thus we can express the change in resistance as, Rt - R0 ∝ R0t or, Rt - R0 = a0 R0t, where α0 is called the temperature coefficient of resistance at 0°C. or, Rt = R0 (1 + a0t) (1.5) R R R2 Rt R2−R1 R0 is the resistance at 0°C R1 Rt is the resistance at t°C t2− t1 R0 Rt Rt − R0 R0 Slope = t R0 −234.5° 0 t t 0 t1 t2 t (a) (b) Figure 1.2 (a) Shows the variation of resistance with temperature; (b) resistances at two different temperatures M01_BHAT0000_01_C01.indd 6 3/3/11 11:35 AM  Basic Concepts, Laws, and Principles 7 This expression can be applied for both increase and decrease in temperature. From the graph of Fig. 1.2 (a) it is seen that resistance of the material continues to decrease with decrease in temperature below 0°C. If we go on decreasing the temperature to a very low value, the material attains a state of zero resistance. The material at that state becomes superconducting, i.e., conducting with no resistance at all. Now suppose a conductor is heated from temperature t1 to t2. The resistance of the conductor at t1 is R1 and at t2 is R2 as has been shown in Fig. 1.2 (b). Using eq. (1.5), R t = R 0 (1 + α 0 t) or, α0 = R t – R 0 R0 t (R t – R 0 ) / t slope of resistance versuus temp. graph or, α0 = = (1.6) R0 original resistance Using eq. (1.5), we can write R 1 = R 0 (1 + α 0 t1 ) and R 2 = R 0 (1 + α 0 t 2 ) From fig 1.2 (b) using the relation in (1.6), we can write (R – R 1 ) / ( t 2 – t1 ) α1 = 2 R1 or, α1R 1 (t 2 – t1 ) = R 2 – R 1 or, R 2 = R 1 + α1R 1 (t 2 – t1 ) or, R 2 = R 1[1 + α1 (t 2 – t1 )] (1.7) Thus, if resistance at any temperature t1 is known, the resistance at t2 temperature can be calculated. Calculation of a at different temperatures We have seen, slope of resistance versus temp. graph α0 = Orriginal resistance, R 0 If α1 and α2 are the temperature coefficients of resistance at t1 and t2 degrees, respectively, then slope of resistance versus temp. graph α1 = R1 slope of resistance versus temp. graph and α2 = R2 Thus, we can write, α 0 R 0 = α1 R 1 = α 2 R 2 = α 3 R 3 =... and so on Therefore, α0 R 0 α0 R 0 α0 α1 = = = (1.8) R1 R 0 (1 + α 0 t1 ) 1 + α 0 t1 M01_BHAT0000_01_C01.indd 7 3/3/11 11:35 AM  8 Basic Electrical Engineering α0 R 0 α2 = R2 α0 R 0 α0 = = R 0 (1 + α 0 t 2 ) 1 + α 0 t 2 and, α 2 R 2 = α1 R 1 α1 R 1 α1 R 1 or, α2 = = R2 R 1 [1 + α1 (t 2 – t1 )] α1 or, α2 = (1.9) 1 + α1 (t 2 – t1 ) Temperature coefficient of resistance, α at 20°C and specific resistance r of certain material have been shown in Table 1.1. Table 1.1 Temperature Coefficient and Specific Resistance of Different Materials Material Temp. coeff. of resistance a20 Specific resistance r in micro–ohm Silver 0.004 0.016 Copper 0.0039 0.018 Aluminium 0.0036 0.028 Iron 0.005 0.100 Brass 0.0015 0.070 Lead 0.0042 0.208 Tin 0.0046 0.110 Carbon -0.00045 66.67 It is to be noted that carbon has a negative temperature coefficient of resistance. This means, the resistance of carbon decreases with increase in temperature. By this time you must be wondering as to why resistance in most materials increases with increase in temperature while resistance in some decreases with increase in temperature. The charged particles inside a material is in the state of vibration. Temperature rise in most materials increases this vibration inside the material obstructing the flow of electrons. Obstruction to the flow of electrons is called resistance. At lower temperatures the vibration gets reduced, and hence the resistance. 1.8 Work, Power, and Energy 1.8.1 Work When a force is applied to a body causing it to move, and if a displacement, d is caused in the direction of the force, then Work done = Force × Distance (1.10) or, W=F×D If force is in Newtons and d is in meters, then work done is expressed in Newton–meter which is called Joules. M01_BHAT0000_01_C01.indd 8 3/3/11 11:35 AM  Basic Concepts, Laws, and Principles 9 1.8.2 Power Power is the rate at which work is done, i.e., rate of doing work. Thus, work done Joules Power, P = = (1.11) time seconds The unit of power is Joules/second which is also called Watt. When the amount of power is more, it is expressed in Kilowatt, i.e., kW. 1 kW = 1 × 103 W We have earlier seen in eq. (1.3), that electrical potential, V is expressed as work done W V= = charge Q  Q or, Work done = VQ = VIt     ∵ I = t    work done VIt Electrical Power, P = = = VI Watts (1.12) t t Thus in a circuit if I is the current flowing, and V is the applied voltage across the terminals, power, P is expressed as V V2 P = VI = V = R R Also, P = VI = IR.I = I 2 R Thus electrical power can be expressed as V2 P = VI = = I 2 R Watts (1.13) R Where V is in Volts, I is in Amperes, and R is in Ohms 1.8.3 Energy Energy is defined as the capacity for doing work. The total work done in an electrical circuit is called electrical energy. When a voltage, V is applied, the charge, Q will flow so that Electrical energy = V × Q        = VIt        = IRIt        = I2Rt V2         = t R   or, Electrical energy = Power × Time (1.14) If power is in kW and time is in hour, the unit of energy will be in Kilowatt hour or kWh. M01_BHAT0000_01_C01.indd 9 3/3/11 11:36 AM  10 Basic Electrical Engineering 1.8.4 Units of Work, Power, and Energy In SI unit, work done is the same as that of energy. Mechanical work or energy When a Force, F Newton acting on a body moves it in the direction of the force by a distance d meters: Work done = F × D     Nm or Joules When a force F Newton is applied tangentially on a rotating body making a radius r meters, then Work done in 1 revolution = F × 2pr (since distance moved is 2pr) = 2pFr Nm Force × Perpendicular distance = Torque, i.e., F × r = T Work done in 1 revolution = 2pT Nm ∴   Work done in N revolutions/second = 2pTN Nm If N is expressed in revolutions per minute (rpm) 2 πTN Work done = Nm or Joules (1.15) 60 When a body of mass m kg is lifted to a height h meters against the gravitational force g m/sec2, work done is converted into potential energy of the body. Potential energy = Weight × Height = mgh Joules. (1.16) 1 Kinetic energy of a body of mass m kg moving at a speed of n meters/sec2 = mv 2 Joules. (1.17) 2 Electrical energy As mentioned earlier, work done in an electrical circuit is its energy. Electrical energy = Applied voltage, V × total flow of charge, Q = VQ = VIt = IRIt = I2Rt V2 = t R work done VIt Electrical power = = = VI time t Electrical energy = Electrical power × time (1.18) If electrical power is expressed is kW and time in hour, then Electrical energy = kWh (1.19) We will now convert kWh into Calories 1 kWh = 103 × 60 × 60 Watt second or Joules = 36 × 105 Joules M01_BHAT0000_01_C01.indd 10 3/3/11 11:36 AM  Basic Concepts, Laws, and Principles 11 Since 1 Calorie = 4.2 Joules 36 × 105 1 kWh = = 860 × 103 Calories 4.2 or, l kWh = 860 kiloCalories (1.20) Thermal energy In SI unit* thermal energy is expressed in calories. One calorie indicates the amount of heat required to raise the temperature of 1 gm of water by 1°C. This heat is also called the specific heat. If m is the mass of the liquid, S is the specific heat, and t is the temperature rise required, then the amount of heat required, H is expressed as H = mst calories = 4.2 × mst Joules (since 1 cal = 4.2J) (1.21) 1 calorie = 4.2 Joules, has been established experimentally Example 1.1 A copper wire has resistance of 0.85 ohms at 20°C. What will be its resistance at 40°C? Temperature coefficient of resistance of copper at 0°C is 0.004°C. Solution: α0 We know, α1 = 1 + α 0 t1 0.004 Here, α 20 = = 0.0037 1+ 0.004 × 20 We know, R 2 = R 1 [1+ α1 ( t 2 – t1 )] In this case, R 40 = R 20 [1 + α 20 (40 – 20)] = 0.85 [1+ 0.0037 × 20] = 0.9129 W Example 1.2 The heating element of an electric heater made of nicrome wire has value of resistivity of 1 × 10–6 Ohm-m. The diameter of the wire is 0.2 mm. What length of this nicrome wire will make a resistance of 100 Ohms? Solution:  We know, R= ρ a R.a or, = ρ given R = 100 W, r = 1 × 10–6 Ohm-m, d = 0.2 mm area, a = pd2 = 3.14 × (0.2 × 10–3)2 = 12.56 × 10–8 m2 *SI system of units SI stands for ‘System International’. This system derives all units from seven basic units, which are: length expressed in m, mass expressed in kg, time expressed in second, electric current expressed in ampere, temperature in Kelvin, luminous intensity in candela (cd), and amount of substance in mole. M01_BHAT0000_01_C01.indd 11 3/3/11 11:36 AM  12 Basic Electrical Engineering Substituting the values, length of wire,  is 100 × 12.56 × 10 –8 = =12.56 m 1 × 10 –6 Example 1.3 It is required to raise the temperature of 12 kg of water in a container from 15°C to 40°C in 30 min through an immersion rod connected to a 230 V supply mains. Assuming an efficiency of operation as 80 per cent, calculate the current drawn by the heating element (immersion rod) from the supply. Also determine the rating of the immersion rod. Specific heat of water is 4.2 kiloJoules/kg/°C. Solution: Output or Energy spent in heating the water, H is H = m s (t2 – t1) Where m is the mass of water and s is the specific heat of water. Here, H = 12 × 4.2 × 103 × (40 – 15) Joules = 126 × 104 Joules Output We know, efficiency = Input Energy Spent, i.e., Output So, Energy input to immersion rod = η 126 × 104 = 0.8 = 157.5 × 104 Joules The time of operation of the heater rod = 30 min = 30 × 60 s =1800 secs. Energy input The power rating of the heater = Time of operation 157.5 × 104 Joules = 1800 seconds = 870 Joules / sec = 870 Watts = 0.87 kW Current drawn from 230 V supply P = VI = 870 Watts. 870 Therefore, I= = 3.78 A 230 Example 1.4 A motor-driven water pump lifts 64 m3 of water per minute to an overhead tank placed at a height of 20 metres. Calculate the power of the pump motor. Assume overall efficiency of the pump as 80 per cent. M01_BHAT0000_01_C01.indd 12 3/3/11 11:36 AM  Basic Concepts, Laws, and Principles 13 Solution: Work done/min = mgh Joules m = 64 × 103 kg (1m3 of water weights 1000 kg) g = 9.81 m/sec2 h = 20 m Substituting values 64 × 103 × 9.81 × 20 Joules Work done/sec = 60 seconds 12.55 × 106 Joules = 60 seconds = 20.91 × 104 Watts = 209.1 kW 209.1 Input power of the pump motor = 0.8   = 261.3 kW Example 1.5 A residential flat has the following average electrical consumptions per day: (i) 4 tube lights of 40 watts working for 5 hours per day; (ii) 2 filament lamps of 60 watts working for 8 hours per day; (iii) 1 water heater rated 2 kW working for 1 hour per day; (iv) 1 water pump of 0.5 kW rating working for 3 hours per day. Calculate the cost of energy per month if 1 kWh of energy (i.e., 1 unit of energy) costs `3.50. Solution: Total kilowatt hour consumption of each load for 30 days are calculated as: 4 × 40 × 5 × 30 Tube lights = = 24 kWh 1000 2 × 60 × 8 × 30 Filament lamps = = 28.8 kWh 1000 Water heaters = 1 × 2 × 1 × 30 = 60 kWh Water pump = 1 × 0.5 × 3 × 30 = 45 kWh Total kWh consumed per month = 24 kWh + 28.8 kWh + 60 kWh + 45 kWh = 157.5 kWh One kWh of energy costs `3.50. The total cost of energy per month = 157.5 × 3.50 = `551.25 Example 1.6 An electric kettle has to raise the temperature of 2 kg of water from 30°C to 100°C in 7 minutes. The kettle is having an efficiency of 80 per cent and is supplied from a 230 V supply. What should be the resistance of its heating element? M01_BHAT0000_01_C01.indd 13 3/3/11 11:36 AM  14 Basic Electrical Engineering Solution: m = 2 kg = 2000 gms t2 – t1 = 100 – 30 = 70°C Specific heat of water = 1 7 Time of heating = 7 minutes = hours 60 Output energy of the kettle = m s t = 2000 × 1 × 70 Calories = 140 kilo Calories 140 = kWh 860 = 0.1627 kWh. [1 kWh = 860 kCal] output energy 0.1627 Input energy = = = 0.203 kWh efficiency 0.8 0.203 0.203 × 60 kW rating of the kettle = = = 1.74 kW time in hours 7 Supply voltage, V = 230 Volts. Power, P = 1.74 kW = 1740 Watts.     V = 230 V V V2 P = VI = V = Watts R R V2 230 × 230 or, R= = = 30.4 Ohms P 1740 Example 1.7 Calculate the current flowing through a 60 W lamp on a 230 V supply when just switched on at an ambient temperature of 25°C. The operating temperature of the filament material is 2000°C and its temperature coefficient of resistance is 0.005 per degree C at 0°C. Solution: V V2 We know, power, W = VI = V = R R Here, W = 60 W, V = 230 V V2 230 × 230 \ R= = = 881.6 Ohms W 60 This resistance of the filament is at 2000°C. Let us call it R2000 = 881.6 Ohms. At the instant of switching, resistance is at room temperature, i.e., at 25°C. Let us call it as R25. We know R2000; we have to calculate R25 given a0 = 0.005 ohm/°C. α0 We know, α1 = 1 + α 0 (t1 – t 0 ) M01_BHAT0000_01_C01.indd 14 3/3/11 11:36 AM  Basic Concepts, Laws, and Principles 15 α0 0.005 \ α 25 = = 1 + α 0 (25 – 0) 1 + 0.005 ( 25) = 4.44 × 10 –3 / °C We know the relation, R 2 = R 1[1 + α1 ( t 2 – t1 )] \ R 2000 = R 25 [1 + α1 (2000 – 25)] 881.6 = R 25 [1 + 4.44 × 10 –3 × 1975] R 25 = 90.25 Ω The current flowing through the 60 W lamp at the instant of switching will be corresponding to its resistance at 25°C. V 230 \ I= = = 2.55 Amps R 25 90.25 Example 1.8 A coil has a resistance of 18 Ω at 20°C and 20 Ω at 50°C. At what temperature will its resistance be 21 Ohms? Solution: R 20 = 18, R 50 = 20, R t = 21 at what t? we know, R 2 = R 1[1 + α1 ( t 2 – t1 )] \ R 50 = R 20[1 + α 20 (50 – 20)] or, 20 = 18 [1 + α 20 (30)] or, α 20 = 3.7 × 10 –3/°C We can write, R 3 = R 1[1 + α1 (t 3 – t1 )] substituting, 21 = 18 [1 + 3.7 × 10–3(t3–20)] or, t3 = 65°C. Example 1.9 The resistance of a wire increases from 40 Ω at 20°C to 50 Ω at 70°C. Calculate the temp. coefficient of resistance at 0°C. Solution: given R 20 = 40 Ω, R 70 = 50 Ω, what is ao? R 2 = R 1 [1 + α1 ( t 2 – t1 )] 50 = 40 [1 + α1 (70 – 20)] α1 =5 × 10 –3/°C M01_BHAT0000_01_C01.indd 15 3/3/11 11:36 AM  16 Basic Electrical Engineering α0 α1 = 1 + α 0 t1