Basic Electrical Engineering

Transcription

1 Basic Elecrical Engineering Third Ediion T.K. NAGSARKAR Former Professor & Head Deparmen of Elecrical Engineering Punjab Engineering College Chandigarh M. S. SUKHIJA Founder & Former Principal Guru Nanak Dev Engineering College Bidar, Karnaaka. All righs reserved.

2 3 is a deparmen of he Universiy of Oxford. I furhers he Universiy s objecive of excellence in research, scholarship, and educaion by publishing worldwide. Oxford is a regisered rade mark of in he UK and in cerain oher counries. Published in India by YMCA Library Building, Jai Singh Road, New Delhi 000, India 005, 07 The moral righs of he auhor/s have been assered. Firs Ediion published in 005 Third Ediion published in 07 All righs reserved. No par of his publicaion may be reproduced, sored in a rerieval sysem, or ransmied, in any form or by any means, wihou he prior permission in wriing of, or as expressly permied by law, by licence, or under erms agreed wih he appropriae reprographics righs organizaion. Enquiries concerning reproducion ouside he scope of he above should be sen o he Righs Deparmen,, a he address above. You mus no circulae his work in any oher form and you mus impose his same condiion on any acquirer. ISBN-3: ISBN-0: Typese in Times New Roman by Anvi Composers, New Delhi Prined in India by Magic Inernaional (P) Ld., Greaer Noida Cover image: NWM / Shuersock Third-pary websie addresses menioned in his book are provided by in good faih and for informaion only. disclaims any responsibiliy for he maerial conained herein.. All righs reserved.

3 Preface o he Third Ediion The moivaion o develop he hird ediion of our immensely popular exbook Basic Elecrical Engineering comes from (i) an in-deph review by faculy from various insiuions, underaken by (India), (ii) inpus from colleagues and sudens, and (iii) our own re-visis o say abreas wih he curricula of various universiies/insiuions. New o he Third Ediion Based on he various inpus and in an effor o provide an all-in-one resource as a firs course a he graduae level, he following addiions are incorporaed. More number of solved examples (Addiional Examples) has been added o furher srenghen he undersanding and applicaions of various laws and principles. Shor heoreical quesions are included o help he readers o prepare for esing and evaluaion. Chaper on Nework Analysis and Nework Theorems has been expanded by including (i) conversion of Thevenin and Noron equivalen neworks, (ii) Compensaion heorem, and (iii) Millman s heorem. New and special opics, such as Swinburne s es for esing dc machines, universal moors, achomeer generaors, and synchros have been included. Elecronic insrumens have been added and Chaper is renamed as Basic Analogue and Elecronic Insrumens. Solar power sysems have been described o updae he chaper on power sysems. A new chaper on Illuminaion is added. While incorporaing he various inpus and evolving a exbook which has universal accepance, he auhors wish o sae ha he lucid syle of wriing and mainaining a smooh flow of he language has no been los sigh of. Conens and Coverage Chaper - Inroducion o Elecrical Engineering - he fundamenal laws of elecrosaics, elecromagneism, and heir applicaions in elecrical engineering are explained. The principles and applicaions of various laws are furher srenghened hrough solved examples. Chaper - Nework Analysis and Nework Theorems - afer concepualizing independen and dependen sources, he chaper defines and explains he applicaion of various nework heorems. Node volage and mesh curren mehods for solving neworks along wih applicaions of super nodes and super meshes have also been explained. Chaper 3 - Magneic Circuis - beginning wih he definiion of he Bio-Savar law, he chaper explains he magneic behaviour of maerials, heir properies and classificaion based on he dipole momen of elecrons. I demonsraes he use of mesh analysis for solving a magneic circui. The do convenion o obain he correc direcion of he saically induced emf in a coupled circui is also explained in deail. Chaper 4 - Alernaing Quaniies - discusses he generaion of ac quaniies, heir represenaion, manipulaion, and applicaion for analysing alernaing neworks. Chaper 5 - Three-phase Sysems - deals wih he generaion of hree-phase volages, curren and power along wih an analyses of hree-phase circuis. Measuremen of power and imporance of power facor are also included.. All righs reserved.

4 Preface o he Third Ediion v Chaper 6 - Transformer Principles - proceeding wih a descripion of he consrucional feaures, he chaper deails ou he principle of operaion and developmen of an equivalen circui of a ransformer. Applicaion of oc and sc es resuls for compuing efficiency, regulaion, ec. of a ransformer have also been demonsraed. Chaper 7 - Synchronous Machines - describes he consrucional feaures of a synchronous machine saor and roor. The seing up of a synchronously roaing magneic field has been concepualized graphically and wih he help of phasor diagrams. The concep of infinie bus and he advanages of operaing generaors in parallel have also been oulined. Chaper 8 - Inducion Moors - includes a deailed descripion of he consrucion and principle of operaion of hree-phase inducion moors. Addiional solved examples have been added o suppor he undersanding of he operaing principles. Chaper 9 - Direc Curren Machines - explains how volage is induced and derives expressions for induced volage and elecromagneic orque and discusses commuaor acion. I also elucidaes armaure reacion leading o cross and demagneizaion mmf. Addiionally, field applicaions of dc machines have also been included. Chaper 0 - Single-phase Inducion Moors and Special Machines - qualiaively discusses he working of fracional kilowa moors such as single-phase inducion moors, ac and dc servo moors, differen ypes of sepper and hyseresis moors. The chaper also explains he working principle of universal moors, synchro sysems, and achomeer generaors. Chaper - Basic Analogue and Elecronic Insrumens - includes he principles of measuremen of elecrical quaniies such as resisance, volage, curren, power and he working principles and calibraion of measuring insrumens. Chaper - Power Sysems - describes he generaion, ransmission, and disribuion sysems and subsysems. Various ypes of domesic wiring, including saircase lighing and earhing sysems are also included. Chaper3 - Illuminaion - defines he differen erminologies relaed o illuminaion such as luminous flux, candela, and luminous inensiy and inroduces he laws of illuminaion such as Proporionaliy law, Inverse Square law, and Lamber s Cosine law of incidence. The chaper also explains he applicaion of he laws for compuing luminosiy hrough solved examples. Acknowledgemens The auhors would like o express heir graiude o he readers of heir exbook, Basic Elecrical Engineering, for being an uninerruped source of inspiraion. Also, no amoun of appreciaion would be enough for he ediorial saff of OUP who always keep us on our oes by heir feedback from he users and heir consrucive approach. T.K. Nagsarkar M.S. Sukhija. All righs reserved.

5 Preface o he Firs Ediion Why anoher book on basic elecrical engineering was our iniial hough when he idea of wriing his book firs came o mind. Basic elecrical engineering is a core course offered o engineering sudens of all sreams. I is exremely imporan o ensure ha he fundamenals of he course are well undersood by all engineering sudens since hese have applicaions in all sreams. In spie of a number of exbooks available in he subjec, we fel ha here was sill a need for a book ha would make he learning and undersanding of he principles of elecrical engineering an enjoyable experience. The book is he oucome of our experience of over hree decades of eaching boh undergraduae and posgraduae courses. The iniial draf of he chapers was wrien by one of us and hen read horoughly by he oher. The conen was also peer reviewed and suggesions of he reviewers incorporaed. In his book, we have ried o ensure ha sudens would easily grasp he basics of elecrical engineering. We hope ha sudens will discover ha heir learning and undersanding of he subjec progressively increases while using he book. Abou he Book The conens of his book have been designed, modelled, and wrien as per he AICTE s model curriculum and he syllabi of several universiies. The book provides a comprehensive coverage of he differen opics prescribed by various universiies, hereby providing i wih wide accepabiliy. I is firmly believed ha his book will help sudens o overcome heir iniial apprehensions and iniiae a lifelong affair wih elecrical engineering. Wrien in a simple, ye lucid syle, he book presens a clear and concise exposiion of he principles and applicaions of elecrical engineering. Sudens will find he smooh flow of language an asse o quickly grasp he basic conceps and build a srong foundaion in he subjec. Key Feaures Provides a chaper overview and recapiulaion of imporan formulae in every chaper Includes a large number of illusraions o supplemen he ex Enhances he undersanding of conceps wih several worked examples Provides numerous chaper-end exercises wih answers and muliple choice quesions o simulae suden ineres Conen and Coverage The book inroduces he fundamenals of elecriciy and elecrical elemens. I provides an exhausive coverage of nework heory and analysis, elecromagneic heory and energy conversion, alernaing quaniies, alernaing and direc curren machines, basic analog insrumens, and power sysems. Finally, we hope ha we have been able o make he subjec of elecrical engineering appealing no only for he sudens bu also for he faculy. On he oher hand, if you find ha i falls shor of expecaions, please share your feedback wih us o enable us o make improvemens. T.K. Nagsarkar M.S. Sukhija. All righs reserved.

6 Conens Preface o he Third Ediion Preface o he Firs Ediion Symbols and Acronyms. Inroducion o Elecrical Engineering. Essence of Elecriciy. Aomic Srucure and Elecric Charge.3 Conducors, Semiconducors, and Insulaors 3.4 Elecrosaics 4.4. Coulomb s Law 4.4. Elecric Field Inensiy Elecric Poenial and Poenial Difference Elecric Flux Elecric Flux Densiy Gauss Law Elecric Field Due o a Long Sraigh Charged Conducor Elecric Field Beween Two Charged Parallel Plaes Elecric Field of a Uniformly Charged Sphere 7.5 Elecric Curren 8.6 Elecromoive Force 9.7 Elecric Power 0.8 Ohm s Law.9 Basic Circui Componens.9. Resisors.9. Inducors Capaciors 9.0 Elecromagneism Relaed Laws.0. Magneic Field Due o Elecric Curren Flow.0. Force on a Curren-carrying Conducor Placed in a Magneic Field.0.3 Faraday s Laws of Elecromagneic Inducion 3. Kirchhoff s Laws 6. Nework Analysis and Nework Theorems 35. Basic Definiions of Some Commonly Used Terms 35 i v vi xii. Nework Sources 36.. Ideal Independen Volage Sources 36.. Ideal Independen Curren Source Dependen Sources Pracical Volage and Curren Sources Source Conversion 40.3 Resisive Neworks 4.3. Series Resisors and he Volage Divider Rule 4.3. Parallel Resisors and he Curren Divider Rule 43.4 Inducive Neworks Inducances in Series Inducances in Parallel 46.5 Capaciive Neworks Capaciances in Series Capaciances in Parallel 48.6 Series-parallel Circuis 49.7 Sar dela or Y D Transformaion Sar Resisances in Terms of Dela Resisances Dela Resisances in Terms of Sar Resisances 5.8 Node Volage Analysis Mehod 5.8. Nodal Analysis wih Volage Sources Circui Analysis wih Super Nodes 56.9 Mesh Curren Analysis Mehod Mesh Analysis wih Curren Sources Circui Analysis Wih Super Meshes 59.0 Nodal and Mesh Analyses wih Dependen Sources Node-volage versus Mesh-curren Techniques 63. Nework Theorems 64.. Superposiion Theorem 64.. Thevenin s Theorem Noron s Theorem 69. All righs reserved.

7 viii Conens..4 Maximum Power Transfer Theorem 7..5 Compensaion Theorem Millman s Theorem 76. Transien Analysis 77.. Naural or Transien Response of Source-free Circuis 77.. Forced Response of Reacive Circuis Magneic Circuis 5 3. Inroducion 5 3. Magneic Circuis Bio Savar Law Magneic Field Srengh Magneomoive Force Ampere s Circuial Law Permeabiliy Permeabiliy of Free Space Relaive Permeabiliy Classificaion of Maerials Based on Magneic Behaviour Relucance 3.8 Analogy Beween Elecric and Magneic Circuis 3.9 Magneic Poenial Drop Magneic Circui Compuaions Series Magneic Circui Parallel Magneic Circui 6 3. Magneizaion Characerisics of Ferromagneic Maerials Hyseresis Loop Hyseresis Losses Eddy Curren Losses 3 3. Self Inducance and Muual Inducance Self Inducance Muual Inducance Energy in Linear Magneic Sysems Coils Conneced in Series Aracing Force of Elecromagnes Alernaing Quaniies Inroducion Generaion of ac Volage Waveforms and Basic Definiions Relaionship Beween Frequency, Speed, and Number of Poles Roo Mean Square and Average Values of Alernaing Curren and Volage Roo Mean Square or Effecive Values Average Value Form Facor and Peak Facor Phasor Represenaion of Alernaing Quaniies Phasor Represenaion of Quaniies wih a Phase Difference Addiion and Subracion of Phasor Quaniies The j Operaor and Phasor Algebra Resoluion of Phasors The j Operaor Represenaion of Phasors in he Complex Plane Phasor Algebra Analysis of ac Circuis wih Single Basic Nework Elemen Resisive Circui Purely Inducive Circuis Purely Capaciive Circui Single-phase Series Circuis Resisance and Inducance in Series Resisance and Capaciance in Series Resisance, Inducance, and Capaciance in Series Impedances in Series Single-phase Parallel Circuis Resisance and Inducance in Parallel Resisance and Capaciance in Parallel Resisance, Inducance, and Capaciance in Parallel Impedances in Parallel Series Parallel Combinaion of Impedances Power in ac Circuis Power in Resisive Circuis Power in a Purely Inducive Circui Power in Purely Capaciive Circuis Power in a Circui wih Resisance and Reacance Need for Power Facor Improvemen Resonance in ac Circuis Resonance in Series Circuis Resonance in Parallel Circuis 4.5 Sar Dela or Y-D Transformaion Nodal Volage and Mesh Curren Analysis of ac Neworks 7. All righs reserved.

8 4.7 Nework Theorems for ac Neworks Superposiion Theorem Thevenin s Theorem Noron s Theorem Maximum Power Transfer Theorem 5. Three-phase Sysems Single-phase Sysems and Three-phase Sysems Comparison Three-phase Supply Volage Generaion of Three-phase Volage The Phase Sequence Represenaion of Three-phase Generaor Connecion of Generaor Phases Three-phase Supply Power in Three-phase ac Sysems wih Balanced Load Insananeous Power in Three-phase Circuis Reacive and Apparen Power Complex Power Analysis of Three-phase Circuis Sar-conneced Supply and Sar-conneced Balanced Load Sar-conneced Supply and Dela-conneced Balanced Load Unbalanced Three-phase Circuis Measuremen of Acive Power in Three-phase Neworks One-wameer Mehod Two-wameer Mehod Transformer Principles Inroducion Response of Magneic Circuis o ac Volages Core Losses Hyseresis Losses Eddy-curren Losses Consrucion of Transformers Magneic Core Windings and Insulaion Transformer Tank Working Principle of a Transformer Ideal Transformer Ideal Transformer on no Load Ideal Transformer Under Load Equivalen Circui of an Ideal Transformer 77 Conens ix 6.7 Pracical Transformer Adding Core Losses o an Ideal Transformer Incorporaing Resisances and Leakage Reacances in he Ideal Transformer and Equivalen Circuis Usefulness of he Equivalen Circui Approximae Equivalen Circuis Transformer Tesing Open-circui (OC) Tes Shor-circui (sc) Tes Transformer Regulaion Transformer Efficiency Maximum Efficiency Condiion All-day Efficiency of a Transformer Types of Transformers Type of Consrucion Type of Connecions Special Types of Transformers Synchronous Machines Inroducion Consrucion Feaures of Synchronous Machines Advanages of Saionary Armaure and Roaing Field Consrucion of Saor Consrucion of Roor Three-phase Armaure Windings Types of Windings Generaed emf in a Synchronous Machine Disribued Winding Shor-piched Coils Winding Facor Roaing Magneic Field due o Three-phase Currens Mahemaical Analysis of he Roaing Magneic Field Characerisics of a Three-phase Synchronous Generaor Armaure Reacion Phasor Diagram and Equivalen Circui Volage Regulaion Open-circui (oc) and Shor-circui (sc) Tess on a Three-phase Synchronous Generaor Synchronous Generaor Conneced o an Infinie Bus Bar Synchronous Generaors in Parallel 343. All righs reserved.

9 x Conens 7.0. Effec of Varying he Prime Mover Torque Effec of Varying he Field Curren Advanages of Operaing Synchronous Generaors in Parallel Principle of Operaion of Three-phase Synchronous Moors Phasor Diagram and Equivalen Circui Elecrical and Mechanical Power Synchronous Moor Operaion a Consan Load and Variable Exciaion Advanages and Disadvanages of Synchronous Moors Inducion Moors Inroducion Consrucion Feaures of Three-phase Inducion Moors Saor Roor Principle of Operaion of Three-phase Inducion Moor Slip and Roor Frequency Volage and Curren Equaions and Equivalen Circui of an Inducion Moor Power Balance in an Inducion Moor Torque slip Characerisics Inducion Moor Tesing Saring of Three-phase Inducion Moors Speed Conrol of Three-phase Inducion Moors Squirrel Cage Moor Versus Wound-roor Inducion Moor Direc Curren Machines Inroducion Consrucion of dc Machines Saor Roor Armaure Windings Lap Windings Wave Windings Generaion of dc Volage in a dc Machine Commuaor Acion Torque Producion in a dc Machine Operaion of a dc Machine as a Generaor Expression for Generaed emf Expression for Elecromagneic Torque in a dc Machine Equivalen Circui of a dc Generaor Classificaion of dc Generaors Open Circui Characerisics of a Separaely Excied Generaor Open Circui Characerisics of a Self-excied (Shun) Generaor Armaure Reacion Characerisics of dc Generaors Operaion of a dc Machine as a Moor Principle of Operaion of a dc Moor Types of dc Moors Back emf in a dc Moor Speed of a dc Moor Torque Developed in a dc Moor Characerisics of dc Moors Saring of dc Moors Speed Conrol of dc Moors Losses in dc Machines Tesing of a dc Machine Efficiency of a Machine Operaing as a Moor Efficiency of a Machine Operaing as a Generaor Advanage of he Swinburne Tes Disadvanage of he Swinburne Tes Limiaion of he Swinburne Tes Condiion of Maximum Efficiency of a dc Machine Condiion for Maximum Efficiency of a Generaor Condiion for Maximum Efficiency of a Shun Moor Applicaions of dc Machines dc Generaors dc Moors Single-phase Inducion Moors and Special Machines Inroducion Single-phase Inducion Moors Magneic Field of a Single-phase Inducion Moor Roor Slip and Torque Slip Characerisics Types of Single-phase Inducion Moors Servo Moors 45. All righs reserved.

10 0.3. dc Servo Moors ac Servo Moors Sepper Moors Types of Sepper Moors Meris and Demeris of Sepper Moors Applicaions of Sepper Moors Hyseresis Moors Advanages of Hyseresis Moors Universal Moors Consrucion of a universal Moor Operaion of a universal Moor Characerisics of a universal Moor Applicaions of Universal Machines Drawbacks of Universal Machines Tachomeer Generaors Types of Tachomeer Generaors Synchro Consrucion Working Principle Applicaion Advanage 464. Basic Analogue and Elecronic Insrumens 470. Inroducion 470. Classificaion of Insrumens Absolue Insrumens 47.. Secondary Insrumens Analogue Insrumens Digial Insrumens 47.3 Operaing Principles 47.4 Essenial Feaures of Measuring Insrumens Deflecing Sysem Conrolling Sysem Damping Sysem Ammeers and Volmeers Types of Ammeers and Volmeers Exension of Range 48.6 Measuremen of Power Dynamomeer Wameer Inducion Wameer Measuremen of Elecrical Energy Types of Energy Meers Inducion Type Energy Meers Measuremen of Insulaion Resisance 49 Addiional Muliple Choice Quesions Bibilography 56 Index Abou he Auhors 569 Conens xi.8. Megger Elecronic Insrumens Common Types of Insrumens Mulimeer Measuremen Errors Human or Operaor Errors Insrumen Errors Environmenal Errors Random Errors 499. Power Sysems 505. Inroducion 505. Componens of a Power Sysem Generaion Subsysem Primary Sources of Energy Types and Characerisics of Generaing Saions Transmission Subsysem 54.5 Sub-ransmission Sysem 55.6 Disribuion Subsysem Types of Disribuion Sysems 56.7 Domesic Wiring Elecrical Energy Disribuion Sysems Domesic Wiring Sysems 59.8 Earhing 5.8. Pipe Earhing 5.8. Plae Earhing Illuminaion Inroducion Ligh Radiaions Definiions Solid Angle Luminous Flux Candela Luminous Inensiy or Candle Power Mean Spherical Candle Power (MSCP) Mean Hemispherical Candle Power (MHSCP) Reducion Facor Illuminaion or Illuminance Laws of Illuminaion or Illuminance Proporionaliy Law Inverse Square Law Lamber s Cosine Law of Incidence 53. All righs reserved.

11 Inroducion o Elecrical Engineering Learning Objecives This chaper will enable he reader o Undersand he naure of srucure of an aom and significance of free elecrons Differeniae beween conducors, semiconducors, and insulaors based upon he energy levels of elecrons Compue he resisance of a conducor from is physical dimensions a differen emperaures Familiarize wih elecrosaic phenomena associaed wih elecric charges and define elecric field inensiy, elecric poenial and poenial difference, elecric flux, and elecric flux densiy Ge familiar wih basic elecrical quaniies: curren, volage, emf, and elecric power Define Ohm s law for a resisor and compue he resisance of a conducor from is physical dimensions a differen emperaures Compue he induced volage due o varying curren, power, and energy sored in an inducor Based upon an undersanding of he charge soring naure of a capacior, compue is capaciance, curren, power, and energy sored Define Ampere s law and use i o esimae he force on a curren carrying conducor when placed in a magneic field, and use Fleming s lef hand rule o deermine direcion of he force Use Faraday s laws of elecromagneic inducion o compue he magniude of dynamic or saic induced volage and apply Fleming s righ hand rule or Lenz s law o deermine he direcion of he induced volage Define Kirchhoff s volage and curren laws and apply hese o compue currens and volages in a circui made up of resisors, inducors, and capaciors. ESSENCE OF ELECTRICITY I is believed ha elecriciy is presen in naure. I is amazing how humankind has been able o pu elecriciy o myriad uses for is own progress and comfor wihou having an exac knowledge of he naure of elecriciy. In fac, based on experimenaion and observaions, heories have been developed o explain he behaviour of elecriciy. Elecrical energy has been acceped as a form of energy ha is mos suied for ransformaion ino oher forms of energy, such as hea, ligh, mechanical energy, ec. Elecriciy can be convered ino many differen forms o bring abou new and enabling echnologies of high value. Conversion of elecrical energy ino pulses and elecromagneic waves has given rise o compuers and communicaion sysems. Is conversion ino microwaves finds use in microwave ovens, indusrial processes, and radars. Elecriciy in he arc form serves in arc furnaces and welding. Efficien lighing, lasers, visuals, sound, robos, medical ools are among many oher examples of he use of elecriciy. Elecrical engineering deals wih he generaion, ransmission, uilizaion, and conrol of elecric energy. Elecric energy is generaed a elecric power generaing saions such as hydroelecric, hermal, and nuclear power saions. In a hydroelecric power saion, he poenial energy of he head of waer sored in dams is convered. All righs reserved.

12 Basic Elecrical Engineering ino kineic energy by regulaing he flow of he sored waer hrough urbines. This kineic energy, in urn, ges ransformed ino elecric energy by he process of elecro-mechanical energy conversion. In a hermal saion, he chemical energy of coal, oil, naural gas, and synheic derivaives is convered by combusion ino hea energy. Hea energy is also produced by nuclear fission of nuclear fuels in a nuclear reacor. I is hen convered ino mechanical energy, which in urn is ransformed by elecro-mechanical energy conversion o elecric energy, hrough hermodynamic processes. Conversion of limiless energy from he sun ino usable elecric energy hrough phoovolaic energy conversion is achieved by using solar cells. Commercially, elecriciy is also being generaed from renewable energy sources such as wind, biomass, and geohermal sources. Wind energy is convered ino elecrical form hrough a wind urbine coupled o an elecrical generaor. Geohermal power generaion convers energy conained in ho rocks ino elecriciy by using waer o absorb hea from rocks and ranspor i o he earh s surface, where i is convered ino elecric energy hrough urbine generaors. The majoriy of biomass elecriciy is generaed using a seam cycle where biomass maerial is firs convered ino seam in a boiler; he resulan seam is hen used o urn a urbine conneced o a generaor. Elecriciy permis he source of generaion o be remoe from he poin of applicaion. Elecric energy ransmission sysems are varied, such as power ransmission sysems and elecronic communicaion sysems. Elecric energy for conversion ino ligh energy, hea energy, and mechanical energy for use in indusries, commercial esablishmens, and households would require bulk ransmission of elecric power from he source, which produces energy, o he load cenre, where he elecric energy is uilized. Elecrical power ransmission sysems consis of chains of ransmission owers on he earh s surface, from which he line conducors carrying curren are suspended by porcelain insulaors. An elecric sysem may be viewed as consising of generaing devices, ransformers, and ransmission sysems which inerconnec erminal equipmen for convering elecrical energy ino ligh, hea, or mechanical energy and vice versa. All devices and equipmen can be represened by idealized elemens called circui elemens. These elemens can be inerconneced o form neworks, which can be used for modelling and analysing he sysem behaviour. Conversely, neworks may be designed o achieve he required performance from a sysem. Elecrical engineering is concerned wih he sudy of all aspecs of elecric power, i.e., is generaion, ransmission, and uilizaion. Therefore, i is necessary o become familiar wih he basic conceps and erms associaed wih elecriciy.. ATOMIC STRUCTURE AND ELECTRIC CHARGE Aom is he smalles paricle of an elemen. As per Bohr Ruherford s planeary model of aom, he mass of an aom and all is posiive charge is concenraed in a iny nucleus, while negaively charged elecrons revolve around he nucleus in ellipical orbis like planes around he sun (see Fig..). The nucleus conains proons and neurons. A neuron carries no charge and is mass is kg, while a proon carries a posiive charge +e and is mass is kg. The elecron carries a negaive charge -e = C and is mass is kg. Thus an elecron is ligher han a proon by a facor of abou 840. There are exacly as many proons in he nucleus of an aom as planeary elecrons. Thus, he nucleus of an aom can be viewed as a core carrying a posiive charge, and he negaive charge of he encircling elecrons is equal o he posiive charge of proons. An aom as a whole is elecrically neural. The orbis for he planeary elecrons are called shells or energy levels. Elecron Nucleus The elecrons in successive shells named K, L, M, N, O, P, Fig.. Srucure of an aom. All righs reserved.

13 Inroducion o Elecrical Engineering 3 and Q are a increasing disance ouwards from he nucleus. Each shell has a maximum number of elecrons for sabiliy. For mos elemens, he maximum number of elecrons in a filled inner shell equals n, where n is he shell number in sequenial order ouward from he nucleus. Thus he maximum number of elecrons in he firs shell is, for he second shell is 8, for he hird shell is 8, and so on. These values apply only o an inner shell ha is filled wih is maximum number of elecrons. To illusrae his rule, a copper aom wih 9 elecrons is chosen. In his case, he number of elecrons in he K, L, M, and N is, 8, 8, and, respecively..3 CONDUCTORS, SEMICONDUCTORS, AND INSULATORS As saed in he preceding secion, elecrons revolve in orbis around he nucleus. The elecrons closer o he nucleus possess lower energies han hose furher from i, which is very much similar o a mass m possessing increasing poenial energy as is disance above he earh s surface increases. Thus he posiion occupied by an elecron in an orbi signifies a cerain poenial energy. Due o he opposie charge, here is a force of aracion beween he elecron and he nucleus. The closer an elecron is o he nucleus, more srongly i is bound o he nucleus. Conversely, furher away an elecron is from he nucleus, lesser is he force of aracion beween he elecron and he nucleus. Since he bond beween he ouer elecrons and he nucleus is weak, i is easy o deach such an elecron from he nucleus. When many aoms are brough close ogeher, he elecrons of an aom are subjeced o elecric forces of oher aoms. This effec is more pronounced in he case of elecrons in he ouermos orbis. Due o hese elecric forces, he energy levels of all elecrons are changed. Some elecrons gain energy while ohers lose i. The ouermos elecrons suffer he greaes change in heir energy levels. Thus he energy levels, which were sharply defined in an isolaed aom, are now broadened ino energy bands. Each band consiss of a large number of closely packed energy levels. In general, wo bands resul, namely, he conducion band associaed wih he higher energy level and he valence band. A region called forbidden energy gap separaes hese wo bands. Each maerial has is own band srucure. Band srucure differences may be used o explain he behaviour of conducors, semiconducors, and insulaors. In meals, aoms are ighly packed ogeher such ha he elecrons in he ouer orbis experience small, bu significan, force of aracion from he neighbouring nuclei. The valence band and he conducion band are very close ogeher or may even overlap. Consequenly, by receiving a small amoun of energy from exernal hea or elecric sources he elecrons readily ascend o higher levels in he conducion band and are available as elecrons ha can move freely wihin he meal. Such elecrons are called free elecrons and can be made o move in a paricular direcion by applying an exernal energy source. This movemen of elecrons is really one of negaive elecric charge and consiues he flow of elecric curren. In meals he densiy of elecrons in he conducion band is quie high. Such meals are caegorized as conducors. In general meals are good conducors, wih silver being he bes and copper being he nex bes. In semiconducors he valence and conducion bands are separaed by a forbidden gap of sufficien widh. A low emperaures, no elecron possesses sufficien energy o occupy he conducion band and hus no movemen of charge is possible. A room emperaures i is possible for some elecrons o gain sufficien energy and make he ransiion o he conducion band. The densiy of elecrons is no as high as in meals and hus canno conduc elecric curren as readily as in conducors. Carbon, germanium, and silicon are semiconducors conducing less han he conducor bu more han he insulaors. A maerial wih aoms ha are elecrically sable, ha is, wih he ouermos shell complee, is an insulaor. In such maerials he forbidden gap is very large, and as a resul he energy required by he elecron o cross over o he conducion band is impracically large. Insulaors do no conduc elecriciy easily, bu are able o hold or sore elecriciy beer han conducors. Insulaing maerials such as glass, rubber, plasic, paper, air, and mica are also called dielecric maerials.. All righs reserved.

14 4 Basic Elecrical Engineering.4 ELECTROSTATICS Elecrosaics is associaed wih maerials in which elecrical charge moves only slowly (insulaing maerials) and wih elecrically isolaed conducors. Charges are saic as insulaion and isolaion preven easy migraion of charge. Elecrosaic phenomena arise from he forces ha elecric charges exer on each oher. There are many examples as simple as he aracion of he plasic wrap o one s hand afer i is removed from a package, o he operaion of phoocopiers. Elecrosaics involves he buildup of charge on he surface of objecs due o conac wih oher surfaces. Alhough exchange of charge happens whenever any wo surfaces conac and separae, he effecs of charge exchange are usually noiced only when a leas one of he surfaces has a high resisance o elecrical flow. This is because he charges ha ransfer o or from he highly resisive surface are more or less rapped here for a long enough ime for heir effecs o be observed. These charges hen remain on he objec unil hey eiher bleed off he ground or are quickly neuralized by a discharge. The space surrounding a charged objec is affeced by he presence of he charge and an elecric field is esablished in ha space. A charged objec creaes an elecric field an aleraion of he space or field in he region ha surrounds i. Elecric field is a vecor quaniy whose direcion is defined as he direcion in which a posiive es charge would be pushed when placed in he field. Thus, he elecric field direcion abou a posiive source charge is always direced away from he posiive source. And he elecric field direcion abou a negaive source charge is always direced oward he negaive source..4. Coulomb s Law Coulomb s law saes ha he force of aracion or repulsion F, beween wo charges q and q coulombs, concenraed a wo differen poins in a medium, is direcly proporional o he produc of heir magniudes and inversely proporional o he square of he disance r beween hem. Mahemaically, i may be expressed as qq F = newon (or N) (.) 4pe r where e is he absolue permiiviy of he surrounding medium and is given by e = e 0 e r (.) where e 0 is he permiiviy of free space and is equal o F/m; e r is he relaive permiiviy of he medium. If he charges are of like polariy, he force beween hem is repulsive, and if he charges are of opposie polariy, he force is aracive..4. Elecric Field Inensiy When a saionary elecric charge is placed wihin an elecrosaic field, i experiences a force of aracion or repulsion depending on he naure of he charge and is posiion in he field. The raio of he force exered on he charge o he magniude of he charge is defined as he elecric field inensiy. Thus, if a charge of magniude q coulomb, when placed wihin an elecric field, experiences a force of F newon, hen he elecric field inensiy E will be given by F E = N/C or V/m (.3) q The force F experienced by charge q due o he presence of charge q is given by Eq. (.). Hence, he field srengh a he poin where change q is locaed will be [from Eq. (.3)] E = F N/C or V/ m q Subsiuing for F from Eq. (.) in he above equaion yields qq E = r q = q N/C or V/m (.4) 4pe 4per. All righs reserved.

15 Inroducion o Elecrical Engineering 5 Example. Find he force in free space beween wo like poin charges of 0. C each and placed m apar. Soluion Using Eq. (.), he force may be obained as F = = N - 4p I may be noed ha he magniude of he force is giganic. This calculaion shows ha 0. C of elecric charge is a very high value and is normally no encounered in engineering compuaions..4.3 Elecric Poenial and Poenial Difference Moving a posiive es charge agains he direcion of an elecric field would require work by an exernal force. This work would in urn increase he poenial energy of he charge. On he oher hand, he movemen of a posiive es charge in he direcion of an elecric field would occur wihou he need for work by an exernal force. This moion would resul in he loss of poenial energy of he charge. Poenial energy is he sored energy of posiion of a charge and i is relaed o he locaion of he charge wihin a field. The above siuaion finds an analogy in mechanics where work has o be done agains he graviaional force in raising a mass o some heigh above sea level. The greaer he mass, he greaer is he poenial energy possessed by he mass. While elecric poenial energy has a dependency upon he charge experiencing he elecric field, elecric poenial is purely locaion dependen. I is he poenial energy per charge. The elecric poenial a any poin wihin an elecric field is defined as he amoun of work done agains he elecric field (or he energy required) o bring a uni posiive charge from infiniy o ha poin, or alernaively, from a place of zero poenial o he poin. The uni of poenial is vol, and vol is equal o joule/coulomb. An alernae name of his quaniy, volage, is named afer he Ialian physicis Alessandro Vola. The poenial difference beween wo poins wihin an elecric field is he work done by he field in shifing a uni posiive charge from one poin o he oher. I is o be noed ha posiive charge always flows from higher poenial poin o lower poenial poin, whereas a negaive charge flows from a lower poenial poin o higher poenial poin. Boh poenial and poenial difference are scalar quaniies as hese are posiion dependen in a field bu are no dependen on he pah by which he posiion is reached. The oal work per uni charge associaed wih he moion of charge beween wo poins is called volage. If v is he volage in vols, w is he energy in joules, and q is he charge in coulombs, hen dw v = J/C (.5) dq Example. Two charges Q = 0-9 C and Q = C are spaced 6 m apar in air as shown in Fig..(a). Derive an expression for he ne force on a uni posiive charge Q a poin A, locaed a x m from Q. If A and B are respecively locaed m and 4 m away from he charge Q as shown in Fig..(b), compue he volage V AB beween he poins A and B. Q = C Q = C 9 Q = 3 0 C C 9 Q = 0 Q = 3 0 C A B A m x m (6 x) m 4 m 6 m 6 m (a) Fig.. (b). All righs reserved.

16 6 Basic Elecrical Engineering Soluion The force of repulsion beween Q and Q a poin A, direced away from Q, is = - 4p x x Similarly, he force of repulsion beween Q and Q a poin A, direced away from Q, is = - 4p x 6 - x ( ) N ( ) The ne force on Q, direced away from Q, is given by 7 8 È F = - = Í 3 ( - x) x Í( - x ) - 9 N 6 6 x Î The work done in moving Q from poin A o poin B is given by b 4 N È 3 È 3 WBA = Fdx = Í - dx = Í ( - x) x x x a ÎÍ ( - ) =-5.4 J Ú Ú 6 Î 6 Since volage is defined as work done per uni charge, he volage beween poins A and B is given by WBA VBA = =-5. 4 J/C or V Q Then, V AB = - V BA = 5.4 V.4.4 Elecric Flux An elecric field exiss in space beween a posiively and a negaively charged body. The presence of an elecric field is shown by cerain imaginary lines hrough space. They are called flux lines. Convenionally, hey radiae from a posiive charge and converge on equal quaniy of negaive charge. The elecric flux lines are no closed on hemselves as a posiive and negaive charge canno exis simulaneously. Elecric flux lines of an isolaed charged conducor are shown in Fig..3. Boh elecric charge q and flux y are measured in coulomb, and one coulomb of posiive charge radiaes one coulomb of flux..4.5 Elecric Flux Densiy Elecric flux densiy D a any poin in a medium is defined as he flux y Fig..3 Elecric flux lines of an isolaed charged conducor (in coulomb) per uni area a (in m ), a righ angles o he direcion of he flux. Thus, q D = = a a C/m (.6) From Eq. (.4), elecric field inensiy E a a disance r from he cenre of a charged body of charge q is q E = 4 per or q ee = 4 pr (.7) Now, he elecric flux radiaing from he charged body is also q coulombs, and 4pr is he oal surface area of he sphere, wih he cenre a he cenre of he charged body and a radius of r. The elecric flux densiy is given by q D = 4 pr (.8) 4 +q. All righs reserved.

17 From Eqs. (.7) and (.8), we ge he following relaion: D = e E Inroducion o Elecrical Engineering Gauss Law Gauss law saes ha he surface inegral of he elecric flux densiy over a closed surface enclosing a specific volume is equal o he algebraic sum of all he charges enclosed wihin he surface, i.e., Dds =Âq (.0) Ú.4.7 Elecric Field Due o a Long Sraigh Charged Conducor A long conducor, having uniform charge q coulombs per mere, is shown in Fig..4. The elecric flux will be radial in all direcions perpendicular o he conducor. Le a poin be chosen a a perpendicular disance r from he conducor. The oal charge enclosed by an elemenary cylindrical surface of lengh dl will be q dl, and he oal flux y coming ou of he cylindrical surface will be y = q dl and he flux densiy D on he cylindrical surface is y qdl q D = = = prdl prdl pr Then, he field inensiy E is given by E D = = e q r pe V/m (.).4.8 Elecric Field Beween Two Charged Parallel Plaes Two parallel plaes, wih charge +q on one plae and charge -q on he oher plae, are shown in Fig..5. The cross-secional area of each plae is a mere. The flux lines in his case will be perpendicular o he charged plaes. The oal flux y = qc and he flux densiy inside he medium is y q D = = a a and he field inensiy is E D = = e q ea V/m (.) Fig Elecric Field of a Uniformly Charged Sphere A hollow meallic sphere wih oal charge q coulombs is shown in Fig..6. Elecric field inensiy inside he hollow sphere is zero because of he fac ha he elecrical charge resides a he surface of he sphere only. Therefore, he elecric field inensiy ouside he charged sphere is o be deermined. The oal elecric flux y going ou of he charged sphere is y = q. The flux densiy D a a disance r from he cenre of he sphere can be deermined by considering a spherical shell of radius r wih he same cenre as he cenre of he sphere. The surface area of his spherical shell is 4pr and he flux densiy will be y q D = = 4pr 4pr dl r + q coulomb per mere Elecric field around a long charged conducor Fig..5 +q -q + + (.9) Elecric field of parallel charged conducors q + Fig A hollow meallic charged sphere. All righs reserved.

18 8 Basic Elecrical Engineering Also, he elecric field inensiy is D q E = = V/m e 4per (.3).5 ELECTRIC CURRENT In an isolaed meallic conducor, such as a lengh of copper wire, numerous free elecrons exis in he conducion band and ye no curren flows. Due o ineracive forces beween he free elecrons hemselves and wih he posiive ions he elecrons are in moion which is essenially random in naure, and a any cross secion of he copper wire he ne movemen of elecrons is zero. In conducors, an orderly movemen of elecrons in a given direcion can be achieved by applying an exernal energy source across he ends of he conducor. This makes curren o flow across he wire/conducor. Figure.7 shows an arrangemen in which an elecrochemical cell, commonly called a baery, is conneced exernally by a conducing wire. Iniially, when he energy source is no conneced exernally, due o he chemical reacion in he baery a large number of elecrons gaher around one elecrode, called cahode, giving i an excess of negaive charge. The oher elecrode, called anode, has an excess of posiively charged nuclei, hereby, charging i posiively. The anode is a a higher poenial han he cahode. When a conducing wire is conneced exernally o he baery erminals, elecrons in he conducion band are se in moion by he elecric force due o accumulaed charges a he baery erminals. The moion of hese elecrons is periodically inerruped by collisions wih saic aoms and ions. However, a any insan of ime he flow of charge a he conducor cross secion is consan. There is no accumulaion of charge in he conducor; as many charges ener he cross secion as leave i. The consan flow of charges consiues elecric curren. As long as he chemical reacions in he baery mainain he anode erminal a a higher poenial wih respec o he cahode erminal, he flow of curren coninues. Furher, he greaer he poenial difference across he baery erminals, he greaer is he accumulaed charge, he rae of flow of charge, and he curren. If he meallic wire is disconneced from he baery erminals, is elecrical neuraliy is preserved. Thus i may be said ha he flow of elecric curren is associaed wih he movemen of elecric charge. Flow of elecric curren in a conducor is possible only when i is conneced o he erminals of an elecric energy source, such as a baery, and here exiss a poenial difference across is erminals. Elecric curren is defined as he ime rae change of charge passing hrough a cross-secional area of a conducor. If Dq coulomb is he amoun of charge flow in D seconds, hen he average curren i av over a period of ime, he insananeous curren i, and he charge q ransferred from ime 0 o are given by i av = D q C/sec (or amperes) (.4) D i = dq C/sec (.5) d or q = Ú id C (.6) 0 Curren Fig..7 Energy source Flow of elecrons and curren The uni of curren is called ampere, named afer he French scienis Andre Marie Ampere. A curren of A means ha he elecric charge is flowing a he rae of C/sec.. All righs reserved.

19 + Inroducion o Elecrical Engineering 9 Currens have direcion. In conducors he curren consiss of he movemen of elecrons. Convenionally, a posiive curren is aken o be a flow of posiive charge in he direcion of a reference arrow used o mark he direcion of he curren flow, as shown in Fig..7. Thus, he posiive direcion of he flow of curren is aken as opposie o ha of he direcion of he movemen of elecrons. Example.3 In a meallic wire, 0 9 elecrons drif across a cross secion per second. Wha is he average curren flow in he wire? Soluion Charge on one elecron = C From Eq. (.4), I av = Toal charge movemen per second = =.6 C/sec =.6 A.6 ELECTROMOTIVE FORCE In an isolaed meallic conducor, free elecrons, which are loosely bonded wih heir nuclei, can be made o flow in a given direcion by applying an elecric pressure across he ends of he conducor. Such a pressure is provided by an exernal energy source, for example, a baery. Due o he chemical reacions inside an elecrochemical cell, commonly called a baery, separaion of elecric charges akes place. Negaive charges accumulae a one erminal, he cahode, and posiive charges accumulae a he oher erminal, he anode. As he charges of unlike polariy arac each oher, work has o be done by an exernal agency agains hese aracive forces o separae hem. In he case of a baery, he work is done chemically. The greaer he number of charges ha are separaed, he greaer is he work ha has o be done o achieve his separaion and he greaer is he poenial energy of he separaed charges. The work done per uni charge is a measure of he amoun of accumulaed charge or a measure of he poenial energy ha has been esablished. The work done per uni charge in a baery is he poenial difference (pd) beween he erminals of he baery. The pd beween he baery erminals is known as he elecromoive force, or emf. The emf represens he driving influence ha causes a curren o flow, and may be inerpreed o represen he energy ha is used during passing of a uni charge hrough he source. The erm emf is always associaed wih energy conversion. The emf is usually represened by he symbol E and has he uni vol. When he baery is conneced exernally hrough a conducor o a load, energy ransfer o he load commences hrough he conducor. The energy ransfer due o he flow of uni charge beween he wo poins in he circui is ermed as poenial difference. When all he energy is ransferred o he load uni, he pd across he load uni becomes equal o ha of he baery emf. In view of his discussion, i may be saed ha boh emf and pd are similar eniies and have he same unis. Thus emf is associaed wih energy while pd causes he passage of charge, or curren. Boh poenial and poenial difference are scalar quaniies. The emf and pd are represened in a diagram following cerain convenions. Each is indicaed by an arrow, as shown in Fig..8. The arrowhead in each case poins o a higher poenial. I may be noed ha he curren leaves he source of emf a he posiive erminal and herefore he direcion of curren flow is he same as ha of he emf arrow. The curren eners he load a he posiive erminal, and hus he direcion of curren is opposie wih respec o he pd arrow of he load. Source Fig..8 Curren flow Source emf Load pd EV The uni of pd is vol and he symbol V is used o represen he pd. A vol is defined as he poenial difference beween wo poins of a conducor carrying a curren of A, when he power dissipaed beween he poins is W. As he pd is measured in vols, i is also ermed as volage drop. Load uni Convenions of represening emf and pd. All righs reserved.

20 0 Basic Elecrical Engineering.7 ELECTRIC POWER Power is defined as work done or energy per uni ime. If force F newon acs for seconds hrough a disance d mere along a sraigh line, hen he work done is F d joules. Then he power p eiher generaed or dissipaed by a circui elemen can be represened by he following relaionship: F d p = = F u (.7) where u is he velociy in m/sec. In he case of roaing machines, NT p = p r (.8) 60 where N r is he speed of roaion of he machine in rpm (revoluions per minue) and T is he orque in N m. Power = work work charge = = volage curren (.9) ime charge ime The uni of power is J/sec or wa (afer he Scoish engineer, James Wa). The uni of energy is joule or wa-second. Commercially, he uni of energy is kilowa-hour (kwh). I represens he work done a he rae of kw for a period of h. The elecric supply auhoriies refer kwh as one uni for billing purposes. Alernaively, if he curren flowing beween wo poins in a conducor is i and he volage is v, hen from he definiions of curren and volage given in Eqs (.5) and (.6), i is apparen ha he produc of curren and volage is power p dissipaed beween wo poins in he conducor carrying he curren. Thus, p = v i (.0) = dw dq joules coulombs, dq d coulomb seconds = dw d, joules or was second (.0a) Jus like volage, power is a signed quaniy. Usually he elecrical engineering communiy adops he passive sign convenion. As per his convenion, if posiive curren flows ino he posiive erminal of an elemen, he power dissipaed is posiive, ha is, he elemen absorbs power; while if he curren leaves he posiive erminal of an elemen, he power dissipaed is negaive, ha is, he elemen delivers power. Example.4 A circui delivers energy a he rae of 30 W and he curren is 0 A. Deermine he energy of each coulomb of charge in he circui. Soluion From Eq. (.0) v = p i = 30 0 = 3 V Also, v = p dw i = d dw d dq = dq \ dw = v dq If i = 0 A, dq = i d = 0 = 0 C, hen dw = 3 0 = 30 J Therefore, he energy of each coulomb of charge is 30/0 = 3 J. Example.5 An elecric moor is developing 5 kw a a speed of 500 rpm. Calculae he orque available a he shaf.. All righs reserved.

21 Inroducion o Elecrical Engineering Soluion Subsiuing ino Eq. (.8), 5,000 W = T p \ T = Nm.8 OHM S LAW This law is named afer he German mahemaician Georg Simon Ohm who firs enunciaed i in 87. I saes ha a consan emperaure, poenial difference V across he ends of a conducor is proporional o he curren I flowing hrough he conducor. Mahemaically, Ohm s law can be saed as V µ I or V = R I or R = V (.) I In Eq. (.), R is he proporionaliy consan and is he resisance of he conducor. Is uni is ohm (W): W = V/A (.) I may be noed ha subsequenly i was esablished ha Ohm s law could no be applied o neworks conaining unilaeral elemens (such as diodes), or non-linear elemens (such as hyrie, elecric arc, ec.). A unilaeral elemen is he one ha does no exhibi he same V-I characerisic when he direcion of he flow of curren hrough i is reversed. Similarly, in non-linear elemens he V-I characerisic is no linear. Using a dc source, volaic cell, Ohm achieved he experimenal verificaion of his law. Laer experimens wih ime-varying sources showed ha his law is also valid when he poenial difference applied across a linear resisance is ime-varying. In his case, Eq. (.) is wrien as v = R i (.3) where v and i are insananeous values of he poenial difference and curren, respecively..9 BASIC CIRCUIT COMPONENTS Resisor, inducor and capacior are he hree basic componens of a nework. A resisor is an elemen ha dissipaes energy as hea when curren passes hrough i. An inducor sores energy by virue of a curren hrough i. A capacior sores energy by virue of a volage exising across i. The behavior of an elecrical device may be approximaed o any desired degree of accuracy by a circui formed by inerconnecion of hese basic and idealized circui elemens..9. Resisors A resisor is a device ha provides resisance in an elecric circui. As already saed in Secion.5, ordinarily he free elecrons in a conducor undergo random movemen bu he ne movemen of elecrons is zero and hence his does no resul in a ne curren flow. The free elecrons in a conducor can be made o flow in a paricular direcion by applying an exernal volage source. The applicaion of he volage source produces an elecric field wihin he conducor, which produces a direced moion of free elecrons. The moion of hese free elecrons is direced opposie o he elecric field. During heir moion hese elecrons collide wih he fixed aoms in he laice srucure of he maerial of he conducor. Such collisions resul in he producion of irreversible hea loss. Thus resisance is he propery of a circui elemen which offers hindrance or opposiion o he flow of curren and in he process elecric energy is convered ino hea energy. Elecric resisance is analogous o pipe fricion in a hydraulic sysem and fricion in a mechanical sysem. The resisance of a conducor opposes he curren, pipe fricion opposes he waer flow hrough he pipe, and fricion opposes he moion of a mechanical sysem, and he energy dissipaed in overcoming his opposiion appears as hea. A physical device whose principal elecrical characerisic is resisance is called resisor. A resisor is said o be linear if i saisfies Ohm s law, ha is, he curren hrough he resisor is proporional o he pd across i.. All righs reserved.

22 Basic Elecrical Engineering If he magniude of resisance varies wih he volage or curren, he resisor is said o be non-linear. Resisors made of semiconducor maerials are non-linear resisors. The resisance of a resisor depends on he maerial of which he conducor is made and he geomerical shape of he conducor. The resisance of a conducor is proporional o is lengh l and inversely proporional o is cross-secional area a. Therefore, he resisance of a conducor can be wrien as l r l R µ or R = (.4) a a The proporionaliy consan r is called he specific resisance or resisiviy of he conducor and is value depends on he maerial of which he conducor is made. Equaion (.4) is valid only if he curren is uniformly disribued hroughou he cross secion of he conducor. In Eq. (.4), if l = m, a = m, hen r = R. Thus specific resisance is defined as he resisance of a conducor having a lengh of m and a cross secion of m. The uni of resisiviy can be obained as under: R a ohm mere r =, = ohm-mere (W m) l mere The inverse of resisance is called conducance and he inverse of resisiviy is called specific conducance or conduciviy. The symbol used o represen conducance is G and conduciviy is s. Thus, from Eq. (.4), conduciviy s = /r, and is unis are siemens per mere or mho. a a a G = = = = s mho (.5) R r l r l l Example.6 Find he resisance of sranded annealed copper wire 00 m long and 5 mm in cross secion. Resisiviy of copper is W m. Soluion -8 rl R = = = W -6 a 5 0 Example.7 Find he resisance of he semicircular copper secion, shown in Fig..9, beween he equipoenial faces A and B. The inner radius is 6 cm, radial hickness 4 cm, and axial hickness 4 cm. Soluion The mean radius of he semicircular secion is 6 + = 8 cm = 0.08 m Then, he mean lengh is l = p r = p 0.08 Area of he cross secion a = = m A B Resisiviy of copper r = W m Fig..9 Therefore, he resisance -8 r l 7. 0 p R = = -8 = W=. 703 mw a Example.8 A coil consiss of 4000 urns of copper wire having a cross-secional area of 0.8 mm. The mean lengh per urn is 80 cm. The resisiviy of copper a normal working emperaure is 0.0 m Wm. Calculae he resisance of he coil and he power dissipaed when i is conneced across a 30-V dc supply. Soluion -6 - r l ( ) R = = = 80 W -6 a Now, power dissipaed = V I = 30 30/80 = 66.5 W. All righs reserved.

23 Inroducion o Elecrical Engineering 3 Example.9 An aluminium wire 7.5 m long is conneced in parallel wih a copper wire 6 m long. When a curren of 5 A is passed hrough he combinaion, i is found ha he curren in he aluminium wire is 3 A. The diameer of he aluminium wire is mm. Deermine he diameer of he copper wire. Resisiviy of copper is 0.07 mw m and ha of aluminium is 0.08 mw m. Soluion The resisance of aluminium wire is -6 R Al = r Al lal = = W a p Al ( ) The poenial drop across aluminium wire is = V. Then he poenial drop across he copper wire is also V. Therefore, Resisance of copper wire = = W The cross secion of copper wire is -6 r Cu l Cu = = m RCu p -6 Then ( d Cu ) = \ d Cu = m = mm Example.0 A porcelain cylinder 5 cm in diameer is wound wih a bare high resisance wire having a resisance of W m lengh and mm cross secion. The disance beween consecuive urns equals he diameer of he wire. If he exernal surface of he cylinder (excluding he ends) can dissipae 0.3 W/cm a he permied emperaure rise, find he lengh of he cylinder and he diameer and lengh of wire for a loading of 00 W and a curren of A. Soluion The area required o dissipae 00 W = 00/0.3 = 3.5 cm Le he lengh of he cylinder be L cm, lengh of he wire be l cm, and he diameer of he wire be d cm. Then L = = (diameer of cylinder) = cm ª 0 cm p p 5 Load, was Resisance of he wire, R = = 00 = 00 W ( curren) Spacing beween wo consecuive urns = d cm Disance along he axis of he cylinder beween consecuive urns = d cm L 0 0 Therefore, Number of urns = = = d d d Lengh of urn of wire = p 5 cm Lengh of wire l = p p = cm d d Now, he resisance of wire of lengh m and area of cross secion mm is W. Then, r = mm - W W 0 cm -4 = = 0 Wcm m 00 cm 0-4 \ R = = = - 50p d pd d. All righs reserved.

24 4 Basic Elecrical Engineering Then, d 3 = 0-4 or d = cm and l = 50p d 50p = = 700 cm = 7 m Temperaure Coefficien of Resisance All curren-carrying conducors and resisors dissipae hea when carrying curren. When V vols applied across a resisor of R ohm causes a curren of I ampere o flow, he elecrical energy absorbed by he resisor is a he rae of V I or I R which is convered ino hea, hereby causing a emperaure rise in he resisor. When he resisor becomes warmer han is surrounding medium, i dissipaes hea ino he surrounding medium. Finally, when he release of hea energy is a he same rae as i receives elecric energy, he emperaure of he resisor no longer rises. All resisors have a power raing, which is he maximum power ha can be dissipaed wihou he emperaure rise being damaging o he resisor. Thus a 4 W resisor of 00 W can pass a curren of 0 ma, whereas a /4 W resisor of 00 W can allow only 50 ma. If he curren level exceeds, he resisances are overheaed and migh burn. The resisance of mos conducors and all meals increases wih increase in emperaure. However, he resisance of carbon and insulaing maerials decreases wih increase in emperaure. Cerain alloys such as consanan (60% copper and 40% nickel) and manganin (84% copper, % manganese, and 4% nickel) show no change in resisance for a considerable variaion in emperaure. This makes hese alloys ideal for he consrucion of accurae resisances used in resisance boxes. Invesigaions reveal ha a linear variaion of resisance wih emperaure for copper prevails over a emperaure range -50 C o 00 C. The change in resisance is usually proporional o he change in emperaure. The emperaure coefficien of resisance is he raio of he change in resisance per degree change in emperaure o he resisance a some definie (reference) emperaure and is denoed by he Greek leer a. Figure.0 shows he linear variaion of he resisance of copper wih he change in emperaure. I may be seen from he graph ha a C is resisance becomes heoreically zero. If R 0 = W is he resisance of copper a 0 C, hen R = 0 W a C, and by definiion he emperaure coefficien of copper a 0 C, a 0 is given by R0 - R W 0 -(-34. 5) a 0 = C = = / C (.6) R0 W In general, resisance R a any emperaure can be expressed in erms of resisance R a emperaure as R = R [ + a ( - ) (.7) Resisance, R R R R Temp. in C Fig..0 Variaion of resisance of copper wih emperaure where a is he emperaure coefficien a emperaure. Suppose he reference emperaure is aken as 0 C. Then. All righs reserved.

25 R = R 0 ( + a 0 ) R = R 0 ( + a 0 ) ( + a0 ) \ R = R ( + a ) 0 Inroducion o Elecrical Engineering 5 (.8) Equaing Eqs (.7) and (.8) and simplifying, he value of a is given as a0 a = (.9) + a0 Similarly, he specific resisance r varies linearly wih emperaure. The expression for r, he resisiviy a emperaure, in erms of r 0, he resisiviy a 0 C, will be r = r 0 ( + a 0 ) (.30) Typical values of resisiviy and emperaure coefficiens of resisances a 0 C are given in Table.. Table. Resisiviy and emperaure coefficien Maerial Resisiviy a 0 C, W m Temperaure coefficien, a 0 Copper, annealed o Aluminium, hard drawn Carbon Tungsen Manganin Consanan (Eureka) Example. A poenial difference of 50 V is applied o a copper field coil a a emperaure of 5 C and he curren is 5 A. Wha will be he mean emperaure of he coil when he curren has fallen o 3.9 A, he applied volage being he same as before? The emperaure coefficien of copper a 0 C is Soluion A 5 C, R 5 = 50 = 50 W 5 A C, R = 50 = W 39. R Then = + a0 R5 + a or = Hence = C. Example. If he resisance emperaure coefficien of a conducor is a a C, derive an expression for he emperaure coefficien a a C in erms of a and he emperaures. Soluion From Eq. (.9), i is seen ha a0 a a = or a + 0 = a0 - a a Similarly, 0 a = + a 0. All righs reserved.

26 6 Basic Elecrical Engineering Subsiuion of a 0 in he expression for a resuls in a Ê a ˆ Ë Á- a = Ê a ˆ + Ë Á- a a = = + a( - ) + ( a - ).9. Inducors The elecrical elemen ha sores energy in associaion wih a flow of curren is called inducor. The idealized circui model for he inducor is called an inducance. Pracical inducors are made of many urns of hin wire wound on a magneic core or an air core. Fig.. Schemaic represenaion of an inducor A unique feaure of he inducance is ha is presence in a circui is fel only when here is a changing curren. Figure. shows a schemaic represenaion of an inducor. For he ideal circui model of an inducor, he volage across i is proporional o he rae of change of curren in i. Thus if he rae of change of curren is di/d and v is he induced volage, hen v µ di d or v = L di V (.3) d In Eq. (.3) he proporionaliy consan L is called inducance. The uni of inducance is henry, named afer he American physicis Joseph Henry. Equaion (.3) may be rewrien as v vol-second L = = di ampere or henrys (H) (.3) d Equaion (.3) can be used o define inducance. If an inducor induces a volage of V when he curren is uniformly varying a he rae of A/sec, i is said o have an inducance of H. Inegraing Eq. (.3) wih respec o ime, i = vd i 0 L Ú + ( ) (.33) 0 where i(0) is he curren a = 0. From Eq. (.33) i may be inferred ha he curren in an inducor canno change suddenly in zero ime. Insananeous power p enering he inducor a any insan is given by p = vi = Li di (.34) d When he curren is consan, he derivaive is zero and no addiional energy is sored in he inducor. When he curren increases, he derivaive is posiive and hence he power is posiive; and, in urn, an addiional energy is sored in he inducor. The energy sored in he inducor, W L, is given by W L = vid Li di Ú = Ú d = L idi = Li 0 0 d Ú joule (.35) 0 Equaion (.35) assumes ha he inducor has no previous hisory, ha is, a = 0, i = 0. The energy is sored in he inducor in a magneic field. When he curren increases, he sored energy in he magneic field also increases. When he curren reduces o zero, he energy sored in he inducor is reurned o he source from which i receives he energy.. All righs reserved.

27 i Example.3 A curren having a variaion shown in Fig.. (A) is applied o a pure inducor having a value of H. Calculae 0 he volage across he inducor a ime = and = 3 sec. Soluion For he period 0 sec Curren, i = 0 A Rae of change of curren di = 0 A/sec d Therefore, a = sec, volage across he inducor is L di = 0 = 0 V d For he period 3 sec Rae of change of curren di = -5 A/sec d Therefore, a = 3 sec, volage across he inducor is L di = -5 = -0 V d v (V) Example.4 A volage wave having he ime variaion 0 shown in Fig..3 is applied o a pure inducor having a value of 0.5 H. Calculae he curren hrough he inducor a imes =,, 3, 4, 5 sec. Skech he variaion of curren 0 hrough he inducor over 5 sec. 0 Soluion For he period 0 sec, v = 0 V; i(0) = 0. The curren i may be expressed using Eq. (.33) as i = vd + i ( 0) = 0 d = 0 d = 0 L Ú0 05. Ú0 Ú0 Then a = sec, i = 0 = 0 A For he period 3 sec, v = -0 V; i() = 0 A, hen curren i = vd+ i () = - 0 d + 0=- 0 d + 0=-0( - ) + 0 LÚ 05. Ú Ú Then a = sec, i = - 0 ( - ) + 0 = = 0 A And a = 3 sec, i = - 0 (3 - ) + 0 = = - 0 A For he period 3 5 sec, v = 0 V; i(3) = - 0 A, i = vd+ i() 3 = 0d - 0 LÚ3 05. Ú3 = 0 d - 0 = 0 ( -3) -0 Ú3 Then a = 4 sec, i = 0 (4-3) - 0 = 0-0 = 0 A And a = 5 sec, i = 0 (5-3) - 0 = 40-0 = 0 A i (A) Fig..4 Inroducion o Elecrical Engineering 7 0 3, sec Fig Fig (sec) Variaion of curren hrough he inducor (sec). All righs reserved.

28 8 Basic Elecrical Engineering Example.5 The volage waveform shown in Fig..5 is applied across an inducor of 5 H. Derive an expression for curren in he circui and skech he curren and energy waveforms agains ime. Assume zero iniial condiion in he circui. Vols 8 Soluion Using Eq. (.3), he generalized relaion for curren hrough he inducor is wrien as i = vd 5Ú0 For he period 0 sec, v = V. Therefore, he curren hrough he inducor is given by i= d = 4. + i Ú ( 0) 5 0 A = 0, i(0) = 0. 0 Fig , sec Thus, i =.4 For he period 3 sec, v = 8 V. Therefore, he curren hrough he inducor is given by i= 8d = i Ú ( 0. ) 5 0 A =.0 sec, i =.4 A. Hence,.4 = i(.0) or i(.0) = -. A The expression for he inducor curren during he period 3 sec is i = For he period 3 4 sec, v = V. Hence, he curren hrough he inducor is expressed as i= d = 4. + i Ú ( 30. ) 5 0 A = 3.0 sec, i = 9.6 A. Hence, 9.6 = i(3.0) or i(3.0) =.4 A \ i = Energy sored in he various periods is as follows. Inducor curren (A) (sec) 4 Inducor energy (J) Time (sec) Fig..6 Fig..7. All righs reserved.

29 For he period 0 sec, WL = ( ) = J For he period 3 sec, WL = ( - ) = J For he period 3 4 sec, WL = ( + ) = J The variaion of inducor curren and energy wih ime is skeched in Figs.6 and.7. Inroducion o Elecrical Engineering Capaciors A capacior is a device ha can sore energy in he form of a charge separaion when i is suiably polarized by an elecric field by applying a volage across i. In he simples form, a capacior consiss of wo parallel conducing plaes separaed by air or any insulaing maerial, such as mica. I has he characerisic of soring elecric energy (charge), which can be fully rerieved, in an elecric field. A significan feaure of he capacior is ha is presence is fel in an elecric circui when a changing poenial difference exiss across he capacior. The presence of an insulaing maerial beween he conducing plaes does no allow he flow of dc curren; hus a capacior acs as an open circui in he presence of dc curren. Figure.8 shows he schemaic represenaion of a capacior. The abiliy of he capacior o sore charge is measured in erms of capaciance C. Capaciance of a capacior is defined as charge sored per vol applied and is uni is farad (F). However, for pracical purposes he uni of farad is oo large. Hence, microfarad (mf) is used o specify he capaciance of he componens and circuis. In Fig..8(b), i is assumed ha he charge on he capacior a any ime afer he swich S is closed is q coulombs and he volage across i is v vols. Then by definiion q C = coulomb (.36) v Curren i flowing hrough he capacior can be obained as i = dq = C dv ampere (.37) d d Equaion (.37) is inegraed wih respec o ime o ge he volage across he capacior as v = id v 0 C Ú + ( ) (.38) 0 where v(0) is an inegraion consan which defines he iniial volage across he capacior a = 0. I may be noed from Eq. (.38) ha he volage across a capacior canno change insananeously, ha is, in zero ime. Power p in he capacior is given as p = vi = Cv dv wa (.39) d Energy sored in he capacior, W C, is given by Ú W C = pd = C vdv = Cv Ú S Fig..8 joule (.40) I C + (a) + C V (b) (a) Schemaic represenaion of a capacior and (b) capacior across a dc source. All righs reserved.

30 0 Basic Elecrical Engineering From Eq. (.40) i is eviden ha he energy sored in he capacior is dependen on he insananeous volage and is reurned o he nework when he volage is reduced o zero. As saed earlier, a capacior consiss of wo elecrodes (plaes) separaed by an insulaing maerial (dielecric). If he area of he plaes is A m and he disance beween hem is d m, i is observed ha C µ A and C µ d \ C = e A (.4) d where e is he absolue permiiviy consan. The absolue permiiviy consan depends on he ype of dielecric employed in he capacior. The raio of he absolue permiiviy consan of he dielecric e o he permiiviy consan of vacuum e 0 is called relaive permiiviy e r, ha is, e r = e e 0 Hence, e = e 0 e r. The unis for absolue permiiviy e can be esablished from Eq. (.4) as under: e = C ( farads ) d ( meres) C d = farads /mere (F /m) A ( meres) A Based on experimenal resuls, he value of he permiiviy consan of vacuum has been found o be equal o F/m. Therefore, he value of e r for vacuum is.0 and for air is For pracical purposes, he value of e r for air is also aken as. Example.6 A volage wave having a ime variaion of 0 V/sec is applied o a pure capacior having a value of 5 mf. Find (a) he curren during he period 0 sec, (b) charge accumulaed across he capacior a = sec, (c) power in he capacior a = sec, and (d) energy sored in he capacior a = sec. Soluion (a) Curren hrough he capacior i may be obained using Eq. (.37) as i = C dv = = 500 ma d (b) A = sec, v = 0V. Charge q a = sec may be obained using Eq. (.36) as q = C v = = 500 mc (c) A = sec, power p = v i = = 0 - W (d) A = sec, energy sored in he capacior, W C, can be obained using Eq. (.40) as W C = -6-3 Cv = 5 0 ( 0) = 5 0 J Example.7 A curren having variaion shown in Fig..9 is applied o a pure capacior having a value of 5 mf. Calculae he charge, volage, power, and energy a ime = sec. Soluion For he period 0 sec, i = = 0. A A = sec, q = id = 0 d = Ú0 Ú È = 0 Î Í =.. =. [ ] = =. 05[ - 0] = 005. C = 0 v = q i(a) ma = 0. d= C CÚ where = 00 = 00 V = sec, 3 4 (sec) Fig..9. All righs reserved.

31 p = v i = = 0 W 4 W C = 3 vi d = d = d= Ú0 Ú0 Ú È Î Í = [ - ] = 05J. For he period 0 sec, i = A A = sec, Charge q = q = + id = d = Ú Ú È. ( 0.. ). Í. -. Î Volage v = q È = + ( - d ) C C Í Î Ú 0. = [ ] Power = = 0 = [0.( - ) ( - ) ] = = 0. C = - = 6 6 = 0 0 [ ( -) ( - )] = 0. = 00 V p = v i = 00 0 = 0 W Energy W C = W C.= + vi d Ú = È Í [ ] ( ) Ú -6 Î500 0 d 6 = [ ] d 500Ú Energy W C = È ÎÍ = = = 75. J 500 Inroducion o Elecrical Engineering = =.0 ELECTROMAGNETISM RELATED LAWS Some laws relaed o elecromagneism are discussed in his secion..0. Magneic Field Due o Elecric Curren Flow Hans Chrisian Oersed, a Danish physicis, in 83 discovered ha curren flowing in a conducor generaes a magneic field all around i. He proved ha he magneic lines of force due o he curren flow in a conducor were concenric circles closed on hemselves as shown in Fig..0. The direcion of he magneic lines of force depends upon he direcion of curren. The convenion adoped o show he direcion of he curren flow is ha curren flowing ino he plane of he paper is indicaed by a cross sign and curren flowing ou of he plane of he paper is shown by a do. Maxwell s corkscrew rule is a convenien mehod of deermining he direcion of he magneic field se up by a curren-carrying conducor. I saes ha if a righ-handed corkscrew is placed along he direcion of he curren flow, Fig..0 = = Magneic field due o curren in a sraigh conducor. All righs reserved.

32 Basic Elecrical Engineering he direcion of moion of he hand, which would advance he screw in he direcion of he curren, gives he direcion of magneic field as shown in Fig..(a). Anoher mehod of deermining he direcion of he field is o employ he righ hand rule. Imagine he curren-carrying conducor o be held in he righ hand wih he humb poining in he direcion of he curren wih he fingers wrapped around i. Then he direcion of he fingers poins in he direcion of he magneic field. Magneic field of a solenoid When a curren-carrying conducor is given he shape of circular coils of he conducor placed side by side and insulaed from one anoher, i is called a solenoid [see Fig..(b)]. The magneic field is represened by he doed lines. If he fingers of he righ hand are wrapped around he curren-carrying conducor wih he fingers poining in he direcion of he curren, hen he humb ousreched parallel o he axis of he solenoid poins in he direcion of he magneic field inside he solenoid. If an iron rod is placed inside he solenoid coil, as shown in Fig..(b), and he coil is conneced o a volage source, he iron rod is magneized and behaves like a magne. The magneic field becomes hundreds of imes sronger. Fig.. (a) I S l + (b) (a) Maxwell s corkscrew rule and (b) solenoid wih a magneic core.0. Force on a Curren-carrying Conducor Placed in a Magneic Field If a curren-carrying conducor is placed a righ angles o he lines of force of a magneic field, a mechanical force will be exered on he conducor. The magniude of he mechanical force can be calculaed by using Ampere s law..0.. Ampere s Law When a sraigh elemenal conducor of lengh l meres and carrying curren I amperes is placed in he same horizonal plane a a disance of r meres from a sraigh, long conducor carrying curren I amperes in he opposie direcion o I, he small conducor experiences a force of repulsion, F, given by F = m I pr Il newon (.4) = B I l newon (.43) where B = m I esla (T) (.44) p r In Eq. (.44) m is a scalar consan of he medium (called permeabiliy of he medium) and B is he magneic flux densiy. From Eq. (.43) i may be noed ha he uni of flux densiy is aken as he densiy of he magneic field such ha a conducor carrying A a righ angles o ha field experiences a force of Nm. The uni is N. All righs reserved.