电路基础chapter2

1Chapter2BasicLaws2.0ObjectivesForThisChapter2.1Introduction.2.2Nodes,Branches,andLoops.2.3Kirchhoff’sLaws.2.4EquivalentSubcircuits2.5SeriesResistorsandVoltageDivision.2.6ParallelResistorsandCurrentDivision.2.7Wye-DeltaTransformations.22.0ObjectivesForThisChapterInthischapter,weseektodevelopour•Understandingofthedistinctionbetweennodes,paths,loops,andbranches•AbilitytoemployKirchhoff’scurrentlaw(KCL)•AbilitytoemployKirchhoff’svoltagelaw(KVL)•Skillsinanalyzingsimpleseriesandparallelcircuits•Abilitytosimplifyseriesandparallelconnectedsources•Competenceatreducingseriesandparallelresistorcombinations•Intuitiveunderstandingofvoltageandcurrentdivision32.1Introduction•Afterhavingintroducedidealvoltageandcurrentsources,aswellastheresistor,wearereadytoinvestigatethebehaviorofbasicelectriccircuits.•Twoimportantlaws,Kirchhoff’scurrentlawandKirchhoff’svoltagelaw,formthefoundationforcircuitanalysisprocedures.•Wewillalsofindthatitisoftenpossibletosimplifycircuitsbycombiningelementsthatareconnectedinseriesorparallel－thisappliestovoltageandcurrentsourcesaswellasresistors.42.2BranchesandLoops,Nodes•Branch:Abranchrepresentsasingleelementsuchasavoltagesourceoraresistor.•Loop:Aloopisanyclosedpathinacircuit.•Idealizedwires:idealizedwiresallowcurrenttoflowwithoutimpediment(nochargeaccumulationsorvoltagedropsalongtheleads,nopowerorenergydissipation)•Lumpedparametercircuit:Lumpedparametercircuittheenergycanbeconsideredtoreside,orbelumped,entirelywithineachcircuitelement.5•Distributedparametercircuit:unsatisfiedthelumpedparametercircuitabovestatedistermedDistributedparametercircuit.•Node:Anodeisthepointofconnectionbetweentwoormorebranches.AnexampleofacircuitwiththreenodesinshowninFig.2.1(a).Fig.2.1(a)Fig.2.1(b)6•Nodecanbeindicatedindiagramsintwoways:byathinlineenclosingthenode,aswithnodesbandc;bymarkingatypicalpointwithinthenode,aswithnodeaofFig.2.1(a).Whicheverisused,itisimportanttorememberthatanodeisallthewireindirectcontactwithagivenpoint,andthusanytwopointthatcanbetraversedbymovingexclusivelyalongconnectingwiresarebothpartofthesamenode.7•Anetworkwithbbranches,nnodes,andlindependentloopswillsatisfythefundamentaltheoremofnetworktopology:•Circuittopologyisofgreatvaluetothestudyofvoltagesandcurrentsinanelectriccircuit.•Twoormoreelementsareinseriesiftheyarecascadedorconnectedsequentiallyandconsequentlycarrythesamecurrent.•Twoormoreelementsareinparalleliftheyareconnectedtothesametwonodesandconsequentlyhavethesamevoltageacrossthem.1nlb（2.1）8Example1Fig.2.22.2BranchesandLoops,Nodes(2)DeterminethenumberofbranchesandnodesinthecircuitshowninFig.2.2Solution:Sincetherearefiveelementsinthecircuit,thecircuithasfourbranches.Inaddition,thecircuithasthreenodes,a,bandc9Example2Howmanybranches,nodesandloopsarethere?Shouldweconsideritasonebranchortwobranches?102.3Kirchhoff’sLaws(1)•Kirchhoff’scurrentlaw(KCL)statesthatthealgebraicsumofcurrentsenteringanode(oraclosedboundary)iszero.01NnniMathematically,KCLimpliesthatWhereNisthenumberofbranchesconnectedtothenodeandinisthenthcurrententeringthenode.(2.2)11Fig.2.3currentsatanodeillustratingKCL•TheotherformsofKCLThealgebraicsumoftheleavinganynodeiszero.ForthenodeinFig.2.3,weobtainThesumofthecurrentsenteringanynodeequalsthesumofthecurrentsleavingthenode.ForthenodeinFig.2.3,thereisfollowingequation123450iiiii13425iiiii12•NotethatKCLalsoappliestoaclosedboundary.Intwodimensions,aclosedboundaryisthesameasaclosedpath.•AsFig.2.4show,thetotalcurrententeringtheclosedsurfaceisequaltothetotalcurrentleavingthesurface.Fig.2.4ApplyingKCLtoclosedboundary132.3Kirchhoff’sLaws(2)Example3•DeterminethecurrentIforthecircuitshowninthefigurebelow.I+4-(-3)-2=0I=-5AWecanconsiderthewholeenclosedareaasone“node”.ThisindicatesthattheactualcurrentforIisflowingintheoppositedirection.14Example4ForthecircuitinFig.2.5a,computethecurrentthroughresistorR3ifisknownthatthevoltagesourcesuppliesacurrentof3A.Fig.2.515•Identifythegoaloftheproblem.ThecurrentthroughresistorR3hasalreadybeenlabelasionthecircuitdiagram.•Collecttheknowninformation.ThiscurrentflowsfromthetopnodeofR3,whichisconnectedtothreeotherbranches.Thecircuitsflowingintothenodefromeachbranchwilladdtoformthecurrenti.•Decidewhichavailabletechniquebestfitstheproblem.WebeginbylabelingthecurrentthroughR1(Fig.2.5b)sothatwemaywriteaKCLequationatthetopnodeofresistorR2andR3.16•Constructanappropriatesetofequations.Summingthecurrentsflowingintothenode:iR1－2－i＋5=0ThecurrentflowingintothisnodeareshownintheexpandeddiagramofFig.2.5cforclarity.•Determineifadditionalinformationisrequire.Weseethatwehaveoneequationbuttwounknowns,whichmeansweneedtoobtainanadditionequation.Atthispoint,thefactthatweknowthe10-Vsourceissupplying3Acomesinhandy:KCLshowsusthatthisisalsothecurrentiR1.17•Attemptasolution.Substituting,wefindthati=3－2＋5=6A.•Verifythesolution.Isitreasonableorexpected?Itisalwaysworththeefforttorecheckourwork.Also,wecanattempttoevaluatewhetheratleastthemagnitudeofthesolutionisreasonable.Inthiscase,wehavetwosources－onesupplies5A,andothersupplies3A.Therearenoothersources,independ