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1、Chapter19Chapter19SummarySuppperpositiontheoremThesuperpositiontheoremthatyoustudiedindccircuitscanbeappliedtoaccircuitsbyusingcircuitscanbeappliedtoaccircuitsbyusingcomplexnumbers.Recallthatitisappliedtocircuitswithmultipleindependentsourcestosolveforthecurrentinanyelement.Onewaytosumm
2、arizethesuperpositiontheoremisInalinearcircuitwithmultipleindependentsources,thecurrentinanyygelementisthealgebraicsumofthecurrentsproducedbyeachsourceactingalone.PrinciplesofElectricCircuits,ConventionalFlow,9thed.©2010PearsonHigherEducation,PrinciplesofElectricCircuits,ConventionalFlo
3、w,9thed.©2010PearsonHigherEducation,FloydUpperSaddleRiver,NJ07458.•AllRightsReservedFloydUpperSaddleRiver,NJ07458.•AllRightsReservedChapter19Chapter19SummarySummarySuppperpositiontheoremSuppperpositiontheoremC1C2C1C2−j10kΩ−j20kΩStepsfromthetextareappliedinStep1.(continued)−j10kΩ−j20kΩVR
4、VS2thefollowingexample.TosimplifyRS16.8kΩVS1686.8kΩVS2LookingfromLookingfromVS1,thetotal,thetotal5500V.00∠°Vzeroedthisexample,reactancesaregiven5.00V∠°7.00V∠°impedance(inkΩ)isforthecapacitors.RX()6.80∠°(20∠−°90)()6.80∠°(20∠−°90)ZX=+++C2=−jj10+=−10++C1RX+−6.8j2021.12∠−71.2°C2Whatisthecur
5、rentinC2?Theinternalsourceresistancesarezero.Step1.C1C2Z=−+∠jj10()6.44−°18.8=−+−10()6.10j2.08=−6.10j12.0813.5=∠−°63.2ReplaceVS2withitsinternalV5.00∠°−j10kΩ−j20kΩThetotalcurrentfromVisI==S1=∠°0.3763.2impedance(zero)andfindIC2RS1S1VVS2Z13.5∠−63.2°duetoVactingalone.S16.8kΩS1g5500V.00∠°Vzee
6、oedroedApplycurrentdividertofindIC2duetoVS1:R∠°06⎛⎞.8∠°0Note:Tosimplifymathequations,unitsarenotshownonthesolution.AllII==⎜⎟0.3763.2∠°=0.119134.4∠°CS21R−∠jX⎝⎠21.12−71.2°impedancesareinkimpedancesareinkΩ,currentsinmAandvoltagesinVcurrentsinmA,andvoltagesinV.C2continued...continued...Prin
7、ciplesofElectricCircuits,ConventionalFlow,9thed.©2010PearsonHigherEducation,PrinciplesofElectricCircuits,ConventionalFlow,9thed.©2010PearsonHigherEducation,FloydUpperSaddleRiver,NJ07458.•AllRightsReservedFloydUpperSaddleRiver,NJ07458.•AllRightsReservedChapter19Chapter19SummaryS
