《大學物理簡明教程》 課件 16-3 RLC Circuit

RLCcircuit-ImpedanceZistheimpedance-combinedeffectofallcomponentsxPhasor-arotatingvectoryPPx

A

o{

simpleharmonicoscillation

PhasedifferenceThephasedifferencebetweentwophasorswon’tchangeduringtherotation,iftheyhavethesamefrequency.Phasorshavingsameangularfrequencyx-componentsvaryingatsamefrequency

vectorsumofthephasorssumoftheoscillationsComplexnumber

orj,unitimaginarynumberAcomplexnumber:aandbarerealnumbersrealpartimaginarypartEuler’sFormula

Acomplexnumber:

ImaginarypartRealpartrotatingphaseangleoscillatingrealpartangularspeed

angularfrequency

The“physics”expressionofsimpleharmonicoscillationWecanexpressvoltageandcurrentinanACcircuitasvectors(phasors)inthecomplexplaneAmplitudePhaseThevaryingvoltage/current

arerepresentedbytherealparts

ofrotatingvectorsThephaseofthevoltageandthecurrentarethesameSimpleresistorcircuitInductors:thevoltageleadsthecurrentbyπ/2inductivereactance:InductorCapacitors:thevoltagelagsthecurrentbyπ/2capacitivereactance:Capacitors

orThephasorsofseveralcomponentsinseries?voltagescurrentsincommonVCVRVLV=VR+VC+VLVvectorsumofthephasorsRCCircuitsVC=VR=

VR

=IRRC

Lasttime,wehadtosolveadifferentialequationThesameresultbyusingphasorsPhasedifferenceinRCCircuitsThephaseanglebetweenthevoltageandthecurrentThesameastheresultofsolvingdifferentialequationThepowerinthecircuitisgivenby:

Itis1forpurelyresistivecircuitItis0forpurelycapacitive/inductivecircuit=3.125

(b)(c)(a)LRCircuitsThepowerfactoris:Currentsinresistors,capacitors,andinductorsasafunctionoffrequency:TheRLCcircuitThecurrentisthesameeverywhere

ImpedanceoftheRLCcircuitPhasebetweenIandV:Thepowerfactor:

positive

:VleadsIOr=0PowerintheACcircuitThisisthe“Powerfactor”ForRLCcircuit40Ω5μF3mHImped