大学物理下课件31-Electromagnetic-Oscillations-and-Alterna

ElectromagneticOscillationsAndAlternatingCurrent

Dr.HuaqiuDengE-mail:hqdeng@LCOscillationsLCOscillationsSampleProblem-LCoscillator:potentialchange,rateofcurrentchangeProblem:A1.5μFcapacitorischargedto57Vbyabattery,whichisthenremoved.Attimet=0,a12μHcoilisconnectedinserieswiththecapacitortoformanLCoscillator.(a)WhatisthepotentialdifferenceVL(t)acrosstheinductorasafunctionoftime?(b)Whatisthemaximumrate(di/dt)maxatwhichthecurrentichangesinthecircuit?Solution:(a)(b)DampedOscillationsInARLCCircuitQuestion:whathappenstotheoscillationofRLCcircuitcontainingresistor,inductor,andcapacitor?Answer:dampedoscillation-theoscillationsofcharge,current,andpotentialdifferencecontinuouslydecreaseinamplitudeAnoscilloscopetraceshowinghowtheoscillationsinanRLCcircuitactuallydieawaybecauseenergyisdissipatedintheresistorasthermalenergy.AnalysisOfDampedOscillationsInARLCCircuitThetotalelectromagneticenergydecreasesasenergyistransferredtothermalenergy:SampleProblem-DampedRLCcircuit:chargeamplitudeProblem:AseriesRLCcircuithasinductanceL=12mH,capacitanceC=1.6μF,andresistanceR=1.5Ωandbeginstooscillateattimet=0.(a)Atwhattimetwilltheamplitudeofthechargeoscillationsinthecircuitbe50%ofitsinitialvalue?(b)Howmanyoscillationsarecompletedwithinthistime?Solution:(a)(b)Answer:theamplitudedecaysby50%inabout13completeoscillationswithin0.011sL=12mH,C=1.6μF,R=1.5Ω

AlternatingCurrentQuestion:whathappensifaconductingloopisforcedtorotatethroughtheexternalmagneticfieldwithdrivingangularfrequencyωd?-Resultedsinusoidallyoscillatinginducedemfεintheloop:-Resultedsinusoidallyoscillatinginducedcurrentiintheloop:Alternatingcurrentintheworld:

-NorthAmericaandJapan:directionofacischanged120timespersecond,andhavingfrequencyf=60Hz;-China:directionofacischanged100timespersecond,andhavingfrequencyf=50Hz)Answer:-ResultinAlternatingcurrent(ac)

(foundbyNikolaTesla，1856—1943)varyingsinusoidallywithtime,andreversingdirectioninhalfperiodForcedOscillationsFreeoscillations(freeofanyexternalemf):-ForbothundampedLCcircuitsanddampedRLCcircuits(withsmallenoughR)Forcedoscillations:-TheexternalalternatingemfisconnectedtoanRLCcircuitResultofforceoscillation:

whateverthenaturalangularfrequencyωofacircuitmaybe,forcedoscillationsofcharge,current,andpotentialdifferenceinthecircuitalwaysoccuratthedrivingangularfrequencyωd.ThreeSimpleCircuits-AResistiveLoadForphasors:ThreeSimpleCircuits-ACapacitiveLoadThreeSimpleCircuits-AnInductiveLoadTheSeriesCircuitResistor:currentandvoltageareinphase;sotheangleofrotationofvoltagephasorVRisthesameasthatofphasorI.Capacitor:

currentleadsvoltageby90°;sotheangleofrotationofvoltagephasorVCis90°lessthanthatofphasorI.Inductor:

currentlagsvoltageby90°;sotheangleofrotationofvoltagephasorvL

is90°greaterthanthatofphasorI.TheCurrentAmplitudeOfSeriesCircuitCurvesforthedrivenRLCcircuitwithL=100μH,C=100pF,andthreevaluesofR.TheCurrentAmplitudeOfSeriesCircuitThePhaseConstantOfSeriesCircuitResonanceofTheSeriesCircuitResonancecurvesforthedrivenRLCcircuitwithL=100μH,C=100pF,andthreevaluesofR.PowerInAlternatingCircuitsPowerInAlternatingCircuitsEnergyTransmissionRequirementsOfTransformersRule:usethelowestpracticalcurrent(hencethelargestpracticalvoltage)tominimizeI2RlossesinthetransmissionlineEnergyTransmission:Highvoltagetransmissionlinesdeliverpowerfrom

electricgeneration

plantsoverlongdistancesusingalternatingcurrent.

ElectricgeneratorEnergyTransmissionRequirementsOfTransformersExample:a735kVlineisusedtotransmitelectricalenergyfromtheLaGrande2hydroelectricplantinQuebectoMontreal,1000kmaway.Supposethatthecurrentis500Aandthepowerfactorisclosetounity.Then,energyissuppliedattheaveragerate:Theresistanceofthetransmissionlineisabout0.220Ω/km,energyisdissipatedabout:Doubledthecurrentandhalvedthevoltage.Energywouldbesuppliedbytheplantatthesameaveragerateof368MWaspreviously,butnowenergywouldbedissipatedattherateofabout:TheIdealTransformerTransformer:raiseacvoltagefortransmissionandloweracvoltageforuseinacircuit,keepingtheproduct(currentxvoltage)essentiallyconstant.Idealtransformer:consistsoftwocoils,withdifferentnumbersofturns,woundaroundanironcore:-Primarywinding:

apureinductance,Npturns-Secondarywinding:

Nsturns,connectedtoloadresistanceRWorking:smallsinusoidallychangingprimarycurrentImag

→asinusoidallychangingmagneticfluxΦintheironcore→Thecoreactstostrengthenthefluxandtobringitthroughthesecondarywinding→inducesanemfƐturn(=dΦ/dt)ineachturnofthesecondarybecauseΦvariesTheidealTransformerSampleProblem-Transformer:turnsratio,averagepower,rmscurrentsProblem:AtransformeronautilitypoleoperatesatVp=8.5kVontheprimarysideandsupplies