Whydoesalternatingcurrentfacilitatethetransmissionanddistributionofelectricpower?為甚麼交流電造就了電力的輸送和分配？EMinductionallowsvoltagetransformation.電磁感應(yīng)讓電壓得以轉(zhuǎn)變。28.1.AlternatingCurrent 交流電Reminder:Allwavescanbeanalyzedintermsofsinusoidalwaves(FourieranalysisChap14).提醒你：所有波動(dòng)都可以用正弦波來(lái)分析(傅里葉分析，14章)。Sinusoidalwave(Chap13):正弦波(13章)：Angularfrequency:角頻（率）：[]=rad/s

=phase相位

=/6Vpsin

Example28.1.CharacterizingHouseholdVoltage

為住宅電壓定性Standardhouseholdwiringsupplies110Vrmsat60Hz.標(biāo)準(zhǔn)住宅線(xiàn)路的電源是60

Hz和110V均方根。Expressthismathematically,assumingthevoltageisrisingthrough0att=0.以數(shù)學(xué)表達(dá)它，並假設(shè)電壓在t=0開(kāi)始從0上升。

28.2.CurrentElementsinACCircuits

AC線(xiàn)路的電流元件Resistors 電阻器Capacitors 電容器Inductors 電感器PhasorDiagrams 相位子圖Capacitors&Inductors:AComparison 電容器和電感器：對(duì)比DisplacingFunctions 移動(dòng)函數(shù)xx

fggismovedtotheright(forward)bytogivef.g往右(前)移

以得f.sincosDisplacement: siniscosmovedforwardby/2.位移： sin是cos往前移/2.Phase: sinlagscosby/2.相位： sin落後

cos/2.Derivative:movessinusoidalfunctionsbackwardby/2.導(dǎo)數(shù)：將正餘弦函數(shù)往後移/2。 phaseisincreasedby/2.相位增/2.Integral:movessinusoidalfunctionsforwardby/2.積分：將正餘弦函數(shù)往前移/2。 phaseisdecreasedby/2.相位減/2.Resistors 電阻器I&VinphaseI&V同相+VR

I+

WhenV(t)>0:V(t)>0時(shí):Capacitors 電容器IleadsVby90

I超前V90

Capacitivereactance電容電抗Static:openckt.直流電：斷路HF:shortckt.高頻：短路Ipeaks?cyclebeforeVI比V早?週期達(dá)峰值+VC

I+

WhenV(t)>0:V(t)>0時(shí):Inductors 電感器ItrailsVby90

I落後V90

Inductivereactance電感電抗DC:shortckt.直流電：短路HF:openckt.高頻：斷路Ipeaks?cycleafterVI比V晚?週期達(dá)峰值I+

WhenV(t)>0:V(t)>0時(shí):

L+Table28.1.Amplitude&PhaseinCircuitElements

線(xiàn)路元件的幅度與相位CircuitElement線(xiàn)路元件PeakCurrentvsVoltage電流對(duì)電壓峰值PhaseRelation相位關(guān)係Resistor電阻器Capacitor電容器Inductor電感器V&IinphaseV&I同相VlagsI90

V落後I90

VleadsI90

V領(lǐng)先I90

GOTIT?28.1.Acapacitorandaninductorareconnectedacrossseparatebutidenticalelectricgenerators,andthesamecurrentflowsineach.一個(gè)電容器和一個(gè)電感器分別連在兩個(gè)同樣的發(fā)電機(jī)上，而且兩者的電流相同。Ifthefrequencyofthegeneratorsisdoubled,whichwillcarrymorecurrent?如果發(fā)電機(jī)的頻率加倍，那一個(gè)的電流較大？Ans.iscapacitor答案是電容器Example28.2. EqualCurrents 一樣的電流?Acapacitorisconnectedacrossa60-Hz,120-Vrmspowerline,&anrmscurrentof200mAflows.一個(gè)電容器接在一條60-Hz,120-Vrms的電力線(xiàn)上，其電流為200mArms。Findthecapacitance. 求其電容量。Whatinductance,connectedacrossthesamepowerline,wouldresultinthesamecurrent?如果用電感器接在同樣的電力線(xiàn)上，電感量要多少才能達(dá)到同樣的電流？Howwouldthephasesoftheinductor&capacitorcurrentscompare?電感器和電容器的相位有何差別？(a)(b)(c)Capacitor:IC

leadsVby90.電容器：IC

領(lǐng)先V90

Inductor:VleadsIL

by90.電感器：V領(lǐng)先

IL

90.IC

leads

IL

by180.IC領(lǐng)先IL

180.

PhasorDiagrams 相位子圖Phasor=Arrow(vector)incomplexplane.Length=mag.Angle=phase.相位子

=複數(shù)平面上的箭(向量)。箭長(zhǎng)=大小。角度=相位。VleadsIby90.V領(lǐng)先I90.VleadsIby

90.V領(lǐng)先I

90.(VlagsIby90)(V落後I90)VleadsIby0.V領(lǐng)先I0.(samephase)(同相位)電阻器電感器電容器CapacitorsRevisited 電容器再探IleadsVby90

I超前V90

+VC

Vpeit

Takingtherealpartasphysical取實(shí)數(shù)部份為物理量：Takingtheimaginarypartasphysical取虛數(shù)部份為物理量：Impedance阻抗IInductorsRevisited 電感器再探IlagsVby90

I落後V90

Vpeit

Takingtherealpartasphysical取實(shí)數(shù)部份為物理量：Takingtheimaginarypartasphysical取虛數(shù)部份為物理量：I

L

+Capacitors&Inductors:AComparison

電容器和電感器：對(duì)比CLtranslator轉(zhuǎn)換:E

Bq

B

V

IZ

Y

Table28.2.Capacitors&Inductors 電容器和電感器Capacitor電容器Inductor電感器Behaviorinlowfreqlimit低頻時(shí)性能Definingrelation;

derivativeform定義；導(dǎo)數(shù)形式Opposeschangein抵抗何者改變Energystorage所儲(chǔ)能量Definingrelation定義Behaviorinhighfreqlimit高頻時(shí)性能Reactance電抗Phase相位VIOpencircuit斷路Shortcircuit短路Opencircuit斷路Shortcircuit短路Ileadsby90

I領(lǐng)先90.Vleadsby90

V領(lǐng)先90.Admittance/Impedance電導(dǎo)納/阻抗Application:LoudspeakerSystems 應(yīng)用：喇叭系統(tǒng)Loudspeaker喇叭Loudspeakersystemwithhigh&lowfrequencyfilters.有高和低頻濾波器的喇叭系統(tǒng)CpasseshighfreqC讓高頻波通過(guò)LpasseslowfreqL讓低頻波通過(guò)28.3.LCCircuits LC線(xiàn)路全是電能，在電容器內(nèi)全是電能，在電容器內(nèi)全是磁能，在電感器內(nèi)全是磁能，在電感器內(nèi)I

V+AnalyzingtheLCCircuit 分析

LC

電路I

V+GOTIT?28.2YouhaveanLCcircuitthatoscillatesatatypicalAMradiofrequencyof1MHz.你有一個(gè)LC

電路，其振盪頻率是典型調(diào)幅電臺(tái)的1MHz。YouwanttochangethecapacitorsoitoscillatesatatypicalFMfrequency,100MHz.你想把電容器換掉以提高振盪頻率到典型調(diào)頻電臺(tái)的100MHz。Shouldyoumakethecapacitor 你應(yīng)該把電容量換成largeror 較大的或smaller? 較小的？Bywhatfactor? 倍數(shù)為何？104Example28.3.TuningaPiano 為鋼琴調(diào)聲YouwishtomakeanLCcircuitoscillateat440Hz(AabovemiddleC)touseintuningpianos.你想做一個(gè)振盪頻率為440Hz(中階C上的A)的LC

電路，再用它來(lái)為鋼琴調(diào)聲。Youhavea20-mHinductor. 你有一個(gè)20-mH電感器。Whatvalueofcapacitanceshouldyouuse? 你應(yīng)該用甚麼電容量？Ifyouchargethecapacitorto5.0V,whatwillbethepeakcurrentinthecircuit?如果你把電容器充電到5.0V，電路的電流峰值為何？(a)(b)

ResistanceinLCCircuits–Damping

LC電路中的電阻–阻尼

(seenextpage)見(jiàn)下頁(yè)I

VC+

L++VR

ResistanceinLCCircuits–Damping

LC電路中的電阻–阻尼

I(seenextpage)見(jiàn)下頁(yè)

VC+

L++VR

SolutionstoDampedOscillator

阻尼振蕩器的解Ansatz:28.4.DrivenRLCCircuits&Resonance

驅(qū)動(dòng)式RLC電路和共振Drivendampedoscillator驅(qū)動(dòng)式阻尼振蕩器:Longtime:oscillateswithfrequency

d.長(zhǎng)期：以頻率

d振蕩。Resonanceif

d=

0. 如

d=

0則共振。I

VC+

L++VR

+

ResonanceintheRLCCircuit

RLC電路的共振

ifi.e.,VC

&VLare180

outofphase. VC

和VL相差180

。低頻

d<

0時(shí)電容器為主。高頻

d>

0時(shí)電感器為主。共振

d=

0時(shí)電容器與電感器的電壓互相抵消。GOTIT?28.3Youmeasurethecapacitor&inductorvoltageinadrivenRLCcircuit,你去量一個(gè)驅(qū)動(dòng)RLC電路內(nèi)電容器和電感器的電壓，andfind10Vforthermscapacitorvoltageand15Vforthermsinductorvoltage.得到電容器的rms電壓為10V，電感器的rms電壓為15V。Isthedrivingfrequency 驅(qū)動(dòng)頻率是aboveor (a)高於，或belowresonance? (b)低於共振值？VCp<VLp

FrequencyResponseoftheRLCCircuit

RLC電路的頻率反應(yīng)Seriescircuit

sameIphasorforall.串聯(lián)電路

全部元件的I相位子都一樣。

VRinphasewithI. VR與I同相位。VClagsIby90

. VC落後I90

。VLleadsIby90

. VL

領(lǐng)先I

90

。HighQLowQSeeProb71fordefinitionofQ.有關(guān)Q的定義請(qǐng)參考Prob71。

Atresonance共振時(shí),

=0.Example28.4.DesigningaLoudSpeakerSystem

設(shè)計(jì)一個(gè)揚(yáng)聲器系統(tǒng)Currentflowstothemidrangespeakerinaloudspeakersystemthrougha2.2-mHinductorinserieswithacapacitor.電流通往揚(yáng)聲器系統(tǒng)的中音喇叭時(shí)，需經(jīng)過(guò)一個(gè)與另一電容器串聯(lián)的2.2-mH電感器。Whatshouldthecapacitancebesothatagivenvoltageproducesthegreatestcurrentat1kHz?若要在1kHz，某一電壓下得到最大電流，所需電容量為何？Ifthesamevoltageproduceshalfthiscurrentat618Hz,whatisthespeaker’sresistance?如果在618Hz，同一電壓下電流減成一半，喇叭的電阻為何？Ifthepeakoutputvoltageoftheamplifieris20V,whatwillbethepeakcapacitorvoltagebeat1kHz?如果擴(kuò)大器的輸出峰壓為20V，電容器的峰壓在1kHz時(shí)何？GreatestIisatresonance:

I的最大值位於共振：Ifthesamevoltageproduceshalfthiscurrentat618Hz,whatisthespeaker’sresistance?

如果在618Hz，同一電壓下電流減成一半，喇叭的電阻為何？Atresonance:共振時(shí)：Ifthepeakoutputvoltageoftheamplifieris20V, whatwillbethepeakcapacitorvoltagebeat1kHz?

如果擴(kuò)大器的輸出峰壓為20V，電容器的峰壓在1kHz時(shí)何？Peakvoltageisatresonance(1kHz).峰壓位於共振(1kHz)。28.5.PowerinACCircuits AC線(xiàn)路的功率Powerfactor功率因子Capacitor電容器:IleadsVby90,P=0Resistor電阻器:I&Vinphase,P>0I&Voutofphase,P

Dissipativepower=I2R 熱損功率=I2RlargepowerfactorreducesI&henceheatloss.功率因子大時(shí)I較小，熱耗損也較低。ConceptualExample28.1.ManagingPowerFactor管理功率因子You’rechiefengineerofapowercompany. 你是一間電力公司的總工程師。Shouldyoustriveforahighoralowpowerfactoronyourlines?你應(yīng)該設(shè)法提高還是降低你的輸出功率因子?Powerfactor功率因子Generator:fixedVrms. 發(fā)電機(jī):Vrms固定。Tomaintainfixed<P>,Irmscos

=const