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1Chapter5SINUSOIDALCIRCUITEmphases：•L,C的VARvoltage-currentrelationofL,Celements•正弦量的三要素threebasicsofsinusoids•正弦量的相量phasorrepresentationofsinusoid•相量形式的KCL,KVL,阻抗,导纳KCLandKVLusingphasors,impedanceandadmittance•相量图phasordiagram2Preface:•Time-varyingvoltage/current•Alternatingvoltage/current:variessinusoidallywithtime.•Assignreferencedirectionstosinusoidalcurrent/voltageTutuTtiuRWeareinterestedinsinusoidsforanumberofreasons:•Natureitselfischaracteristicallysinusoidal.•Asinusoidalsignaliseasytogenerateandtransmit.•Asinusoidiseasytohandlemathematically.•Anypracticalperiodicsignalcanberepresentedbyasumofsinusoids.•Asinusoidisbeneficialtotheoperationofelectronicdevices.3||unit:法拉(Farad,F),常用F、nF、pF等表示。uq5-1电容和电感元件CapacitorandInductor+++++q-qu+uc-iccdttductic)()(cdttductic)()(c1.icduc/dt2.Acapacitoractslikeanopencircuittodcvoltage.ttccdictutu0)(1)()(0cttccdictutu0)(1)()(0cVARofcapacitor:1.uCdependsonthepasthistoryofiC.Memoryelement2.uCcannotchangeabruptly.1.CapacitoruqCdefuqCdefq(t)=Cu(t)410V3K+uc－2FFindtheenergystoredin2μFcapacitor.Theenergystoredinthecapacitor:tuCuuipabsorbdd)(2121ddd2)()(2tCuCuξξuCuWtuutCAveragepower：01()d0TCCPpttT5Functionsofcapacitors:Storeelectricenergy储存电荷、电能由于静电感应使两极板电荷同步变化→位移电流，——filter(high-passandlow-reject通高频、阻低频、隔直通高频、阻低频、隔直)ICVccGND6Example1:（Answer:40V,2.4mJ）Whatisthevoltageacrossa3μFcapacitorifthechargeononeplateis0.12mC?Howmuchenergyisstored?Example2:Thevoltageattheterminalsof0.6μFcapacitorisshownbelow.Findthecapacitorcurrent.t/msu/V102030401057Whenwasthefirstcapacitorinvented?•A1745•B1820•C1826•D1876•A1745right•B1820Electricityproducingmaganetismwasfound.•C1826Ohm’slaw•D1876telephone8L称为自感系数Unit：亨(利)，符号：H(Henry）VARofinductor:()()LLditutLdt()()LLditutLdt2.InductorLiL+–uLi0i+–u–+ettuLtiti0d)(1)()(0ttuLtiti0d)(1)()(01.uLdiL/dt2.Aninductoractslikeashortcircuittodccurrent.iLiscontinuous(cannotchangeabruptly).iψLdefiψLdef(t)=Li(t)9twLpLuLTheenergystoredinaninductor:)(21dξdd2tLiξiLiWtInstantaneouspower：Averagepower：0011()dsin20TTLLLPpttUItdtTTStoredmagneticenergy：Functionsofinductors:•Storemagneticenergy•Filter(low-passandhigh-reject)/(通低频、阻高频)106V2iL2mHmJW931022123Example3:Theenergystoredintheinductorintherightfigureis当u=5sin10tV时，i=10cos10tA，则元件A为元件，参数为。流过1H电感的电流i的波形如左下图所示，若u和i为关联方向，则在ｔ=1ｓ时电压u为，ｔ=3ｓ时电压u为。Practiceproblem:115-2IntroductiontoSinusoidsIm=amplitude(ormaximumvalue)；振幅=angularfrequency,inradians/second;角频率(弧度/秒,rad/s)=phase,inradiansordegrees;初相,－tiTIm1.Threebasics正弦交流电的三要素i=Imcos(t+)121.period/周期T：insecond(s)/秒(s),毫秒(ms)2.frequency/频率f：inHertz(Hz)/赫兹(Hz),千赫兹(kHz)3.angularfrequency/角频率ω：弧度/秒(rad/s)Tf1fT222.periodandfrequency周期与频率it2Severalmethodstodescribehowfastasinusoidchanges:13振动频率低于1Hz时，人感觉头内振动；肌肉等不适；振动频率为1~2Hz时，时间较久会使人打瞌睡；3~4Hz时，腰、胸局部有较大的振动感；5~8Hz时，呼吸、讲话受干扰；8Hz时，腰部振动；9~30Hz时感到脸、颊、颈部振动，视觉受到干扰；超过30Hz时，感...