Chapter 1 Fundamentals of Electric Circuits section 1-1 Current and Voltage 电气工程及其自动化专

Chapter1FundamentalsofElectricCircuitsSection1CurrentandVoltageTextNewWordsandExpressionsExercisesEndSection1CurrentandVoltageTwovariablesu(t)andi(t)arethemostbasicconceptsinanelectriccircuit,theycharacterizethevariousrelationshipsinanelectriccircuit.ChargeandCurrentTheconceptofelectricchargeistheunderlyingprincipleforexplainingallelectricalphenomena.Also,themostbasicquantityinanelectriccircuitistheelectriccharge.Chargeisanelectricalpropertyoftheatomicparticlesofwhichmatterconsists,measuredincoulombs(C).Section1CurrentandVoltageWeknowfromelementaryphysicsthatallmatterismadeoffundamentalbuildingblocksknownasatomsandthateachatomconsistsofelectrons,protons,andneutrons.Wealsoknowthatthechargeeonanelectronisnegativeandequalinmagnitudeto1.60210×1019C,whileaprotoncarriesapositivechargeofthesamemagnitudeastheelectron.Thepresenceofequalnumbersofprotonsandelectronsleavesanatomneutrallycharged.Section1CurrentandVoltageWeconsidertheflowofelectriccharges.Auniquefeatureofelectricchargeorelectricityisthefactthatitismobile;thatis,itcanbetransferredfromoneplacetoanother,whereitcanbeconvertedtoanotherformofenergy.Whenaconductingwireisconnectedtoabattery(asourceofelectromotiveforce),thechargesarecompelledtomove;positivechargesmoveinonedirectionwhilenegativechargesmoveintheoppositedirection.Thismotionofchargescreateselectriccurrent.ItisconventionaltotakethecurrentSection1CurrentandVoltageflowasthemovementofpositivecharges,thatis,oppositetotheflowofnegativecharges,asFig.l-1illustrates.ThisconventionwasintroducedbyBenjaminFranklin(l706～l790),theAmericanscientistandinventor.Althoughwenowknowthatcurrentinmetallicconductorsisduetonegativelychargedelectrons,wewillfollowtheuniversallyacceptedconventionthatcurrentisthenetflowofpositivecharges.Thus,Electriccurrentisthetimerateofcharge,measuredinamperes(A).Mathematically,therelationshipamongcurrenti,chargeq,andtimetisSection1CurrentandVoltageThechargetransferredbetweentimet0andtisobtainedbyintegratingbothsidesofEq.(1-1).WeobtainThewaywedefinecurrentasiinEq.(1-l)suggeststhatcurrentneednotbeaconstant-valuedfunction,chargecanvarywithtimeinseveralwaysthatmayberepresentedbydifferentkindsofmathematicalfunctions.(1-1)(1-2)Section1CurrentandVoltageVoltage,Energy,andPowerTomovetheelectroninaconductorinaparticulardirectionrequiressomeworkorenergytransfer.Thisworkisperformedbyanexternalelectromotiveforce(emf),typicallyrepresentedbythebatteryinFig.l-1.Thisemfisalsoknownasvoltageorpotentialdifference.Thevoltageuabbetweentwopointsaandbinanelectriccircuitistheenergy(orwork)neededtomoveaunitchargefromatob;mathematicallySection1CurrentandVoltagewherewisenergyinjoules(J)andqischargeincoulombs(C).Thevoltageuabismeasuredinvolts(V),namedinhonoroftheItalianphysicistAlessandroAntonioVolta(l745～l827),whoinventedthefirstvoltaicbattery.Thus,Voltage(orpotentialdifference)istheenergyrequiredtomoveaunitchargethroughanelement,measuredinvolts(V).(1-3)Section1CurrentandVoltageFig.l-2showsthevoltageacrossanelement(representedbyarectangularblock)connectedtopointsaandb.Theplus(+)andminus(-)signsareusedtodefinereferencedirectionorvoltagepolarity.Theuabcanbeinterpretedintwoways:①pointaisatapotentialofuabvoltshigherthanpointb;②thepotentialatpointawithrespecttopointbisuab.ItfollowslogicallythatingeneralFig.1-2Polarityofvoltageuab(1-4)Section1CurrentandVoltageAlthoughcurrentandvoltagearethetwobasicvariablesinanelectriccircuit,theyarenotsufficientbythemselves.Forpracticalpurposes,weneedtoknowpowerandenergy.Torelatepowerandenergytovoltageandcurrent,werecallfromphysicsthatpoweristhetimerateofexpendingorabsorbingenergy,measuredinwatts(W).Wewritethisrelationshipas(1-5)Section1CurrentandVoltageWherepispowerinwatts(W),wisenergyinjoules(J),andtistimeinseconds(s).FromEq.(1-1),Eq.(1-3),andEq.(1-5),itfollowsthatBecauseuandiaregenerallyfunctionoftime,thepowerpinEq.(1-6)isatime-varyingquantityandiscalledtheinstantaneouspower.Thepowerabsorbedorsuppliedbyanelementistheproductofthevoltageacrosstheelementandthecurrentthroughit.Ifthepowerhasaplussign,powerisbeingdeliveredtoorabsorbedbytheelement.If,(1-6)Section1CurrentandVoltageontheotherhand,thepowerhasaminussign,powerisbeingsuppliedbytheelement.Buthowdoweknowwhenthepowerhasanegativeorapositivesign？Currentdirectionandvoltagepolarityplayamajorroleindeterminingthesignofpower.ItisthereforeimportantthatwepayattentiontotherelationshipbetweencurrentiandvoltageuinFig.1-3(a).Fig.1-3ReferencepolaritiesforpowerusingthepassivesignconventionSection1CurrentandVoltageThevoltagepolarityandcurrentidirectionmustconformwiththoseshowninFig.1-3(a)inorderforthepowertohaveapositivesign.Thisisknownasthepassivesignconvention.Bythepassivesignconvention,currententersthroughthepositivepolarityofthevoltage.Inthiscase,p=uiorui﹥0impliesthattheelementisabsorbingpower.However,ifp=-uiorui﹤0,asinFig.1-3(b),theelementisreleasingorsupplyingpower.Section1CurrentandVoltageInfact,thelawofconservationofenergymustbeobeyedinanyelectriccircuit.Forthisreason,thealgebraicsumofpowerinacircuit,atanyinstantoftime,mustbezeroThisagainconfirmsthefactthatthetotalpowersuppliedtothecircuitmustbalancethetotalpowerabsorbed.FromEq.(l-7),theenergyabsorbedorsuppliedbyanelementfromtimet0totimetis(1-7)(1-8)ReturnNewWordsandExpressionscurrent['kʌrənt]n.电流alternatingcurrent交流电流directcurrent直流电流currentdensity电流密度activecurrent有功电流reactivecurrent无功电流voltage['vəultidʒ]n.电压voltagedrop电压降落voltagegain电压增益voltagedivider分压器voltagestabilizer稳压器NewWordsandExpressionsvariable['vεəriəbl]n.变量；a.可变的，可调的，易变的complexvariable复变量dependentvariable因变量independentvariable自变量inputvariable输入变量chargen.电荷，充电；v.充电，带电，起电chargedistribution电荷分布chargeparticle带电粒子testcharge试验电荷positivecharge正电荷negativecharge负电荷NewWordsandExpressionscoulombn.库仑（电荷的单位）coulombmeter库仑计circuit['sə:kit]n.电路circuitdiagram电路图analoguecircuit模拟电路shortcircuit短路opencircuit开路activecircuit无源电路passivecircuit无源电路underlying[,ʌndə'laiiŋ]a.①基本的，根本的②潜在的，在下（面）的，下伏的NewWordsandExpressionselectron[i'lektrɔn]n.电子magnitude['mæɡnitju:d]n.大小，尺寸，数量，数值electromotivea.电动的，起电的electromotiveforce电动势ampere['æmpεə]n.安，安培（电流的单位）amperemeter安培计ampereturn安匝voltampere伏安integrate['intiɡreit,'intiɡrit,-ɡreit]v.积分，求积分workn.功NewWordsandExpressionspotentiala.势的，位的，电位的；n.势（能）,位(能),电势(位,压)potentialdifference电位差，电势差earthpotential地电势（位）potentialenergy势（位）能referencepotential参考（基准）电位rectangular['rek'tæŋɡjulə]a.矩形的，直角的，正交的joule[dʒu:l,dʒaul]n.焦尔（能量、热量、功的单位）volt[vɔlt]n.伏特（电压、电位、电势的单位）electronvolt电子伏特NewWordsandExpressionsvoltaica.动[流]的，电压的，电镀的，伏打(式)的voltaicbattery伏打电池convention[kən'venʃən]n.习惯，惯例，常规byconvention按照惯例referencedirection参考方向polarity[pəu'lærəti]n.极性powern.①功率，效率②动力，电力，能力，电源③乘方，幂wattn.瓦特（功率的单位）time-varyinga.时变的NewWordsandExpressionsinstantn.瞬间，瞬时，即刻，时，时刻；a.立刻的，直接的，紧急的，迫切的instantaneous[,instən'teinjəs]a.瞬时（作用）的，瞬息的，即刻的instantaneouspower瞬时功率passivea.①无源的②消极的，被动的；n.无源passivenetwork无源网络algebraica.代数的ReturnExercisesI.Choosethebestanswerintotheblank1.Itisconventionaltotakethecurrentflowasthemovementof.A.negativechargesB.positivechargesC.anychargeD.protons2.Electriccurrentisthetimerateofcharge,measuredin.A.wattsB.voltsC.joulesD.amperesExercisesI.Choosethebestanswerintotheblank3.Theenergyrequiredtomoveaunitchargethroughanelementis.A.currentB.powerC.voltageD.potential4.Theplus(+)andminus(-)signsinanelectriccircuitdiagramareusedtodefine.A.voltagepolarityB.currentdirectionC.powerflowD.absorbedpowerExercisesI.Choosethebestanswerintotheblank5.Accordingtothepassivesignconvention,ifthepowerhasaplussign,powerisbytheelement.A.suppliedB.absorbedC.generatedD.transferredExercisesII.Answerthefollowingquestionsaccordingtothetext1.Iscurrentinanyelectriccircuitalwaysaconstant-valuedfunction?Why?2.Howdoescurrentchangewhenthetimerateofchargesisgreater?3.Howtointerprettheuab=-1voltintwoways?4.Whatrelationisbetweenpowerandenergy?5.Whydocurrentdirectionandvoltagepolarityplayamajorroleindeterminingthecharacteristicsofpower?ReturnSection1End