1第一章第一篇sectiongTwovariablesu(t)andi(t)arethemostbasicconceptsinanelectriccircuit,theycharacterizethevariousrelationshipsinanelectriccircuitu(t)和i(t)这两个变量是电路中最基本的两个变量,它们刻划了电路的各种关系。ChargeandCurrentTheconceptofelectricchargeistheunderlyingprincipleforexplainingallelectricalphenomena.Also,themostbasicquantityinanelectriccircuitistheelectriccharge.Chargeisanelectricalpropertyoftheatomicparticlesofwhichmatterconsists,measuredincoulombs(C).电荷和电流电荷的概念是用来解释所有电气现象的基本概念。也即,电路中最基本的量是电荷。电荷是构成物质的原子微粒的电气属性,它是以库仑为单位来度量的。Weknowfromelementaryphysicsthatallmatterismadeoffundamentalbuildingblocksknownasatomsandthateachatomconsistsofelectrons,protons,andneutrons.Wealsoknowthatthechargeeonanelectronisnegativeandequalinmagnitudeto1.60210×1019C,whileaprotoncarriesapositivechargeofthesamemagnitudeastheelectron.Thepresenceofequalnumbersofprotonsandelectronsleavesanatomneutrallycharged.我们从基础物理得知一切物质是由被称为原子的基本构造部分组成的,并且每个原子是由电子,质子和中子组成的。我们还知道电子的电量是负的并且在数值上等于1.602100×10-12C,而质子所带的正电量在数值上与电子相等。质子和电子数量相同使得原子呈现电中性。Weconsidertheflowofelectriccharges.Auniquefeatureofelectricchargeorelectricityisthefactthatitismobile;thatis,itcanbetransferredfromoneplacetoanother,whereitcanbeconvertedtoanotherformofenergy让我们来考虑一下电荷的流动。电荷或电的特性是其运动的特性,也就是,它可以从一个地方被移送到另一个地方,在此它可以被转换成另外一种形式的能量。Whenaconductingwireisconnectedtoabattery(asourceofelectromotiveforce),thechargesarecompelledtomove;positivechargesmoveinonedirectionwhilenegativechargesmoveintheoppositedirection.Thismotionofchargescreateselectriccurrent.Itisconventionaltotakethecurrentflowasthemovementofpositivecharges,thatis,oppositetotheflowofnegativecharges,asFig.l-1illustrates.ThisconventionwasintroducedbyBenjaminFranklin(l706~l790),theAmericanscientistandinventor.Althoughwenowknowthatcurrentinmetallicconductorsisduetonegativelychargedelectrons,wewillfollowtheuniversallyacceptedconventionthatcurrentisthenetflowofpositivecharges.Thus,Electriccurrentisthetimerateofcharge,measuredinamperes(A).Mathematically,therelationshipamongcurrenti,chargeq,andtimet2is当我们把一根导线连接到某一电池上时(一种电动势源),电荷被外力驱使移动;正电荷朝一个方向移动而负电荷朝相反的方向移动。这种电荷的移动产生了电流。我们可以很方便地把电流看作是正电荷的移动,也即,与负电荷的流动方向相反,如图1-1所示。这一惯例是由美国科学家和发明家本杰明-富兰克林引入的。虽然我们现在知道金属导体中的电流是由负电荷引起的,但我们将遵循通用的惯例,即把电流看作是正电荷的单纯的流动。于是电流就是电荷的时率,它是以安培为单位来度量的。从数学上来说,电流i、电荷q以及时间t之间的关系是:Thechargetransferredbetweentimet0andtisobtainedbyintegratingbothsidesofEq.(1-1).Weobtain从时间t0到时间t所移送的电荷可由方程(1-1)两边积分求得。我们算得:ThewaywedefinecurrentasiinEq.(1-l)suggeststhatcurrentneednotbeaconstant-valuedfunction,chargecanvarywithtimeinseveralwaysthatmayberepresentedbydifferentkindsofmathematicalfunctions我们通过方程(1-1)定义电流的方式表明电流不必是一个恒值函数,电荷可以不同的方式随时间而变化,这些不同的方式可用各种数学函数表达出来。电压,能量和功率Tomovetheelectroninaconductorinaparticulardirectionrequiressomeworkorenergytransfer.Thisworkisperformedbyanexternalelectromotiveforce(emf),typicallyrepresentedbythebatteryinFig.l-1.Thisemfisalsoknownasvoltageorpotentialdifference.Thevoltageuabbetweentwopointsaandbinanelectriccircuitistheenergy(orwork)neededtomoveaunitchargefromatob;mathematically在导体中朝一个特定的方向移动电荷需要一些功或者能量的传递,这个功是由外部的电动势来完成的。图1-1所示的电池就是一个典型的例子。这种电动势也被称为电压或电位差。电路中a、b两点间的电压等于从a到b移动单位电荷所需的能量(或所需做的功)。数学表达式为:wherewisenergyinjoules(J)andqischargeincoulombs(C).Thevoltageuabismeasuredinvolts(V),namedinhonoroftheItalianphysicistAlessandroAntonioVolta(l745~l827),whoinventedthefirstvoltaicbattery.Thus,Voltage(orpotentialdifference)istheenergyrequiredtomoveaunitchargethroughanelement,measuredinvolts(V).式中w是单位为焦耳的能量而q是单位为库仑的电荷。电压Uab是以伏特为单位来度量的,它是为了纪念意大利物理学家AlessandroAntonioVolta而命名的,这位意大利物理学家发明了首个伏达电池。于是电压(或电压差)等于将单位电荷在元件中移动所需的能量,它是以伏特为单位来度量的。Fig.l-2showsthevoltageacrossanelement(representedbyarectangularblock)connectedtopointsaandb.Theplus(+)andminus(-)signsareusedtodefinereferencedirectionorvoltagepolarity.Theuabcanbedqidt0ttqidtabdwudq3interpretedintwoways:①pointaisatapotentialofuabvoltshigherthanpointb;②thepotentialatpointawithrespecttopointbisuab.Itfollowslogicallythatingeneral图1-2显示了某个元件(用一个矩形框来表示)两端a、b之间的电压。正号(+)和负号(-)被用来指明参考方向或电压的极性,Uab可以通过以下两种方法来解释。1)在Uab伏特的电位中a点电位高于b点,2)a点电位相对于b点而言是Uab,通常在逻辑上遵循Althoughcurrentandvoltagearethetwobasicvariablesinanelectriccircuit,theyarenotsufficientbythemselves.Forpracticalpurposes,weneedtoknowpowerandenergy.Torelatepowerandenergytovoltageandcurrent,werecallfromphysicsthatpoweristhetimerateofexpendingorabsorbingenergy,measuredinwatts(W).Wewritethisrelationshipas虽然电流和电压是电路的两个基本变量,但仅有它们两个是不够的。从实际应用来说,我们需要知道功率和能量。为了把功率和能量同电压、电流联系起来,我们重温物理学中关于功率是消耗或吸收的能量的时率,它是以瓦特为单位来度量的。我们把这个关系式写成:Wherepispowerinwatts(W),wisenergyinjoules(J),andtistimeinseconds(s).FromEq.(1-1),Eq.(1-3),andEq.(1-5),itfollowsthat式中p是以瓦特为单位的功率,w是以焦耳为单位的能量,t是以秒为单位的时间,从方程(1-1)、(1-3)和(1-5)可以推出Becauseuandiaregenerallyfunctionoftime,thepowerpinEq.(1-6)isatime-varyingquantityandiscalledtheinstantaneouspower.Thepowerabsorbedorsuppliedbyanelementistheproductofthevoltageacrosstheelementandthecurrentthroughit.Ifthepowerhasaplussign,powerisbeingdeliveredtoorabsorbedbytheelement.If,ontheotherhand,thepowe