ElectricCurrent
FlowofCharge 23 ElectricCurrent VoltageSources ElectricalResistance OhmsLaw OhmsLawandElectricShock DirectCurrentandAlternatingCurrent Convertingactodc SpeedandSourceofElectronsinaCircuit ElectricPower FuelCells ElectricalCircuits SeriesCircuits ParallelCircuits ParallelCircuitsandOverloading SafetyFuses
ConceptualPhysicsInstructorsManual,10thEdition
Thischapterseekstobuildagoodeveryonesunderstandingofcurrentelectricity,andtodispelsomeof the popular misconceptions about electricity. The treatment of series and parallel circuits avoids the calculationofequivalentcircuitresistances,multipleemfs,andthelike.Thischaptermaybeskipped,asa knowledgeofelementarycircuitsisnotneededelsewhereinthetext. Theanalogyofwaterpumpedinapipeisusefulforunderstandingelectriccurrentinacircuit.Whenyou buyawaterpipeinahardwarestore,thepipecomeswithnowater.Yousupplythewater.Whenyoubuy anelectronpipe(awire),itcomeswithelectronsquitedifferentthanawaterpipe. Ifyoureintopunsinyourlecturesonrainydays,MarshallEllensteinhasafewpictorialpunsonthe symbol for resistance that he and coworkers Connie Bownell and Nancy McClure came up with (OhmworkorF D,PhysicsTeachermagazine,Sept.1991,page347).Afeware:
Answers in order are: Mobile Ohm; Ohm Run; Ohm Stretch; Ohm Sick; Ohmwork; Ohmless;OhmontheRange;BrokenOhm.
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Takenoteoftheboxonpowerlinesandcancer.ThepublicscareoftheE&Mfieldssurroundingthese linessignificantlyhamperstheconstructionofnewones. Theproblemswithpowerblackoutshasmoretodowithoverloadingpowergridsthanfaultygenerators. Triggeringofoutages oftenbeginswithoverheated linesonhotdaysandwhenloads arehigh.Lines expandandsag,touchingtreesthatshortthemout.Wereverydependentuponelectricpower.Withoutit, thewholemachinestops.
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Interestinglybutsadly,AndreAmperewasforcedtowitnesstheguillotinedeathofhis fatherduringtheFrenchRevolution.
Thereare2 OHTs:onetransparencywithFigures23.1and23.4,andtheotherwithFigures23.17and 23.18. Anexcellent overviewofthetermsofthischapterispresentedinPracticeProblem1ofthe Problem SolvinginConceptualPhysicsbook.Otherproblemsfollow. InthePracticingPhysicsbook: FlowofCharge ParallelCircuits OhmsLaw CircuitResistance ElectricPower ElectricPowerinCircuits SeriesCircuits IntheNextTimeQuestionsbook: 3BulbCircuit BatteryDemo CircuitCurrent ClayResistance 40and100WattBulbs PowerLines GlowingTube DirectCurrent Choosefrom3activitiesand2experimentsoncircuitsintheLaboratoryManual.
SUGGESTEDLECTUREPRESENTATION FlowofCharge;ElectricCurrent: Defineelectriccurrentandrelateittothelightingofthelampviathe VandeGraaffgeneratorattheendofyourlastlecture.Explainthisintermsofcurrentbeingdirectly proportionaltoadifferenceinvoltage.Thatis,oneendofthelampwasinastrongerpartoftheenergy fieldthantheothermoreenergyperchargeononeendthantheothermorevoltageatoneendthanthe other. Write on the board Current voltage difference. (Youre on your way to Ohms law. Strictly speaking, the voltage term in Ohms law implies the difference in potential, so voltage difference is redundant.Nevertheless,itunderscoresapointthatmaybemissed,sogoforit.) VoltageSources:Relatevoltagetotheideaofelectricalpressure.Emphasizethatadifferenceinelectric potentialmustexistorasabove,avoltagedifference.Citehowabatteryprovidesthisdifferenceina sustainedwaycomparedtosuddenlydischargingaVandeGraaffgenerator.Generatorsatpowerplants alsoprovideavoltagedifferenceacrosswiresthatcarrythisdifferencetoconsumers(moredetailonthisin Chapter25).Citeexamplesofvoltagedifferences incases ofbirdssittingonbarehighvoltagewires, walkingunharmedonthethirdrailofelectricpoweredtraintracks,andtheinadvisabilityofusingelectric appliancesinthebathtub. DimmedHeadlights:Anautobattery,likeallbatteries,hasinternalresistance.Whenchargeflowsin battery,thereisavoltagedropacrossthisresistance,andsomeheatingoccurs.Thismakesthevoltage acrosstheterminalsdropasthecurrentincreases.Whenthecarsstarterisactivated,considerablecurrent
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is delivered bythebattery,lowering thevoltageoutputofthebattery. Thisisevident inthedimmed headlights. Discussthefunctionofthe thirdprongonelectricplugs (thatitprovidesagroundwirebetweenthe applianceandtheground).Thegroundprongislongerthanthepairofflatprongs.Why?(Soitwillbefirst to be connected when plugging it into a socket, establishing a ground connection slightly before the applianceiselectricallyconnected.Thispathtogroundpreventsharmtotheuserifthereisashortcircuit intheappliancethatwouldotherwiseincludetheuserasapathtoground.)
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Whenapowerlinefallsnearyou,dontwalkfromithopwithbothfeettogether.Why?Becausethere maybeavoltagedifferenceacrosstheground.Ifonefootisanchoredtoavoltagemuchdifferentthan whereyourotherfootis,youcouldbeelectrocuted. Discuss electricshock andwhyelectriciansputonehandbehindtheirbackwhenprobingquestionable circuits[tonotcauseamuscularcontractionthatwillkeeptheirhandsgrippingawire,andtopreventa difference in potential across the heart of the body]. Discuss how being electrified produces muscle contractionsthataccountforsuchinstancesasnotbeingabletoletgoofhotwires,andbeingthrown byelectricshock. ElectricalResistance:Introducetheideaofelectricalresistance,andcompleteOhmslaw.Comparethe resistancesofvariousmaterials,andtheresistancesofvariousthicknessofwiresofthesamemetal.Call attentiontotheglasssupportsonthewiresthatmakeuphighvoltagepowerlines;therubberinsulation thatseparatesthepairofwiresinacommonlampcord. OhmsLaw: Completeyourchalkboard equationbyintroducingresistanceandyouhaveOhms law. ManyinstructorswriteOhmslawintheform,V=IR.Ouch!ItisconceptuallyeasiertounderstandatI= V/R,justasNewtonssecondlawismoreconceptualasa=F/mthanF=ma. DEMONSTRATION:Connecttwoorthreelampstoabatteryandrelatethecurrent,asviewedby theemittedlight,tothevoltageofthebatteryandtheresistanceofthelamps.(Besurethelamps are not bright enough to make viewing uncomfortable). Interchange lamps of low and high resistance,relatingthistothebrightnessofthelamps. DCandAC:DiscussthedifferencesbetweenDCandAC.ComparetheDCcurrentthatflowsinacircuit poweredwithabatterytotheACcurrentthatflowsinahouseholdcircuit(poweredbyagenerator).A hydrodynamicanalogyforACisuseful:Imaginepoweringawashingmachineagitatorwithwaterpower. Verballydescribewithgesturesapairofclearplasticpipesconnectedtoapaddlewheelatthebottomof theagitator,fashionedsowaterthatsloshestoandfrointhepipescausestheagitatortorotatetoandfro. Supposethefreeendsoftheplasticpipeare connectedtoaspecial socket inthewall.Thesocketis poweredbythepowerutility.Itsuppliesnowater,butconsistsofacoupleofpistonsthatexertapumping action,oneoutandtheotherin,thenviceversa,inrapidalternation.Whentheendsofthepipecontaining water are connected tothepistons,thewater inthepipes is made tosloshbackand forth: Power is delivered to the washing machine. There is an important point to note here: The source of flowing substance,waterorelectrons,issuppliedbyyou.Thepowercompanysuppliesnowater,justasthepower utilitiessupplynoelectrons!Thegreatertheloadontheagitator,themoreenergythepowercompanymust delivertotheactionofthealternatingpistons.Thisanalogyaffordsavisualmodelforhouseholdcurrent especiallywiththetransparentplasticpipeswhereyourstudentscanseethesloshingwater! ThewateranalogyalsoservestoshowthefunctionofacapacitorinsmoothingtheconversionofACto DC,Figure23.12. SpeedofElectrons in aCircuit:Toimpart theideaofhowDCcurrent travels inacircuit,usethe followinganalogy.Asktheclasstosupposethatthereisalongcolumnofmarchersatthefrontofthe room,everyonestandingatrestclosetogether.Walktotheendofthisimaginarycolumnandgiveashove tothelastperson.Asktheclasstoimaginetheresultingimpulsetravelingalongthelineuntilthefirst
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marcherisjostledagainstthewall.(Orusetheanalogyoflooselycoupledrailroadcars.)Thenaskifthisis agoodanalogyforhowelectricitytravelsinawire.Theanswerisno.Suchisagoodanalogyforhow sound travels,butnotelectriccurrent.Citehowslowlythedisturbancetravels,andhowslowlysound travelscomparedtolightorelectricity.Againcallattentiontothecolumnofmarchersandwalktothefar endandcallout,Forwardmarch!Assoonasthecommandreacheseachindividual,eachstepsforward. Themarcheratthebeginningofthecolumn,exceptfortheslighttimerequiredforthesoundtogettoher, stepsimmediately.Statethatthisisananalogyforelectriccurrent.Exceptforthebrieftimeittakesforthe electricfieldsetupatthepowersourcetotravelthroughthewire,nearlythespeedoflight,electronsatthe farendofthecircuitrespondimmediately.Statethatthespeedatwhichthecommandforwardmarch travelsisaltogetherdifferentfromhowfasteachmarchermoveduponreceivingthatcommandandthat thevelocityoftheelectricsignal(nearlythespeedoflight)isverymuchdifferentthanthedriftvelocityof electrons(typically0.01cm/s)inacircuit. CHECKQUESTION:Whenyouturnonyourkeytostartyourcar,electronsmigratefromthe negativebatteryterminalthroughtheelectricnetworktothestartermotorandbacktothepositive batteryterminal.Abouthowlongisrequiredforelectronstoleavethenegativeterminalandgo throughthecircuitandbackagain?Lessthanamillisecond?Lessthanasecond?Aboutasecond ortwo?Oraboutaday?(Classinterestshouldbehighwhenyouannouncethelatteranswer!) Askforanestimateofthenumberofelectrons pumpedbythelocal powerplantintothehomesand industrieslocallyinthepastyear.Thenstresstheideathatpowerplantsdonotsellelectronsthatthey sellenergy.Discusstheoriginofelectronsinelectriccurrentflow. ElectricPower:Distinguishbetweenenergyandpower.Electricpowerisusuallyexpressedinkilowatts, andelectricenergyinkilowatthours.Itiseffectiveifyouuseanactualelectricbillto makeyourpoint. Notethatakilowatthouris1000joulespersecondtimes3600secondsor3600kJ. Electrical Circuits: You simply must use an automobile storage battery with extended terminalsasshownhere.Theextendedterminals aresimplyapairofrigidrods,weldingrodsor simply pieces of thick wire. They are easily insertedandremovediffemaleconnectors are permanentlyfastenedintothebatteryterminals .Alsofastenalligatorclipstotheendsofshort lengths of wire fastened to about three or so lamps of equal resistance. If you use a 6volt batteryandlampsdesignedfor12volts,theyll glow at a brightness just right for viewing. Brighterlampsaretoomuchforyourstudentseyes. DEMONSTRATION:Connecttheendsofoneofthelampsdirectlytothebatteryterminals.It glows,evidenceofcurrentflow.Theninserttherodsandrepeat.Itglowsasbefore.Slidethelamp fartheruptherodsanditsglowisthesame.Itiseasilyacceptedthatthe6voltpotentialdifference betweentheterminalsisalsoestablishedalongandacrossthefulllengthoftherods.Statehowthe rodscouldextendacrosscampusandsomeonefarawaycouldsimilarlylightupalamp.Statehow
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theresistanceoftherodsisverysmallcomparedtotheresistanceofthelampfilament.Compare therodstoalonglampcord.Thentopowerlinesfrompowerplantstoconsumers.Takeyourtime withtheseideas,fortheyarecentral! SeriesCircuits: DEMONSTRATION CONTINUED: Attach two lamps in series via alligator clips. Before connecting the double lamp circuit to the rods, ask for a neighbor check about the relative brightness of light. [Since the resistance is doubled, the current is halved and the brightness diminishedbrightnessislessthanhalfbecausemostoftheenergyisgoingtoheatandnot light.Theeffectsofheatcanbediscernedforlowcurrentswhennolightisseen.]Pointoutthat thevoltageacrosseachlampishalfthevoltageacrossthebatteryterminalswhenconnectedin series.Repeattheprocess forthreelampsinseries,wherethreelampssharethe6volts,and describethereducedcurrentintermsofOhmslaw.Thisisevenmoreeffectiveifyouconnecta lecturesizeammetertoyourcircuit.
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ParallelCircuits: DEMONSTRATIONCONTINUED:Nowconnectapairoflampsinseries.Beforemakingthe secondconnection,askforaneighborcheckabouttherelativebrightnesses.Itseasytoseethat thevoltageacrosseachlampisnotreducedaswiththeseriesconnection,buteachisimpressed withafull6volts.[Nearlyafull6volts;linevoltagediminisheswithincreasedcurrentthrough thebatteryperhapsinformationoverloadatthisstageoflearning.]Repeatwiththreelampsafter aneighborcheck.Askabouttheequivalentresistanceofthecircuitasmorelampsareattached in parallel (or the equivalent resistance to people flow if more doors are introduced to the classroom).ThelesserresistanceisconsistentwithOhmslaw.Anammeterbetweenoneofthe rodsandtheterminalshowslinecurrent,whichisseentoincreaseaslampsareadded.Thisisthe simplestandmostvisuallycomprehensibledemoofparallelcircuitsIhavedevised. CHECKQUESTION:Considertworesistorstobeconnectedinacircuit.Whichwillhavemore resistance,iftheyareconnectedinseriesorinparallel?[Aseriesconnectionwillhavemore resistance,regardlessofthevaluesofresistance;theequivalentresistanceofaparallelconnection willalwaysbelessthanthatofthesmallerresistor.] HomeCircuitsandFuses: Discusshomelightingcircuits.Drawasimpleparallelcircuitoflampsand appliancesontheboard.Estimatethecurrentflowingthrougheachdevice,andpointoutthatitmakesno differencehowmanyoftheotherdevicesareturnedon.Showonyourdiagramthecurrentsinthebranches andintheleadwires.Showwherethefusegoesanddescribeitsfunction.Thenshortyourcircuitandblow thefuse. Overloading:Discuss theconsequences oftoomanyappliances operating onthesame line,andwhy differentsetsoflinesaredirectedtovariouspartsofthehome.Mosthomewiringisratedat30amperes maximum.Acommonairconditionerusesabout2400watts,soifoperatingon120voltsthecurrentwould be20amps.Tostart,thecurrentismore.(Whythestartingcurrentislargerwouldbeprematuretoexplain hereifitcomesupyoucanexplainthateverymotorisalsoagenerator,andtheinputelectricityismet withageneratedoutputthatreducesthenetcurrentflow.)Ifotherdevicesaredrawingcurrentonthesame line,thefusewillblowwhentheairconditioneristurnedon,soa220voltlineisusuallyusedforsuch heavyappliances.Pointoutthatmostoftheworldoperatesnormallyat220240volts. CHECKQUESTION:Howdoestheamountoflinecurrentintheschoolbuildingdifferfromthe amountofcurrentthatlightsthelampsoverheadinthisroom?[Unlessyourroomistheonlyroom intheschooltobeusingelectricityatthemoment,thecurrentthatfeedsthelightstotheroomis onlypartofthelinecurrentthatservicesthewholeschool.]
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SolutionstoChapter23Exercises
1. Make the pipe of lowresistant material and wider. Make the conducting wire of low electrical resistanceandwider. 2. Sixgallonsperminute(104=6). 3. Sixamperes(104=6). 4. Thecoolingsystemofanautomobileisabetteranalogytoanelectriccircuitbecauselikeanelectric inacircuit.Thewaterhosedoesnotre-circulatethewaterastheautocoolingsystemdoes. systemitisaclosedsystem,anditcontainsapump,analogoustothebatteryorothervoltagesource 5. Asthecurrentinthefilamentofalightbulbincreases,thebulbglowsbrighter. 6. Disagree,forthebatterysuppliestheelectricfieldinthecircuit.Theelectronsalreadyexistinthe circuit. 7. Normallyacurrentcarryingwireisnotelectricallychargedbecauseforeveryelectroninthewireisa protoninthematerial.Awirecanbecharged,butordinarilywiresarenotcharged. 8. Your tutor is wrong. An ampere measurescurrent,andavoltmeasureselectricpotential(electric pressure).Theyareentirelydifferentconcepts;voltageproducesamperesinaconductor. 9. Onlycircuitnumber5iscompleteandwilllightthebulb.(Circuits1and2areshortcircuitsandwill quicklydrainthecellofitsenergy.Incircuit3bothendsofthelampfilamentareconnectedtothe sameterminalandarethereforeatthesamepotential.Onlyoneendofthelampfilamentisconnected tothecellincircuit4.) 10. Currentflows through electricaldevices,justaswaterflowsthroughaplumbingcircuitofpipes.Ifa waterpumpproduceswaterpressure,waterflowsthroughboththepumpandthecircuit.Likewisewith electriccurrentinanelectriccircuit.Forexample,inasimplecircuitconsistingofabatteryandalamp, theelectriccurrentthatflowsinthelampisthesameelectriccurrentthatflowsthroughthewiresthat connectthelampandthesameelectriccurrentthatflowsthroughthebattery.Currentflowsthrough thesedevices.(Asasidepoint,itiscommontospeakofelectriccurrentflowinginacircuit,butstrictly speaking,itiselectric charge thatflowsinanelectriccircuit;theflowofcharge is current.Soifyou wanttobepreciselycorrectgrammatically,saythatcurrentisinacircuitandchargeflowsinacircuit.) 11. Agreewiththefriendwhosaysenergy,notcurrent,isconsumed. 12. Yourfriendissharingvoltagefromhisbatterybyconnectingthetwobatteriesinparallel. 13. Agree,forthenthesameappropriatevoltagewillpowerthecircuit. 14. Allotherthingsbeingequal,amaterialwithashortmeanfreepathoffersmoreresistancetoelectron flowandhasahigherelectricalresistance.Forallmaterials,theapplicationofheatimposesmore molecular chaosand shortensthepathevenmore,increasingresistanceinmostmaterials.Soto
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lengthen the path, simply cool thematerial.Conductivitiesaregreatlyincreasedinmostmaterials whentheyarecooledtolowtemperatures.
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15. Youhavewarmedit,andincreaseditsresistanceslightly.(Haveyouevernoticedthatwhenbulbsburn out,itisusuallyamomentaftertheyhavebeenturnedon?Ifthefilamentisweak,theinitialpulseof highercurrentresultingfromthelowerresistanceofthestillcoolfilamentcausesittofail.) 16. Beforeitheatsup,thefilamentiscoolerandmoreconducting. 17. Aliedetectorcircuitreliesonthelikelihoodthattheresistivityofyourbodychangeswhenyoutellalie. Nervousness promotes perspiration, which lowers the bodys electrical resistance, and increases whatever current flows. If a person is able to lie with no emotional change and no change in perspiration,thensuchaliedetectorwillnotbeeffective.(Betterlyingindicatorsfocusontheeyes.) 18. Mostoftheenergy,typically95%,oftheelectricalenergyinanincandescentlampgoesdirectlyto heat.Thermalenergyisthegraveyardofelectricalenergy. 19. Thickwireshavelessresistanceandwillmoreeffectivelycarrycurrentswithoutexcessiveheating. 20. Glowoccurswherethemostenergyisbeingdissipated,inthefilament. 21. Thethickfilamenthaslessresistanceandwilldraw(carry)morecurrentthanathinwireconnected across the same potential difference. (Importantpoint: Itis commonto saythat acertain resistor drawsacertaincurrent,butthismaybemisleading.Aresistordoesntattractordrawcurrent,just asapipeinaplumbingcircuitdoesntdrawwater;itinsteadallowsorprovidesforthepassageof currentwhenanelectricalpressureisestablishedacrossit.) 22. (a)Theresistancewillbehalf,5ohms,whencutinhalf.(b)Theresistancewillbehalfagainwhenthe crosssectionalareaisdoubled,soitwillbe2.5ohms. 23. Ifbothvoltageandresistancearedoubled,currentremainsunchanged.Likewiseifbothvoltageand resistancearehalved. 24. Currentwillbegreaterinthebulbconnectedtothe220voltsource.Twicethevoltagewouldproduce twicethecurrentiftheresistanceofthefilamentremainedthesame.(Inpractice,thegreatercurrent producesahighertemperatureandgreaterresistanceinthelampfilament,sothecurrentisgreater thanthatproducedby110volts,butappreciablylessthantwiceasmuchfor220volts.Abulbratedfor 110voltshasaveryshortlifewhenoperatedat220volts.) 25. Damagegenerallyoccursbyexcessheatingwhentoomuchcurrentisdriventhroughanappliance. Foranappliancethatconvertselectricalenergydirectlytothermalenergythishappenswhenexcess voltage is applied. So dont connecta110voltiron,toaster,orelectricstovetoa220voltcircuit. Interestinglyenough,iftheapplianceisanelectricmotor,thenapplyingtoolittlevoltagecanresultin overheatingandburnupthemotorwindings.(Thisisbecausethemotorwillspinatalowspeedand thereversegeneratoreffectwillbesmallandallowtoogreatacurrenttoflowinthemotor.)Sodont hookupa220voltpowersaworany220voltmotordrivenapplianceto110volts.Tobesafeusethe recommendedvoltageswithappliancesofanykind. 26. Inthefirstcasethecurrentpassesthroughyourchest;inthesecondcasecurrentpassesonlythrough yourarm.Youcancutoffyourarmandsurvive,butyoucannotsurvivewithoutyourheart. 27. Electricpowerinyourhomeislikelysuppliedat60hertzand110120voltsviaelectricaloutlets.Thisis ac(anddeliveredtoyourhomeviatransformersbetweenthepowersourceandyourhome.Wewill
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seeinChapter25thattransformersrequireacpowerforoperation.)Electricpowerinyourcarmustbe abletobesuppliedbythebattery.Sincethe+andterminalsofthebatterydonotalternate,the currenttheyproducedoesnotalternateeither.Itflowsinonedirectionandisdc. 28. Autoheadlightsarewiredinparallel.Thenwhenoneburnsout,theotherremainslit.Ifyouveever seenanautomobilewithoneburnedoutheadlight,youhaveevidencetheyrewiredinparallel. 29. Thereislessresistanceinthehigherwattagelamp.Sincepower=current voltage,morepowerfor thesamevoltagemeansmorecurrent.AndbyOhmslaw,morecurrentforthesamevoltagemeans lessresistance.(AlgebraicmanipulationoftheequationsP=IVandI=V/RleadstoP=V2/R.) 30. (a)volt,(b)ampere,(c)joule. 31. Theequivalentresistanceofresistorsinseriesistheirsum,soconnectapairofresistorsinseriesfor moreresistance. 32. Theequivalentresistanceofresistorsinparallelislessthanthesmallerresistanceofthetwo.So connectapairofresistorsinparallelforlessresistance. 33. Currentremainsthesameinalltheresistorsinaseriescircuit. 34. Voltageacrossparallelbranches,whatevertheresistance,remainsthesame. 35. Theamountofcurrentanydeviceputsthroughanyconductordependsuponthevoltageofthedevice andtheresistanceoftheconductor.Alsoimportantistheamountofchargethedevicecandeliver;a relativelylargeamountofchargeathighvoltagerepresentshighenergy(likethatfromapowerline) while a small amount of charge athighvoltagerepresentslowenergy(likedischargingaballoon rubbedonyourhair).Thedevicebeingwarnedaboutislikelyhighlyenergizedtoahighvoltage,and shouldberespected.Itpossessesnocurrenttobewarnedabout,butbecauseofitshighenergyand highvoltage,mayproducealethalcurrentinanyoneofferingaconductingpathfromittotheground. 36. The sign is a joke. High voltage may be dangerous, but high resistance is a property of all nonconductors. 37. Nocauseforconcern.Thelabelisintendedashumor.Itdescribeselectrons,whichareinallmatter. 38. Iftheparallelwiresarecloserthanthewingspanofbirds,abirdcouldshortcircuitthewiresbycontact withitswings,bekilledintheprocess,andpossiblyinterruptthedeliveryofpower. 39. Zero.Powercompaniesdonotsellelectrons;theysellenergy.Whatevernumberofelectronsflowinto ahome,thesamenumberflowsout. 40. Howquicklyalampglowsafteranelectricalswitchiscloseddoesnotdependonthedriftvelocityof theconductionelectrons,butdependsonthespeedatwhichtheelectricfieldpropagatesthroughthe circuitaboutthespeedoflight.
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41. Electricenergyispropagatedthroughacircuitbyelectricfieldsmovingatclosetothespeedoflight, notbyelectroncollisions.Sound,ontheotherhand,travelsbymolecularoratomiccollisionsamuch slowerprocess. 42. Alightbulbburnsoutwhenabreakoccursinthefilamentorwhenthefilamentdisintegratesorfalls apart. 43. Bulbswillglowbrighterwhenconnectedinparallel,forthevoltageofthebatteryisimpressedacross each bulb. When two identical bulbs are connected in series, half the voltage of the battery is impressedacrosseachbulb.Thebatterywillrundownfasterwhenthebulbsareinparallel. 44. Brightnessremainsthesame. 45. Mostoftheelectricenergyinalampfilamentistransformedtoheat.Forlowcurrentsinthebulb,the heatthatisproducedmaybeenoughtofeelbutnotenoughtomakethefilamentglowredorwhitehot. 46. BulbCisthebrightestbecausethevoltageacrossitequalsthatofthebattery.BulbsAandBshare the voltage of the parallel branch of the circuit and have half the current of bulb C (assuming resistancesareindependentofvoltages).IfbulbAisunscrewed,thetopbranchisnolongerpartof thecircuitandcurrentceasesinbothAandB.Theynolongergivelight,whilebulbCglowsasbefore. IfbulbCisinsteadunscrewed,thenitgoesoutandbulbsAandBglowasbefore. 47. Asmorebulbsareconnectedinseries,moreresistanceisaddedtothesinglecircuitpathandthe resultingcurrentproducedbythebatteryisdiminished.Thisisevidentinthedimmerlightfromthe bulbs.Ontheotherhand,whenmorebulbsareconnectedtothebatteryinparallel,thebrightnessof thebulbsispracticallyunchanged.Thisisbecauseeachbulbineffectisconnecteddirectlytothe batterywithnootherbulbsinitselectricalpathtoaddtoitsresistance.Eachbulbhasitsowncurrent path. 48. Linecurrentdecreasesasmoredevicesareconnectedinseries.Butlinecurrentincreasesasmore devicesareconnectedinparallel.Thisisbecausethecircuitresistanceisincreasedwhendevicesare addedinseries,butdecreased(morepathways)whendevicesareaddedinparallel. 49. Whataffectstheotherbranchesisthevoltageimpressedacrossthem,andtheirownresistance period.Openingorclosingabranchdoesntaltereitherofthese. 50. Agree,forresistancesinseriesadd. 51. Agree,becauseevenforthesmallestresistor,currenthasanalternativepath(s),makingforanoverall smallerresistance. 52. Connectapairof40ohmresistorsinparallel. 53. Connectfour40ohmresistorsinparallel. 54. Allarethesameforidenticalresistorsinseries.Iftheresistorsarenotthesame,theoneofgreater resistance will have less voltage across it and less power dissipated in it. Regardless of the resistances,however,thecurrentthroughbothwillbethesame.
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55. Allarethesameforidenticalresistorsinparallel.Iftheresistorsarenotthesame,theoneofgreater resistance will have less current through it and less power dissipation in it. Regardless of the resistances,thevoltageacrossbothwillbeidentical. 56. Yes,therewillbeadecreaseinbrightnessiftoomanylampsareconnectedinparallelbecauseofthe increasedcurrentthatflowsthroughthebattery.Internalvoltagedropincreaseswithcurrentinthe battery,whichmeansreducedvoltagesuppliedatitsterminalstothecircuititpowers.(Iftheparallel circuitispoweredbyastrongersourcesuchasthepowerutilityprovidesviacommonwallsockets,no dimmingofbulbswillbeseenasmoreandmoreparallelpathsareadded.) 57. Allthreeareequivalentparallelcircuits.Eachbranchisindividuallyconnectedtothebattery. 58. Afuseinserieswithanyoneoftheappliancescouldbeuseful,foritwouldmeltonlyifsomethingwent wrongwiththatparticularappliance. 59 . Morecurrentflowsinthe100wattbulb.Weseethisfromtherelationshippower=current voltage. More current for the same voltage means less resistance. So a 100watt bulb has less resistancethana60wattbulb.Lessresistanceforthesamelengthofthesamematerialmeansa thickerfilament.Thefilamentsofhighwattagebulbsarethickerthanthoseoflowerwattagebulbs.(It isimportanttonotethatbothwattsandvoltsareprintedonalightbulb.Abulbthatislabeled100W, 120V,is100W only ifthereare120voltsacrossit.Ifthereareonly110voltsacrossit,andthe resistanceremainsunchanged,thenthepoweroutputwouldbeonly84watts!) 60. The100wattbulbhasthethickerfilamentandlowerresistance(asdiscussedinthepreviousanswer) soinserieswherethecurrentisthesameineachbulb,lessenergyisdissipatedingoingthroughthe lowerresistance.Thiscorrespondstolowervoltageacrosstheresistancealowervoltagedrop.So thegreatervoltagedropisacrossthe60wattbulbinseries.Interestingly,inseriesthe60wattbulbis brighterthanthe100wattbulb!Whenconnectedinparallel,thevoltageacrosseachbulbisthesame, andthecurrentisgreaterinthelowerresistance100wattbulb,whichglowsbrighterthanthe60watt bulb.
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Chapter23ProblemSolutions
1. FromPower=current voltage,60watts=current 120volts,current= =0.5A. 2. Fromcurrent=,resistance===6 . 3. Frompower=current voltage,current===10A. Fromtheformuladerivedabove,resistance===12 . 4. Twoheadlightsdraw6amps,sothe60amperehourbatterywilllastforabout10hours. 5 . $2.52 .First,100watts=0.1kilowatt.Second,thereare168hoursinoneweek(7days 24hours/day=168hours).So168hours 0.1kilowatt=16.8kilowatthours,whichat15centsper kWhcomesto$2.52. 6. (a)Frompower=current voltage,current=power/voltage=4W/120V=1/30A. (b)Fromcurrent=voltage/resistance(Ohmslaw),resistance=voltage/current= 120V/(1/30A)=3600 . (c)First,4watts=0.004kilowatt.Second,thereare8760hoursinayear (24hours/day 365days=8760hours).So8760hours 0.004kilowatt=35.0kWh. (d)Attherateof15centsperkWh,theannualcostis35.0kWh $0.15/kWh=$5.25. 7. TheironspowerisP=IV=(110V)(9A)=990W=990J/s.Theheatenergygeneratedin1minuteis E=power time=(990J/s)(60s)=59,400J. 8 . Sincecurrentischargeperunittime,chargeiscurrent time: q = It =(9A)(60s)=(9 C/s)(60 s)= 540C.(Chargesofthismagnitudeonthemovearecommonplace,butthisquantityofcharge accumulatedinoneplacewouldbeincrediblylarge.) 9. Itwasdesignedforuseina120Vcircuit.Withanappliedvoltageof120V,thecurrentinthebulbis I =V/R=(120V)/(95)=1.26A.ThepowerdissipatedbythebulbisthenP=IV=(1.26A)(120V)= 151W,closetotheratedvalue.Ifthisbulbisconnectedto240V,itwouldcarrytwiceasmuchcurrent andwoulddissipatefourtimesasmuchpower(twicethecurrent twicethevoltage),morethan600 W. Itwould likelyburn out.(This problemcanalsobesolvedbyfirstcarryingoutsomealgebraic manipulation.Sincecurrent=voltage/resistance,wecanwritetheformulaforpoweras P=IV=(V/ R)V = V2/R.Solvingfor V gives V = PR.Substitutingforthepowerandtheresistancegives V = (150)(95)=119V.) 10. TheresistanceofthetoasterisR=V/I=(120V)/(10A)=12 .Sowhen108Visapplied,thecurrent isI=V/R=(108V)/(12)=9.0AandthepowerisP=IV=(9.0A)(108V)=972W,only81percentof thenormalpower.(Canyouseethereasonfor81percent?Currentandvoltagearebothdecreasedby 10percent,and0.9 0.9=0.81.)
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