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Induction_P2
1a.[1mark]
Acapacitorconsistsoftwoparallelsquareplatesseparatedbyavacuum.Theplatesare2.5cm×2.5cm
squares.Thecapacitanceofthecapacitoris4.3pF.
Calculatethedistancebetweentheplates.
1b.[2marks]
Thecapacitorisconnectedtoa16Vcellasshown.
CalculatethemagnitudeandthesignofthechargeonplateAwhenthecapacitorisfullycharged.
2
1c.[2marks]
Thecapacitorisfullychargedandthespacebetweentheplatesisthenfilledwithadielectricof
permittivityε=3.0ε0.
ExplainwhetherthemagnitudeofthechargeonplateAincreases,decreasesorstaysconstant.
1d.[3marks]
Inadifferentcircuit,atransformerisconnectedtoanalternatingcurrent(ac)supply.
Thetransformerhas100turnsintheprimarycoiland1200turnsinthesecondarycoil.Thepeakvalue
ofthevoltageoftheacsupplyis220V.Determinetherootmeansquare(rms)valueoftheoutput
voltage.
4
2a.[1mark]
AnegativelychargedthundercloudabovetheEarth’ssurfacemaybemodelledbyaparallelplate
capacitor.
ThelowerplateofthecapacitoristheEarth’ssurfaceandtheupperplateisthebaseofthe
thundercloud.
Thefollowingdataareavailable.
ShowthatthecapacitanceofthisarrangementisC=6.6×10–7F.
5
2b.[2marks]
CalculateinV,thepotentialdifferencebetweenthethundercloudandtheEarth’ssurface.
2c.[2marks]
CalculateinJ,theenergystoredinthesystem.
6
2d.[3marks]
Lightningtakesplacewhenthecapacitordischargesthroughtheairbetweenthethundercloudandthe
Earth’ssurface.Thetimeconstantofthesystemis32ms.Alightningstrikelastsfor18ms.
Showthatabout–11CofchargeisdeliveredtotheEarth’ssurface.
2e.[1mark]
Calculate,inA,theaveragecurrentduringthedischarge.
7
2f.[1mark]
StateoneassumptionthatneedstobemadesothattheEarth-thundercloudsystemmaybemodelled
byaparallelplatecapacitor.
8
3a.[2marks]
ThereisaproposaltopoweraspacesatelliteXasitorbitstheEarth.Inthismodel,Xisconnectedbyan
electronically-conductingcabletoanothersmallersatelliteY.
SatelliteXorbits6600kmfromthecentreoftheEarth.
MassoftheEarth=6.0x1024kg
ShowthattheorbitalspeedofsatelliteXisabout8kms–1.
9
3b.[1mark]
SatelliteYorbitsclosertothecentreofEarththansatelliteX.Outlinewhy
theorbitaltimesforXandYaredifferent.
3c.[2marks]
satelliteYrequiresapropulsionsystem.
10
3d.[3marks]
ThecablebetweenthesatellitescutsthemagneticfieldlinesoftheEarthatrightangles.
ExplainwhysatelliteXbecomespositivelycharged.
11
3e.[3marks]
SatelliteXmustreleaseionsintothespacebetweenthesatellites.Explainwhythecurrentinthecable
willbecomezerounlessthereisamethodfortransferringchargefromXtoY.
3f.[2marks]
ThemagneticfieldstrengthoftheEarthis31μTattheorbitalradiusofthesatellites.Thecableis15
kminlength.Calculatetheemfinducedinthecable.
12
3g.[3marks]
Thecableactsasaspring.SatelliteYhasamassmof3.5x102kg.Undercertaincircumstances,satellite
Ywillperformsimpleharmonicmotion(SHM)withaperiodTof5.2s.
Estimatethevalueofkinthefollowingexpression.
T=
Giveanappropriateunitforyouranswer.IgnorethemassofthecableandanyoscillationofsatelliteX.
3h.[2marks]
DescribetheenergychangesinthesatelliteY-cablesystemduringonecycleoftheoscillation.
13
4a.[2marks]
StateFaraday’slawofinduction.
4b.[4marks]
Thediagramshowsasketchofanidealstep-downtransformer.
Thenumberofturnsintheprimarycoilis1800andthatinthesecondarycoilis90.
Explain,usingFaraday’slawofinduction,howthetransformerstepsdownthevoltage.
15
4d.[2marks]
Outlinehowenergylossesarereducedinthecoreofapracticaltransformer.
4e.[2marks]
Step-uptransformersareusedinpowerstationstoincreasethevoltageatwhichtheelectricityis
transmitted.Explainwhythisisdone.
16
5a.[1mark]
Theelectricalcircuitshownisusedtoinvestigatethetemperaturechangeinawirethatiswrapped
aroundamercury-in-glassthermometer.
Apowersupplyofemf(electromotiveforce)24Vandofnegligibleinternalresistanceisconnectedtoa
capacitorandtoacoilofresistancewireusinganarrangementoftwoswitches.SwitchS1isclosedand,
afewsecondslater,opened.ThenswitchS2isclosed.
Thecapacitanceofthecapacitoris22mF.Calculatetheenergystoredinthecapacitorwhenitisfully
charged.
5b.[3marks]
Theresistanceofthewireis8.0Ω.Determinethetimetakenforthecapacitortodischargethroughthe
resistancewire.Assumethatthecapacitoriscompletelydischargedwhenthepotentialdifference
acrossithasfallento0.24V.
17
5c.[2marks]
Themassoftheresistancewireis0.61ganditsobservedtemperatureriseis28K.Estimatethe
specificheatcapacityofthewire.Includeanappropriateunitforyouranswer.
18
5d.[2marks]
Suggestoneotherenergylossintheexperimentandtheeffectitwillhaveonthevalueforthespecific
heatcapacityofthewire.
19
6a.[2marks]
Acableconsistingofmanycopperwiresisusedtotransferelectricalenergyfromanalternating
current(ac)generatortoanelectricalload.Thecopperwiresareprotectedbyaninsulator.
Thecableconsistsof32copperwireseachoflength35km.Eachwirehasaresistanceof64Ω.The
cableisconnectedtotheacgeneratorwhichhasanoutputpowerof110MWwhenthepeakpotential
differenceis150kV.Theresistivityofcopperis1.7x10–8Ωm.
outputpower=110MW
Calculatetheradiusofeachwire.
20
6b.[1mark]
Calculatethepeakcurrentinthecable.
6c.[3marks]
Determinethepowerdissipatedinthecableperunitlength.
21
6d.[1mark]
Toensurethatthepowersupplycannotbeinterrupted,twoidenticalcablesareconnectedinparallel.
Calculatetherootmeansquare(rms)currentineachcable.
6e.[2marks]
Thetwocablesinpart(c)aresuspendedaconstantdistanceapart.Explainhowthemagneticforces
actingbetweenthecablesvaryduringthecourseofonecycleofthealternatingcurrent(ac).
22
6f.[2marks]
Theenergyoutputoftheacgeneratorisatamuchlowervoltagethanthe150kVusedfortransmission.
Astep-uptransformerisusedbetweenthegeneratorandthecables.
Suggesttheadvantageofusingastep-uptransformerinthisway.
6g.[1mark]
Theuseofalternatingcurrent(ac)inatransformergivesrisetoenergylosses.Statehoweddycurrent
lossisminimizedinthetransformer.
23
7a.[4marks]
Thefollowingdataareavailableforanaturalgaspowerstationthathasahighefficiency.
Rateofconsumptionofnaturalgas =14.6kgs–1
Specificenergyofnaturalgas =55.5MJkg–1
Efficiencyofelectricalpowergeneration =59.0%
MassofCO2
generatedperkgofnaturalgas
=2.75kg
Oneyear =3.16×107s
Electricalpoweroutputisproducedbyseveralalternatingcurrent(ac)generatorswhichuse
transformerstodeliverenergytothenationalelectricitygrid.
Thefollowingdataareavailable.Rootmeansquare(rms)valuesaregiven.
acgeneratoroutputvoltagetoatransformer=25kVacgeneratoroutputcurrenttoatransformer=
3.9kATransformeroutputvoltagetothegrid=330kVTransformerefficiency=96%
(i)Calculatethecurrentoutputbythetransformertothegrid.Giveyouranswertoanappropriate
numberofsignificantfigures.
(ii)Electricalenergyisoftendeliveredacrosslargedistancesat330kV.Identifythemainadvantageof
usingthisveryhighpotentialdifference.
24
7b.[5marks]
Inanalternatingcurrent(ac)generator,asquarecoilABCDrotatesinamagneticfield.
Theendsofthecoilareconnectedtoslipringsandbrushes.Theplaneofthecoilisshownattheinstant
whenitisparalleltothemagneticfield.Onlyonecoilisshownforclarity.
Thefollowingdataareavailable.
25
Dimensionsofthecoil=8.5cm×8.5cmNumberofturnsonthecoil=80SpeedofedgeAB=2.0ms–1
Uniformmagneticfieldstrength=0.34T
(i)Explain,withreferencetothediagram,howtherotationofthegeneratorproducesanelectromotive
force(emf)betweenthebrushes.
(ii)Calculate,forthepositioninthediagram,themagnitudeoftheinstantaneousemfgeneratedbya
singlewirebetweenAandBofthecoil.
(iii)Hence,calculatethetotalinstantaneouspeakemfbetweenthebrushes.
27
8a.[2marks]
Twocellsofnegligibleinternalresistanceareconnectedinacircuit.
Thetopcellhaselectromotiveforce(emf)12V.Theemfofthelowercellisunknown.Theideal
ammeterreadszerocurrent.
CalculatetheemfEofthelowercell.
28
8b.[3marks]
ThediagramshowschargecarriersmovingwithspeedvinametallicconductorofwidthL.The
conductorisexposedtoauniformmagneticfieldBthatisdirectedintothepage.
(i)ShowthatthepotentialdifferenceVthatisestablishedacrosstheconductorisgivenbyV=vBL.
(ii)Onthediagram,labelthepartoftheconductorwherenegativechargeaccumulates.
29
9a.[2marks]
Anunchargedcapacitorinavacuumisconnectedtoacellofemf12Vandnegligibleinternalresistance.
AresistorofresistanceRisalsoconnected.
30
Att=0theswitchisplacedatpositionA.ThegraphshowsthevariationwithtimetofthevoltageV
acrossthecapacitor.Thecapacitorhascapacitance4.5μFinavacuum.
Ontheaxes,drawagraphtoshowthevariationwithtimeofthevoltageacrosstheresistor.
9b.[2marks]
31
(i)Thetimeconstantofthiscircuitis22s.Statewhatismeantbythetimeconstant.
(ii)CalculatetheresistanceR.
9c.[2marks]
Adielectricmaterialisnowinsertedbetweentheplatesofthefullychargedcapacitor.Statetheeffect,if
any,on
(i)thepotentialdifferenceacrossthecapacitor.
(ii)thechargeononeofthecapacitorplates.
32
9d.[3marks]
(i)Thepermittivityofthedielectricmaterialin(c)istwicethatofavacuum.Calculatetheenergy
storedinthecapacitorwhenitisfullycharged.
(ii)TheswitchinthecircuitisnowmovedtopositionBandthefullychargedcapacitordischarges.
Describewhathappenstotheenergyin(d)(i).
10a.[3marks]
Part2Powertransmissions
Thediagramshowsthemainfeaturesofanidealtransformerwhoseprimarycoilisconnectedtoa
sourceofalternatingcurrent(ac)voltage.
33
Outline,withreferencetoelectromagneticinduction,howavoltageisinducedacrossthesecondary
coil.
10b.[2marks]
Theprimarycoilhas25turnsandisconnectedtoanalternatingsupplywithaninputvoltageofroot
meansquared(rms)value12V.Thesecondarycoilhas80turnsandisnotconnectedtoanexternal
circuit.Determinethepeakvoltageinducedacrossthesecondarycoil.
34
10c.[1mark]
Adifferenttransformerisusedtotransmitpowertoasmalltown.
Thetransmissioncablesfromthepowerstationtothetransformerhaveatotalresistanceof4.0Ω.The
transformeris90%efficientandstepsdownthevoltageto120V.Atthetimeofmaximumpower
demandtheeffectiveresistanceofthetownandofthecablesfromthetransformertothetownis60
mΩ.
Calculatethecurrentinthecablesconnectedtothetown
10d.[2marks]
35
Calculatethepowersuppliedtothetransformer.
10e.[2marks]
Determinetheinputvoltagetothetransformerifthepowerlossinthecablesfromthepowerstationis
2.0kW.
10f.[2marks]
Outlinewhylaminatingthecoreimprovestheefficiencyofatransformer.
36
11a.[2marks]
Thisquestionisintwoparts.Part1isabouttheelectricalandmagneticcharacteristicsofa
loudspeaker.Part2isaboutvibrationsandwaves.
Part1Electricalandmagneticcharacteristicsofaloudspeaker
ThediagramshowsthemainfeaturesofaloudspeakerL.Acurrent-carryingcoilispositionedwithin
themagneticfieldprovidedbyapermanentmagnet.Thediagramalsoshowsthedirectionsofthe
magneticfieldandofthecurrentinthecoilataparticularinstant.ThedustcapDpreventsdustfrom
blockingthegapbetweenthecardboardtubeandthesouthpoleofthemagnet.
37
Thecoilconsistsof150turns,eachofaveragediameter2.5cm.Themagneticfieldofthepermanent
magnethasstrength0.40mT.Thepeakcurrentinthecoilis0.45mA.
Identify,onthediagram,thedirectionoftheforceonthecoilwiththecurrentdirectionsshown.
11b.[3marks]
Calculatethemaximummagneticforceactingonthecoil.
11c.[3marks]
Explain,withreferencetoelectromagneticinduction,theeffectofthemotionofthecoilonthecurrent.
38
12a.[3marks]
Thisquestionisaboutchangingmagneticfields.
Asingle-turnconductingsquarecoilisreleasedandfallsverticallyfromrest.Attheinstantitis
released,thecoilisattheboundaryofaregionofauniformhorizontalmagneticfielddirectedintothe
planeofthepaperasshown.Theendsofthecoilarenotjoinedtogether.
39
Eachsideofthecoilis0.050mlong.Thedimensionsofthemagneticfieldregionaregreaterthanthat
ofthecoil.Themagneticfieldstrengthis25mT.
Calculatetheelectromotiveforce(emf)inducedinthecoilattheinstantjustbeforethewholeofthe
coilentersthemagneticfield.
12b.[3marks]
40
Suggestwhythetimetakenforthewholeofthecoiltoenterthemagneticfieldincreasesifthecoilisa
continuousloop.
13a.[3marks]
Thisquestionisaboutelectromagneticinduction.
Ametalringisplacedinamagneticfieldwhichisdirectedupwards.Themagneticfluxthroughthering
increasesoveratimeinterval.
41
Stateandexplainthedirectionofthecurrentinducedintheringduringthischange.
13b.[3marks]
Thefollowingdataareavailable.
Resistanceofring=3.0×10–3Ω
Initialmagneticflux=1.2×10–5Wb
42
Finalmagneticflux=2.4×10–5Wb
Timeinterval=2.0×10–3s
Calculatetheaveragecurrentinducedinthering.
14a.[1mark]
Thisquestionisaboutgeneratingemfs.
Definemagneticflux.
43
14b.[5marks]
Averticalmetalrodoflength0.25mmovesinahorizontalcircleaboutaverticalaxisinauniform
horizontalmagneticfield.
Themetalrodcompletesonecircleofradius0.060min0.020sinthemagneticfieldofstrength61mT.
(i)Determinethemaximumemfinducedbetweentheendsofthemetalrod.
(ii)Usingtheaxes,sketchagraphtoshowthevariationwithtimeoftheemfofthemetalrod.
45
15a.[4marks]
Thisquestionisaboutinducedelectromotiveforce(emf).
Aloopofcopperwireinaregionofuniformmagneticfieldisrotatedaboutahorizontalaxis.
ThemagnitudeofthemagneticfieldstrengthisBandtheareaoftheloopisA.
(i)Statetheminimumvalueandthemaximumvalueofthemagneticfluxlinkingtheloop.
(ii)OutlinewithreferencetoFaraday’slawwhy,ifthespeedofrotationoftheloopisincreased,the
maximumemfinducedintheloopisincreased.
15b.[4marks]
Theloopin(a)isconnectedinserieswitharesistorofresistance15Ω.Therootmeansquared(rms)
valueofthesinusoidalcurrentintheresistoris2.3mA.
(i)Explainwhatismeantbythermsvalueofasinusoidalcurrent.
(ii)Determinethemaximumpowerdissipatedintheresistor.
47
16a.[6marks]
Thisquestionisintwoparts.Part1isaboutelectromagneticinduction.Part2isaboutnuclearfusion.
Part1Electromagneticinduction
Abarmagnetfallsverticallyfromrestthroughacoilofwire.Thepotentialdifference(pd)acrossthe
coilisrecordedbyadatalogger.
Thegraphshowsthevariationwithtimeofthepdacrossthecoil.
48
(i)Explain,withreferencetoFaraday’sandLenz’slaws,theshapeofthegraph.
(ii)Thecoilhas1500turns.Calculatethemagnitudeofthemaximumrateofchangeofmagneticflux.
49
16b.[5marks]
Themagnetisnowsuspendedfromaspring.Themagnetisdisplacedverticallyandstartstooscillatein
andoutofthecoil.Asinusoidalalternatingcurrentofrmsvalue280nAisinducedinthecoil.
(i)Stateinwordshowthermsvalueofthealternatingcurrentrelatestoadirectcurrentof280nA.
(ii)Thecoilhasaresistanceof1.5MΩ.Calculatethepeakvoltageacrossthecoil.
(iii)Explainwhateffectthegenerationofthecurrenthasontheoscillationofthemagnet.
51
17a.[1mark]
Thisquestionisaboutelectromagneticinduction.
StateLenz’slaw.
17b.[4marks]
Twoidenticalaluminiumballsaredroppedsimultaneouslyfromthesameheight.BallPfallsthrougha
regionwithnomagneticfield.BallQfallsthrougharegionofuniformhorizontalmagneticfluxdensity
B.
ExplainwhyballQtakeslongerthanballPtoreachtheground.
53
18a.[4marks]
Thisquestionisaboutinducedelectromotiveforce(emf).
Arodmadeofconductingmaterialisinaregionofuniformmagneticfield.Itismovedhorizontally
alongtwoparallelconductingrailsXandY.Theotherendsoftherailsareconnectedbyathin
conductingwire.
Thespeedoftherodisconstantandisalsoatrightanglestothedirectionoftheuniformmagneticfield.
(i)Describe,withreferencetotheforcesactingontheconductionelectronsintherod,howanemfis
inducedintherod.
(ii)Aninducedemfisproducedbyarateofchangeofflux.Statewhatismeantbyarateofchangeof
fluxinthissituation.
54
18b.[4marks]
Thelengthoftherodin(a)is1.2manditsspeedis6.2ms–1.Theinducedemfis15mV.
(i)Determinethemagnitudeofthemagneticfieldstrengththroughwhichtherodismoving.
(ii)ExplainhowLenz’slawrelatestothesituationdescribedin(a).
55
19a.[3marks]
Part2Electromagneticinduction
Thediagramshowsahorizontalmetalrodsuspendedbytwoverticalinsulatedsprings.
TherodmovesverticallyupanddownwithsimpleharmonicmotionwithatimeperiodTatright
anglestoauniformmagneticfield.
Thediagramshowsthevariationwithtimetoftheverticaldisplacementxoftherod.
Ontheaxesprovided,drawagraphtoshow
(i)thevariationwithtimetoftheverticalvelocityvoftherod.
56
(ii)thevariationwithtimetoftheemfgeneratedbetweentheendsoftherod.
19b.[3marks]
Thelengthoftherodis0.18mandthemagnitudeofthemagneticfieldis58μT.Thefrequencyofthe
simpleharmonicmotionis2.5Hz.Theamplitudeofthemotionis8.2×10-2m.
Determinethemagnitudeofthemaximumemfεmaxbetweentheendsoftherod.
57
19c.[4marks]
Thefrequencyofthemotionisdoubledwithoutanychangeintheamplitudeofthemotion.
Stateandexplainthechangestothevariationwithtimetoftheemf generatedasaresultofthis
changeinfrequency.
58
20a.[1mark]
Thisquestionisaboutmotioninamagneticfield.
Anelectron,thathasbeenacceleratedfromrestbyapotentialdifferenceof250V,entersaregionof
magneticfieldofstrength0.12Tthatisdirectedintotheplaneofthepage.
Theelectron’spathwhileintheregionofmagneticfieldisaquartercircle.Showthatthe
timetheelectronspendsintheregionofmagneticfieldis7.5×10−11s.
20b.[4marks]
AsquareloopofconductingwireisplacednearastraightwirecarryingaconstantcurrentI.Thewireis
inthesameplaneastheloop.
59
Theloopismadetomovewithconstantspeedvtowardsthewire.
(i)Explain,byreferencetoFaraday’sandLenz’slawsofelectromagneticinduction,whyworkmustbe
doneontheloop.
(ii)Suggestwhatbecomesoftheworkdoneontheloop.
60
21a.[2marks]
Thisquestionisabouttheemfinducedinacoil.
Definemagneticflux.
21b.[3marks]
Acoilisrotatedatconstantspeedinaregionofuniformmagneticfield.
Thegraphshowsthevariationwithtimetoftheemfεinducedinthecoilforonecycleofrotation.