1

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.

3

1e.[3marks]

Describetheuseoftransformersinelectricalpowerdistribution.

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.

14

4c.[2marks]

Theinputvoltageis240V.Calculatetheoutputvoltage.

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.

26

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.

44

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.

46

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.

50

51

17a.[1mark]

Thisquestionisaboutelectromagneticinduction.

StateLenz’slaw.

17b.[4marks]

Twoidenticalaluminiumballsaredroppedsimultaneouslyfromthesameheight.BallPfallsthrougha

regionwithnomagneticfield.BallQfallsthrougharegionofuniformhorizontalmagneticfluxdensity

B.

ExplainwhyballQtakeslongerthanballPtoreachtheground.

52

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.

61

(i)Onthegraphlabel,withtheletterT,atimeatwhichthefluxlinkageinthecoilisamaximum.

(ii)Usethegraphtodeterminetherateofchangeoffluxatt=4.0ms.Explainyouranswer.

(iii)Calculatetherootmeansquarevalueoftheinducedemf.