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CapacitanceandCharge
WesawintheprevioustutorialsthataCapacitorconsistsoftwoparallelconductiveplates(usuallyametal)whichare
preventedfromtouchingeachother(separated)byaninsulatingmaterialcalledthe"dielectric".Wealsosawthatwhena
voltageisappliedtotheseplatesanelectricalcurrentflowscharginguponeplatewithapositivechargewithrespectto
thesupplyvoltageandtheotherplatewithanequalandoppositenegativecharge.
Then,acapacitorhastheabilityofbeingabletostoreanelectricalchargeQ(unitsinCoulombs)ofelectrons.Whena
capacitorisfullychargedthereisapotentialdifference,p.d.betweenitsplates,andthelargertheareaoftheplates
and/orthesmallerthedistancebetweenthem(knownasseparation)thegreaterwillbethechargethatthecapacitorcan
holdandthegreaterwillbeitsCapacitance.
TheCapacitorsabilitytostorethiselectricalcharge(Q)betweenitsplatesisproportionaltotheappliedvoltage,Vfora
capacitorofknowncapacitanceinFarads.CapacitanceCisalwayspositiveandnevernegative.Thegreatertheapplied
voltagethegreaterwillbethechargestoredontheplatesofthecapacitor.Likewise,thesmallertheappliedvoltagethe
smallerthecharge.Therefore,theactualchargeQontheplatesofthecapacitorandcanbecalculatedas:
ChargeonaCapacitor
Where:Q(Charge,inCoulombs)=C(Capacitance,inFarads)xV(Voltage,inVolts)
Itissometimeseasiertorememberthisrelationshipbyusingpictures.HerethethreequantitiesofQ,CandVhave
beensuperimposedintoatrianglegivingchargeatthetopwithcapacitanceandvoltageatthebottom.Thisarrangement
representstheactualpositionofeachquantityintheCapacitorChargeformulas.
andtransposingtheaboveequationgivesusthefollowingcombinationsofthesameequation:
Unitsof:QmeasuredinCoulombs,VinvoltsandCinFarads.
ThenfromabovewecandefinetheunitofCapacitanceasbeingaconstantofproportionalitybeingequaltothe
coulomb/voltwhichisalsocalledaFarad,unitF.Ascapacitancerepresentsthecapacitorsability(capacity)tostorean
electricalchargeonitsplateswecandefineoneFaradasthe"capacitanceofacapacitorwhichrequiresachargeofone
coulombtoestablishapotentialdifferenceofonevoltbetweenitsplates"asfirstlydescribedbyMichaelFaraday.Sothe
largerthecapacitance,thehigheristheamountofchargestoredonacapacitorforthesameamountofvoltage.
TheabilityofacapacitortostoreachargeonitsconductiveplatesgivesititsCapacitancevalue.Capacitancecanalso
bedeterminedfromthedimensionsorarea,Aoftheplatesandthepropertiesofthedielectricmaterialbetweenthe
plates.Ameasureofthedielectricmaterialisgivenbythepermittivity,(ε),orthedielectricconstant.Soanotherwayof
expressingthecapacitanceofacapacitoris;
withAirasitsdielectric
withaSolidasitsdielectric
whereAistheareaoftheplatesinsquaremetres,mwiththelargerthearea,themorechargethecapacitorcan
store.disthedistanceorseparationbetweenthetwoplates.Thesmalleristhisdistance,thehigheristheabilityofthe
platestostorecharge,sincethe-vechargeonthe-Qchargedplatehasagreatereffectonthe+Qchargedplate,
resultinginmoreelectronsbeingrepelledoffofthe+Qchargedplate,andthusincreasingtheoverall
charge.ε(epsilon)isthevalueofthepermittivityforairwhichis8.84x10F/m,andεisthepermittivityofthe
dielectricmediumusedbetweenthetwoplates.
ParallelPlateCapacitor
WehavesaidpreviouslythatthecapacitanceofaparallelplatecapacitorisproportionaltothesurfaceareaAand
inverselyproportionaltothedistance,dbetweenthetwoplatesandthisistruefordielectricmediumofair.However,the
capacitancevalueofacapacitorcanbeincreasedbyinsertingasolidmediuminbetweentheconductiveplateswhich
hasadielectricconstantgreaterthanthatofair.
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0-12r
Typicalvaluesofepsilonεforvariouscommonlyuseddielectricmaterialsare:Air=1.0,Paper=2.5-3.5,Glass=3
-10,Mica=5-7etc.
Thefactorbywhichthedielectricmaterial,orinsulator,increasesthecapacitanceofthecapacitorcomparedtoairis
knownastheDielectricConstant,(k)."k"istheratioofthepermittivityofthedielectricmediumbeingusedtothe
permittivityoffreespaceotherwiseknownasavacuum.Therefore,allthecapacitancevaluesarerelatedtothe
permittivityofvacuum.Adielectricmaterialwithahighdielectricconstantisabetterinsulatorthanadielectricmaterial
withalowerdielectricconstant.Dielectricconstantisadimensionlessquantitysinceitisrelativetofreespace.
ExampleNo1
Aparallelplatecapacitorconsistsoftwoplateswithatotalsurfaceareaof100cm.Whatwillbethecapacitanceinpico-
Farads,(pF)ofthecapacitoriftheplateseparationis0.2cm,andthedielectricmediumusedisair.
thenthevalueofthecapacitoris44pF.
Charging&DischargingofaCapacitor
Considerthefollowingcircuit.
Assumethatthecapacitorisfullydischargedandtheswitchconnectedtothecapacitorhasjustbeenmovedto
positionA.Thevoltageacrossthe100ufcapacitoriszeroatthispointandachargingcurrent(i)beginstoflowcharging
upthecapacitoruntilthevoltageacrosstheplatesisequaltothe12vsupplyvoltage.Thechargingcurrentstopsflowing
andthecapacitorissaidtobe"fully-charged".
Then,Vc=Vs=12v.
Oncethecapacitoris"fully-charged"intheoryitwillmaintainitsstateofvoltagechargeevenwhenthesupplyvoltagehas
beendisconnectedastheyactasasortoftemporarystoragedevice.However,whilethismaybetrueofan"ideal"
capacitor,arealcapacitorwillslowlydischargeitselfoveralongperiodoftimeduetotheinternalleakagecurrents
flowingthroughthedielectric.Thisisanimportantpointtorememberaslargevaluecapacitorsconnectedacrosshigh
voltagesuppliescanstillmaintainasignificantamountofchargeevenwhenthesupplyvoltageisswitched"OFF".
Iftheswitchwasdisconnectedatthispoint,thecapacitorwouldmaintainitschargeindefinitely,butduetointernal
leakagecurrentsflowingacrossitsdielectricthecapacitorwouldveryslowlybegintodischargeitselfastheelectrons
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passedthroughthedielectric.Thetimetakenforthecapacitortodischargedownto37%ofitssupplyvoltageisknown
asitsTimeConstant.
IftheswitchisnowmovedfrompositionAtopositionB,thefullychargedcapacitorwouldstarttodischargethroughthe
lampnowconnectedacrossit,illuminatingthelampuntilthecapacitorwasfullydischargedastheelementofthelamp
hasaresistivevalue.Thebrightnessofthelampandthedurationofilluminationwouldultimatelydependuponthe
capacitancevalueofthecapacitorandtheresistanceofthelamp(t=CxR).Thelargerthevalueofthecapacitorthe
brighterandlongerwillbetheilluminationofthelampasitcouldstoremorecharge.
ExampleNo2
Calculatethechargeintheabovecapacitorcircuit.
thenthechargeonthecapacitoris1.2millicoulombs.
CurrentthroughaCapacitor
Thecurrentthatflowsthroughacapacitorisdirectlyrelatedtothechargeontheplatesascurrentistherateofflowof
chargewithrespecttotime.Asthecapacitorsabilitytostorecharge(Q)betweenitsplatesisproportionaltotheapplied
voltage(V),therelationshipbetweenthecurrentandthevoltagethatisappliedtotheplatesofacapacitorbecomes:
Current-Voltage(I-V)Relationship
Asthevoltageacrosstheplatesincreases(ordecreases)overtime,thecurrentflowingthroughthecapacitance
deposits(orremoves)chargefromitsplateswiththeamountofchargebeingproportionaltotheappliedvoltage.Then
boththecurrentandvoltageappliedtoacapacitancearefunctionsoftimeandaredenotedbythe
symbols,iandvHowever,fromtheaboveequationwecanalsoseethatifthevoltageremainsconstant,thecharge
willbecomeconstantandthereforethecurrentwillbezero!.Inotherwords,nochangeinvoltage,nomovementof
chargeandnoflowofcurrent.Thisiswhyacapacitorappearsto"block"currentflowwhenconnectedtoasteadystate
DCvoltage.
TheFarad
WenowknowthattheabilityofacapacitortostoreachargegivesititscapacitancevalueC,whichhastheunitof
theFarad,F.Butthefaradisanextremelylargeunitonitsownmakingitimpracticaltouse,sosubmultiple''sorfractions
ofthestandardFaradunitareusedinstead.TogetanideaofhowbigaFaradreallyis,thesurfaceareaoftheplates
requiredtoproduceacapacitorwithavalueofoneFaradwithareasonableplateseparationofjust1mmoperatingina
vacuumandrearrangingtheequationforcapacitanceabovewouldbe:
A=Cd÷8.85pF/m=(1x0.001)÷8.85x10=112,994,350m
or113millionmwhichwouldbeequivalenttoaplateofmorethan10kilometresx10kilometressquare.
CapacitorswhichhaveavalueofoneFaradormoretendtohaveasoliddielectricandas"OneFarad"issuchalarge
unittouse,prefixesareusedinsteadinelectronicformulaswithcapacitorvaluesgiveninmicro-Farads(μF),nano-
Farads(nF)andthepico-Farads(pF).Forexample:
Sub-unitsoftheFarad
(t)(t)
-122
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Convertthefollowingcapacitancevaluesfroma)22nFtouF,b)0.2uFtonF,c)550pFtouF.
a)22nF=0.022uF
b)0.2uF=200nF
c)550pF=0.00055uF
WhileoneFaradisalargevalueonitsown,capacitorsarenowcommonlyavailablewithcapacitancevaluesofmany
hundredsofFaradsandhavenamestoreflectthisof"Supercapacitors"or"Ultracapacitors".Thesecapacitorsare
electrochemicalenergystoragedeviceswhichutiliseahighsurfaceareaoftheircarbondielectrictodelivermuchhigher
energydensitiesthanconventionalcapacitorsandascapacitanceisproportionaltothesurfaceareaofthecarbon,the
thickerthecarbonthemorecapacitanceithas.
Lowvoltage(fromabout3.5Vto5.5V)supercapacitorsarecapableofstoringlargeamountsofchargeduetotheirhigh
capacitancevaluesastheenergystoredinacapacitorisequalto1/2(CxV).Lowvoltagesupercapacitorsare
commonlyusedinportablehandhelddevicestoreplacelarge,expensiveandheavylithiumtypebatteriesastheygive
battery-likestorageanddischargecharacteristicsmakingthemidealforuseasanalternativepowersourceorfor
memorybackup.Supercapacitorsusedinhandhelddevicesareusuallychargedusingsolarcellsfittedtothedevice.
Ultracapacitorarebeingdevelopedforuseinhybridelectriccarsandalternativeenergyapplicationstoreplacelarge
conventionalbatteriesaswellasDCsmoothingapplicationsinvehicleaudioandvideosystems.Ultracapacitorscanbe
rechargedquicklyandhaveveryhighenergystoragedensitiesmakingthemidealforuseinelectricvehicleapplications.
EnergyinaCapacitor
Whenacapacitorchargesupfromthepowersupplyconnectedtoit,anelectrostaticfieldisestablishedwhichstores
energyinthecapacitor.TheamountofenergyinJoulesthatisstoredinthiselectrostaticfieldisequaltotheenergythe
voltagesupplyexertstomaintainthechargeontheplatesofthecapacitorandisgivenbytheformula:
sotheenergystoredinthe100uFcapacitorcircuitaboveiscalculatedas:
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ThenexttutorialinoursectionaboutCapacitors,welookatCapacitorColourCodesandseethedifferentwaysthat
thecapacitanceandvoltagevaluesofthecapacitoraremarkedontoitsbody.
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