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CapacitorsinParallel
Capacitorsaresaidtobeconnectedtogether"inparallel"whenbothoftheirterminalsarerespectivelyconnectedtoeach
terminaloftheothercapacitororcapacitors.Thevoltage(Vc)connectedacrossallthecapacitorsthatareconnectedin
parallelisTHESAME.Then,CapacitorsinParallelhavea"commonvoltage"supplyacrossthemgiving
V=V=V=V=12V
Inthefollowingcircuitthecapacitors,C,CandCareallconnectedtogetherinaparallelbranchbetween
pointsAandBasshown.
Whencapacitorsareconnectedtogetherinparallelthetotalorequivalentcapacitance,Cinthecircuitisequaltothe
sumofalltheindividualcapacitorsaddedtogether.Thisisbecausethetopplateofcapacitor,Cisconnectedtothetop
plateofCwhichisconnectedtothetopplateofCandsoon.Thesameisalsotrueofthebottomplates.Thenitisthe
sameasifthethreesetsofplatesweretouchingeachotherandequaltoonelargesingleplatetherebyincreasingthe
effectiveplateareainm.
Sincecapacitance,Cisrelatedtoplatearea(C=εA/d)thecapacitancevalueofthecombinationwillalsoincrease.
Thenthetotalcapacitancevalueofthecapacitorsconnectedtogetherinparallelisactuallycalculatedbyaddingtheplate
areatogether.Inotherwords,thetotalcapacitanceisequaltothesumofalltheindividualcapacitancesinparallel.You
mayhavenoticedthatthetotalcapacitanceofparallelcapacitorsisfoundinthesamewayasthetotalresistanceof
seriesresistors.
Thecurrentsflowingthrougheachcapacitorandaswesawintheprevioustutorialarerelatedtothevoltage.Thenby
applyingKirchoff''sCurrentLaw,(KCL)totheabovecircuit,wehave
andthiscanbere-writtenas:
C1C2C3AB
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Thenwecandefinethetotalorequivalentcircuitcapacitance,Casbeingthesumofalltheindividualcapacitancesadd
togethergivingusthegeneralizedequationof
ParallelCapacitorsEquation
Whenaddingtogethercapacitorsinparallel,theymustallbeconvertedtothesamecapacitanceunits,whetherit
isuF,nForpF.Also,wecanseethatthecurrentflowingthroughthetotalcapacitancevalue,Cisthesameasthetotal
circuitcurrent,i
WecanalsodefinethetotalcapacitanceoftheparallelcircuitfromthetotalstoredcoulombchargeusingtheQ=
CVequationforchargeonacapacitorsplates.ThetotalchargeQstoredonalltheplatesequalsthesumofthe
individualstoredchargesoneachcapacitortherefore,
Asthevoltage,(V)iscommonforparallelconnectedcapacitors,wecandividebothsidesoftheaboveequationthrough
bythevoltageleavingjustthecapacitanceandbysimplyaddingtogetherthevalueoftheindividualcapacitancesgives
thetotalcapacitance,C.Also,thisequationisnotdependantuponthenumberofCapacitorsinParallelinthebranch,
andcanthereforebegeneralizedforanynumberofNparallelcapacitorsconnectedtogether.
ExampleNo1
Sobytakingthevaluesofthethreecapacitorsfromtheaboveexample,wecancalculatethetotalequivalentcircuit
capacitanceCasbeing:
C=C+C+C=0.1uF+0.2uF+0.3uF=0.6uF
Oneimportantpointtorememberaboutparallelconnectedcapacitorcircuits,thetotalcapacitance(C)ofanytwoor
morecapacitorsconnectedtogetherinparallelwillalwaysbeGREATERthanthevalueofthelargestcapacitorinthe
groupasweareaddingtogethervalues.SoinourexampleaboveC=0.6uFwhereasthelargestvaluecapacitoris
only0.3uF.
When4,5,6orevenmorecapacitorsareconnectedtogetherthetotalcapacitanceofthecircuitCwouldstillbethesum
ofalltheindividualcapacitorsaddedtogetherandasweknownow,thetotalcapacitanceofaparallelcircuitisalways
greaterthanthehighestvaluecapacitor.Thisisbecausewehaveeffectivelyincreasedthetotalsurfaceareaofthe
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plates.Ifwedothiswithtwoidenticalcapacitors,wehavedoubledthesurfaceareaoftheplateswhichinturndoubles
thecapacitanceofthecombinationandsoon.
ExampleNo2.
Calculatethecombinedcapacitanceinmicro-Farads(uF)ofthefollowingcapacitorswhentheyareconnectedtogether
inaparallelcombination:
a)twocapacitorseachwithacapacitanceof47nF
b)onecapacitorof470nFconnectedinparalleltoacapacitorof1uF
a)TotalCapacitance,
C=C+C=47nF+47nF=94nFor0.094uF
b)TotalCapacitance,
C=C+C=470nF+1uF
therefore,C=470nF+1000nF=1470nFor1.47uF
So,thetotalorequivalentcapacitance,CofacircuitcontainingCapacitorsinParallelisthesumofthealltheindividual
capacitancesaddedtogetherandinournexttutorialaboutCapacitors,welookatconnectingtogetherCapacitorsin
Seriesandtheaffectthiscombinationhasonthecircuitstotalcapacitance,voltageandcurrent.
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