Download 7.8.1 The parallel plate capacitor

7.8.1Theparallelplatecapacitor
Acapacitorisadevicewhichisusedtostoreelectriccharge.Thesimplest
capacitorconsistsoftwometalplatesseparatedbyanairgap.Iftheplatesare
connectedtoabattery,electronsareremovedfromoneplateandmovedaround
thecircuittotheotherplate.Thisleavesthefirstplatewithapositivechargeand
theotherwithanegativecharge.Thereisanequalandoppositechargeonboth
plates.Thebiggerthevoltagesuppliedthebiggerthechargethataccumulates.
+
-
-
+
Symbolfora
+
-
capacitor.
+
-
electronflow
Iftheareaoftheplatesisincreased,morechargecanbestoredforthesame
appliedvoltage.Thecapacitance(C)isameasureoftheamountofcharge(Q)
thatcanbestoredforagivenvoltage(V):
𝑄
𝐶= 𝑉
Capacitanceismeasuredinfarads(F).Thefaradis,practically,quitealarge
valueforcapacitorsthatareusedineverydaycircuits.Wearemorelikelytosee
valuesinmicrofarads(μF)andpicofarads(pF).
(1)$Acapacitorwithavalueof900pFisfullychargedbya9Vbattery.What
chargeisstoredonthecapacitor?
Awatermodelofacapacitor
Ananalogyforacapacitorisarubbermembranestretchedacrossapipe
containingwater.Waterflowisanalogoustoelectriccurrent.Currentwill
continuetoflowuntilthemembraneisfullystretched.Atthispointcurrentflow
willstop.
Thepressureofwaterisanalogoustothevoltage.Asthemembranebecomes
moreandmorestretchedthepressurebuildsup.
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Onemethodtoexplorethebehaviourofacapacitoristousethefollowing
circuit:
Aconstantcurrent
V
canbemaintainedby
adjustingthe
variableresistor.
Readingsofvoltage
canbetakenat
differenttimesasthe
A
capacitorchargesup.
Theswitchcanbe
openedatcertain
timestotakea
reading.
(2)$Acapacitorischargedbymeansofaconstantcurrentof0.7μAfor60
secondsandavoltageof4.5Visrecorded.Calculatethechargestoredand,hence,
workoutthecapacitanceofthecapacitor.
A
Inthecircuit,left,atwo
2
wayswitchcanbeusedto
connectthecapacitorto
connector1or2.
1
(3)$Describewhathappenswhentheswitchisinposition1.
(4)$Describewhathappenswhentheswitchisinposition2.
(5)$Dosomeresearchandfindoutsomeoftheusesofcapacitorsincircuits.
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Combiningcapacitorsinseriesandparallel
Whencapacitorsarecombinedinseries,thetotalcapacitance𝐶% isgivenbythe
following:
1
1
1
1
= + + + ⋯
𝐶% 𝐶' 𝐶) 𝐶*
(6)$Workoutthetotalcapacitanceforthefollowingcombination:
3.2μF 4.6μF 1.9μF
Whencapacitorsarecombinedinparallel,thetotalcapacitance𝐶% isgivenbythe
following:
𝐶% = 𝐶' + 𝐶) + 𝐶* + ⋯
(7)$Workoutthetotalcapacitanceforthefollowingcombination:
4.6μF
6.2μF
3.2μF
1.9μF
(8)$Howdoesaddingcapacitorsinseriesandparallelcomparetoadding
resistorsinseriesandparallel?
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