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Parallel-plateCapacitors

Twoparallelplatesadistancedapartarechargedtoapoten2aldifferenceV

Oneplategainsthee-theotheroneloses Chargestoredoneachplateassumingemptyspacebetweenplates

Waystoincreasechargestored:increaseA,increaseV,decreased

Q0 = AV0

d

1

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Parallel-plateCapacitors

Thereisanotherwaytoincreasethechargestored:Useadielectric

Dielectrics=insula2ngmaterialsusedtoincreasethecapacityoftheplatestostorecharge

Whenadielectricisplacedbetweenthechargedplates,itsmoleculesbecomepolarized

ForafixedV,inser2ngadielectricwillincreasethechargestoredintheplates

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Relativepermittivity

Therela2vepermiGvity(ordielectricconstant)risthera2oof(chargestoredwithdielectric)/(chargestoredwithout

dielectric)

Chargestoredoneachplate(withdielectric)

Sometypicalvaluesforr Vacuum/Air=1,Acrylic(Plexiglass)=4.5,Beeswax=.6 Silk=3.5,Silicon=1,Pyrexglass=5,Paper=3

Q = rQ0 =AV

0r

d

3

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Capacitance(ofparallelplatecapacitor)

ThecapacitanceCofacapacitorisdefinedasthechargestoredperunitp.d.(voltage)appliedacrossitsplates

Unit:Farad(F)=1CoulombperVolt Capacitancevaluesareusuallygivenin

F(1F=10-6F) pF(1pF=10-1F)

LargecapacitancecanbeachievedbyincreasingA,decreasingd,usingdielectrics

C=Q

V=

A0r

d

4

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Example

Consideracapacitormadeoftwo0.05mplatesseparatedby

0.5mm.Ifthecapacitanceis3.0nF,whatistherela2ve

permiGvityofthematerialbetweentheplates?Whatisthe

unitofrela2vepermiGvity?[Assume0=8.85x10-1Fm-1]

5

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CapacitorsinSeries

Capacitorsaredevicesthatstorecharge ChargestoredQ=It CapacitanceC=Q/V EnergystoredE=CV2

C1 C C3

I

V1 V V3

V

1

C=

1

C1

+

1

C2

+

1

C3

6

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CapacitorsinParallel

Capacitorsaredevicesthatstorecharge ChargestoredQ=It CapacitanceC=Q/V EnergystoredE=CV2 C1

C

C3

V

I I

I1

I

I3

C=C1+C

2+C

3

7

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Example

a)Whatistheequivalentcapacitanceofthefollowingsegment

ofacircuitifC1=C=C3=3.0mF?

b)IfavoltageVab=6.0Visapplied,whatisthechargeoneach

capacitor?

c)Whatisthevoltageacrosseachcapacitor?

8

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Example

Anair-filledparallelplatecapacitorhasacapacitanceof5.0pF.

Apoten2alof100Visappliedacrosstheplates,whichare1.0

cmapart,usingastoragebaery.Whatistheenergystoredin

thecapacitor?Supposethatthebaeryisdisconnected,and

theplatesaremovedun2ltheyare.0cmapart.Whatnowistheenergystoredinthecapacitor?Suppose,instead,thatthe

baeryisleconnected,andtheplatesareagainmovedun2l

theyare.0cmapart.Whatistheenergystoredinthe

capacitorinthiscase?

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ChargingaCapacitor

Tochargeacapacitorweconnectittoabaery Resistanceofthewire+resistanceofbaery=R e-flowingfromnega2veterminalchargeoneplateve Electricrepulsionchargestheotherplate+ve Electronbuilduponveplatereduceselectronflow As2mepassedtherateofchargeaccumula2ondecreases.

+ -

Baery

C

t

I

Q0

t

V0

t

Q V

10

C

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ChargingaCapacitor:

Equations AtstartI0=E/RwhereI0istheini2alcurrent,Ethee.m.f.ofthebaeryandRtheresistance

Aer2metthecurrentisIandthep.d.acrossthecapacitorisVC

ButI=dQ/dtandVC=Q/C.Subs2tu2ngandsimplifying

Integra2ngthisweget

+ -

C

Q =Q0 (1et/RC

)

E

VCR

I=EV

C

R

CRdQ

dt=CEQ =Q

0Q

1

CRdt

0

t

=dQ

Q0Q

0

Q

t

CR= ln

Q0Q

Q0

$

%&

'

()

I= I0e

t/RC

11

V=V0(1e

t/RC

)

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DischargingaCapacitor

Todischargeacapacitorweconnectittoaresistance Chargedropswith2me Voltagedropswith2me Currentdropswith2me Energystoredconvertedtoheatattheresistor

R

C

IQ

tt

V

t 1

C

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DischargingaCapacitor:

Equations Atstartcapacitorchargedtop.d.V0=Q0/C Ini2alcurrentI0=V0/R Currentaer2met:I=VC/R=Q/CR=-dQ/dt Integra2ng

R

C

dQ

QQ

0

Q

= 1

CRdt

0

t

lnQ

Q0

$

%&

'

()=

t

CR

I= I0et/RC

V=V0et/RC

Q =Q0et/RC

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Example

A00Fcapacitorischargedtoap.dof9Vthendischarged

througha100kresistor.

a) Whatistheini2alchargestoredbythecapacitor?b) Whatisthe2meconstantofthecircuit?c) Calculatethep.d.aera2meequaltothe2meconstantd) Calculatethep.d.aer300s.

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Pastexamquestionpartc

A.Fcapacitorisconnectedinparallelwithapowersupplyof5V.ItisalsoconnectedinparallelwithadigitaldisplayonaDVDrecorder.Thedisplayhasaresistanceof6.8k.Thepurposeofthecapacitoristokeepthedisplayworkingiftheelectricalpoweriscutoff.Thediagramshowsthearrangement

i) Showthatthe2meconstantforthecircuitismorethan4

hours.

ii) Findtheenergylostbythecapacitorasitdischargesfrom5Vto4V[8marks]

15

Display

R=6.8k.F5V

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Pastexamquestionpartd

Thevoltageacrossthecapacitorvarieswith2meaccordingto

theequa2on

Calculatethe2methatittakesforthevoltagetofallfrom5Vto

4Vinhours.[4marks]

16

V=V0et/RC

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ToDo

Fromchapterreadsec2ons.5(Capacitors) HomeworkAssignmentwk4:.1,.,.3,.5,.8,.30

Handitinnolaterthan4:00pmnextWednesday-LATEWORKWILLNOTBEACCEPTED

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