capacitors - p3, week 4
TRANSCRIPT
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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
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Example
Consideracapacitormadeoftwo0.05mplatesseparatedby
0.5mm.Ifthecapacitanceis3.0nF,whatistherela2ve
permiGvityofthematerialbetweentheplates?Whatisthe
unitofrela2vepermiGvity?[Assume0=8.85x10-1Fm-1]
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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
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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
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Example
a)Whatistheequivalentcapacitanceofthefollowingsegment
ofacircuitifC1=C=C3=3.0mF?
b)IfavoltageVab=6.0Visapplied,whatisthechargeoneach
capacitor?
c)Whatisthevoltageacrosseachcapacitor?
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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
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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]
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Display
R=6.8k.F5V
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Pastexamquestionpartd
Thevoltageacrossthecapacitorvarieswith2meaccordingto
theequa2on
Calculatethe2methatittakesforthevoltagetofallfrom5Vto
4Vinhours.[4marks]
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V=V0et/RC
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ToDo
Fromchapterreadsec2ons.5(Capacitors) HomeworkAssignmentwk4:.1,.,.3,.5,.8,.30
Handitinnolaterthan4:00pmnextWednesday-LATEWORKWILLNOTBEACCEPTED
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