§ 4-2 The capacitor
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C
i q?
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dt
dCi
dtdqiCq
/
/
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The displacement current flowing internally between the
capacitor plates is exactly equal to the conduction current
flowing in the capacitor leads.
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)(1)( 0
0
ti d tCt tt ?? ??? ?
The voltage appearing across the terminals of a linear time-
invariant capacitor must always be a continuous function.
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0
0)0(
)(
)0()0(
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21
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s
ia n d
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ii
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c i r c u i ts h o r t
If
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CC
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32
RRR
RRtat s
C ??
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s o u r cevo l t a g eaRRR RRtat sCC ??? ???? ??? )( )()0()0(,0:
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)0(
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s
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1R 2R
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3Rs?
2i
Ci
C
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1i
2R
The power p (accepted) by a capacitor:
dt
dCip ??? ??
The energy:
)}t()t({CdCdtdtdCp d tdw )t( )t(tt)t(w )t(w ttCC
C 0
22
2
1
000 0
?????? ?? ????? ??? ?
2
0 2
1)(0)( ?? CtwtIf
C ??
)}()({21)()( 0220 ttCtwtwor CC ?? ???
Example 1:
tAdtCd vi C ?? 2co s104/ 3????
00 ??? Cwt
0,2/1
1.0,4/1
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C
C
wst
Jwst
? ? ??? 2/10 2/10 2 5.2 mJdtRidtpw RRR
tVt ?? 2s i n100)( ?
tARvi R ?2s i n10/ 4???
tJCvw C ?2s i n1.021 22 ??
c apa c ito rph y sic al ?
tV?2s in100
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Ri Ci
F20??M1
Some of important characteristics of a capacitor
are now apparent:
2,A finite amount of energy can be stored in a capacitor
even if the current through the capacitor is zero,such as
when the voltage across it is constant.
1,The current through a capacitor is zero,if the
voltage across it is not changing with time,A capacitor
is therefore an open circuit to dc.
3,It is impossible to change the voltage across a
capacitor by a finite amount in zero time,for this
requires an infinite current through the capacitor,It
will be advantageous later to hypothesize that such a
current may be generated or applied to a capacitor,but
for the present we shall avoid such a forcing function or
response,A capacitor resists an abrupt change in the
voltage across it in a manner analogous to the way a
spring resists an abrupt change in its displacement.
4,The capacitor never dissipated energy,but only stores
it,Although this is true for the mathematical model,it is
not true for a physical capacitor.