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Physics

PCS 211

Alexandre Douplik

Winter

Description

▯ ▯ ▯ ▯ Capacitance Use CapacCito26. Capacitance and Dielectrics
Unitstfreapsciteaci:srlrotitalntlpyntgtve.nergy.
mmF = micromicrofarad = picofarads = 1x10 AC fciter,iterunestereni)lyanfrruice,siteceenge and a
r: two conductors having
: C
▯Q/V
F = 1
▯
F,
-12
F = 1 pF
General procedureion of Capacitance
StepS3teCSteQa/l.ulcearge of magnitude of Q is assumed. To increase capacitance: increase (2) 1)eAeectiefindpbatehasawchprats:, and other –Q.acitor:
The potential difference between two plates:
(3)
C C
= =
▯ V Q
d A = V E
Qd = =
Ed ▯ ▯
▯ Q 0 =
A = ▯
0▯ Qd A Q
A
Aor decrease
+Q
d
d
Area =A -Q
In case of an isolated conducting sphere, assume b)hess(Geuhs’sLarg):is Q and -Q
Example: The capacitance of an spherical conductor
C
=
V Q MagnibVde E
= C ▯ =
e a = aV e
= V Q = r2 Q
▯▯ = V ▯ (b > r > a)
0 ek E
a b ab k rdr
▯ eQ =
) ( ▯
ab ▯ ek
a ▯
(>0)ra dr -Q
2
k
eQ b
▯ ▯ ▯
b ▯
a 1 a
▯ (<0) +Q
▯ Example: If C, C Potential difference in a parallel cParallel Combination: of Capacitors
Total Capacitance: Q
1 eq eq eq
= 2 = C= C = Q
▯
F, C1+ C+ Ctotal
/V = (Q V = V
2= 4 2 2 total
+ C = Q
▯ 1= V
F the+ C 1+ Q 1+ Q
••• ,
2 2
)/V = Q
eq
= 6
1
▯ /V + Q
F
2
/V
C ExampleGenerally, must be the same on all the plates.ies Combination of Capacitors
CapacPotentiadifarence:s ombination, the magnitude of the charge
C
C eq 1
eq 1 =
eq 1= C = V
= 4 C 1 Q total C
2= 8 1 + eq
F C = =
▯ 2 1 1V V
F then + Q + totaQ
3 1 V total
+••• =2 = V
C Q V
eq 1 1 1
= + + V
8 Q 2V
▯ 1 = 2,
F C 1
+ 1
▯ 1 +
F 2 1
=
4
F 1 26.4
Energy Stored in a Charged Capacitor
Define: is stored in the electric field created between the platesork needed to transfer +acitor.
The above 3 expressions are totally equivalent.
Energy density
U U W dW
= ▯ = =
2▯1 0A/d into W 0 ▯ Q =
0E = C q Vdq
Eu 2 2 Q dq
= (Ad) C 2 = =
2 1 U = 2 Q Cdqq
0▯ or = , QV1 C 2
E energy per unit▯volume
2 ene0Ey stored in a c=pacitor dq
2

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