 1 
Physics 2213 HW #9 — Solutions
Fall 2008
24.59
[Capacitor Network]
(a)
Replace series and parallel combinations of capacitors by their equivalents.
The network is sketched below.
1
5
8.4 F
C
C
μ
=
=
2
3
4
4.2 F
C
C
C
μ
=
=
=
Simplify the circuit by replacing the capacitor combinations by their equivalents:
3
4
and
C
C
are in series
and can be replaced by
34
C
:
34
3
4
1
1
1
C
C
C
=
+
3
4
34
3
4
1
C
C
C
C C
+
=
(
)(
)
3
4
34
3
4
4.2 F
4.2 F
2.1 F
4.2 F
4.2 F
C C
C
C
C
μ
μ
μ
μ
μ
=
=
=
+
+
2
34
and
C
C
are in parallel and can be replaced by their equivalent:
234
2
34
C
C
C
=
+
234
4.2 F
2.1 F
C
μ
μ
=
+
234
6.3 F
C
μ
=
1
5
234
,
and
C
C
C
are in series and can be replaced by
eq
C
:
eq
1
5
234
1
1
1
1
C
C
C
C
=
+
+
eq
1
2
1
8.4 F
6.3 F
C
μ
μ
=
+
eq
2.5 F
C
μ
=
Note: For capacitors in series the equivalent capacitor is smaller than any of those in series. For
capacitors in parallel the equivalent capacitance is larger than any of those in parallel.
(b)
In each equivalent network apply the rules for
Q
and
V
for capacitors in series and parallel; start with
the simplest network and work back to the original circuit.
The equivalent circuit is drawn below.
eq
eq
Q
C V
=
(
)(
)
eq
2.5 F
220 V
550 C
Q
μ
μ
=
=
1
5
234
550 C
Q
Q
Q
μ
=
=
=
(capacitors in series have same charge)
1
1
1
550 C
65 V
8.4 F
Q
V
C
μ
μ
=
=
=
5
5
5
550 C
65 V
8.4 F
Q
V
C
μ
μ
=
=
=
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 2 
234
234
234
550 C
87 V
6.3 F
Q
V
C
μ
μ
=
=
=
Now draw the network as:
2
34
234
87 V
V
V
V
=
=
=
capacitors in parallel have the same
potential
(
)(
)
2
2
2
4.2 F
87 V
370 C
Q
C V
μ
μ
=
=
=
(
)(
)
34
34
34
2.1 F
87 V
180 C
Q
C V
μ
μ
=
=
=
Finally, consider the original circuit (see below).
3
4
34
180 C
Q
Q
Q
μ
=
=
=
capacitors in series have the same charge
3
3
3
180 C
43 V
4.2 F
Q
V
C
μ
μ
=
=
=
4
4
4
180 C
43 V
4.2 F
Q
V
C
μ
μ
=
=
=
Summary:
1
1
550 C,
65 V
Q
V
μ
=
=
2
2
370 C,
87 V
Q
V
μ
=
=
3
3
180 C,
43 V
Q
V
μ
=
=
4
4
180 C,
43 V
Q
V
μ
=
=
5
5
550 C,
65 V
Q
V
μ
=
=
Note:
3
4
2
1
2
5
and
220 V
V
V
V
V
V
V
+
=
+
+
=
(apart from some small rounding error)
1
2
3
5
2
4
and
Q
Q
Q
Q
Q
Q
=
+
=
+
24.60
[Throw the Switch]
Apply the rules for combining capacitors in series and in parallel. With the switch open each pair of
3.00 F
μ
and
6.00 F
μ
capacitors are in series with each other and each pair is in parallel with the other pair.
When the switch is closed each pair of
3.00 F
μ
and
6.00 F
μ
capacitors are in parallel with each other and
the two pairs are in series.
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 Fall '07
 PERELSTEIN,M
 Electrostatics, Magnetism, Work, Heat, Potential difference, Electric charge, Ceq, Capacitor Network

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