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2416
Chapter 24
24.59.
(a)
IDENTIFY:
Replace series and parallel combinations of capacitors by their equivalents.
SET UP:
The network is sketched in Figure 24.59a.
15
8.4 F
CC
μ
==
234
4.2 F
CCC
===
Figure 24.59a
EXECUTE:
Simplify the circuit by replacing the capacitor combinations by their equivalents:
34
and
are in
series and can be replaced by
34
C
(Figure 24.59b):
34
3
4
111
C
=+
34
3
4
1
C
+
=
Figure 24.59b
()
34
4.2 F 4.2 F
2.1 F
4.2 F
4.2 F
C
μμ
=
++
23
4
and
are in parallel and can be replaced by their equivalent (Figure 24.59c):
234
2
34
C
234
4.2 F
2.1 F
C
234
6.3 F
C
=
Figure 24.59c
1
5
234
,
and
C
are in series and can be replaced by
eq
C
(Figure 24.59d):
eq
1
5
234
1111
C
C
=++
eq
12
1
8.4 F
6.3 F
C
eq
2.5 F
C
=
Figure 24.59d
EVALUATE:
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) IDENTIFY
and
SET UP:
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.
EXECUTE:
The equivalent circuit is drawn in Figure 24.59e.
eq
eq
QC
V
=
( )( )
eq
2.5 F 220 V
550 C
Q
Figure 24.59e
1
5
234
550 C
QQQ
== =
(capacitors in series have same charge)
1
1
1
550 C
65 V
8.4 F
Q
V
C
=
5
5
5
550 C
65 V
8.4 F
Q
V
C
=
234
234
234
550 C
87 V
6.3 F
Q
V
C
=
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View Full DocumentCapacitance and Dielectrics
2417
Now draw the network as in Figure 24.59f.
2
34
234
87 V
VV V
==
=
capacitors in parallel have the same potential
Figure 24.59f
()
(
)
22
2
4.2 F 87 V
370 C
QC
V
μ
=
(
)
34
34 34
2.1 F 87 V
180 C
V
=
Finally, consider the original circuit (Figure 24.59g).
343
4
180 C
QQQ
== =
capacitors in series have the same charge
Figure 24.59g
3
3
3
180 C
43 V
4.2 F
Q
V
C
=
4
4
4
180 C
43 V
4.2 F
Q
V
C
=
Summary:
11
550 C,
65 V
QV
370 C,
87 V
33
180 C,
43 V
44
180 C,
43 V
55
550 C,
65 V
EVALUATE:
342
125
and
220 V
VVV
+=
++=
(apart from some small rounding error)
123
524
and
=+
24.60.
IDENTIFY:
Apply the rules for combining capacitors in series and in parallel.
SET UP:
With the switch open each pair of 3.00 F
and 6.00 F
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
and 6.00 F
capacitors are in
parallel with each other and the two pairs are in series.
EXECUTE:
(a)
With the switch open
eq
4.00 F
3F 6F
3
F 6F
C
μμ
−−
⎛⎞
+
+
=
⎜⎟
⎝⎠
.
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 Spring '06
 Buchler
 Physics, Work

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