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Unformatted text preview: DENTIFY:! Replace series and parallel combinations of capacitors by their equivalents. 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.
(a) SET UP:! The network is sketched in Figure 24.63a. C1 # 6.9 $ F
C2 # 4.6 $ F
Figure 24.63a
EXECUTE:! Simplify the network by replacing the capacitor combinations by their equivalents. Make the
replacement shown in Figure 24.63b. 1
3
#
Ceq C1
Ceq # C1 6.9 $ F
#
# 2.3 $ F
3
3 Figure 24.63b Next make the replacement shown in Figure 24.63c. Ceq # 2.3 $ F 0 C2
Ceq # 2.3 $ F 0 4.6 $ F # 6.9 $ F
Figure 24.63c Make the replacement shown in Figure 24.63d.
1
2
1
3
#0
#
Ceq C1 6.9 $ F 6.9 $ F
Ceq # 2.3 $ F
Figure 24.63d Make the replacement shown in Figure 24.63e.
Ceq # C2 0 2.3 $ F # 4.6 $ F 0 2.3 $ F Ceq # 6.9 $ F
Figure 24.63e Make the replacement shown in Figure 24.63f.
1
2
1
3
#0
#
Ceq C1 6.9 $ F 6.9 $ F
Ceq # 2.3 $ F
Figure 24.63f
(b) Consider the network as drawn in Figure 24.63g. From part (a) 2.3 $ F is the equivalent
capacitance of the rest of the network.
Figure 24.63g 2420 Chapter 24 The equivalent network is shown in Figure 24.63h.
The capacitors are in series,
so all three capacitors have
the same Q.
Figure 24.63h But here all three have the same C, so by V = Q/C all three must have the same V. The three voltages must add
to 420 V, so each capacitor has V = 140 V. The 6.9 $ F to the right is the equivalent of C2 and the 2.3 $ F
capacitor in parallel, so V2 # 140 V. (Capacitors in parallel have the same potential difference.) Hence Q1 # C1V1 # (6.9 $ F)(140 V) # 9.7 " 10!4 C and Q2 # C2V2 # (4.6 $ F)(140 V) # 6.4 " 10!4 C.
(c) From the potentials deduced in part (b) we have the situation shown in Figure 24.63i.
From part (a) 6.9 $ F is the
equivalent capacitance of the
rest of the network. Figure 24.63i 24.64. The three rightmost capacitors are in series and therefore have the same charge. But their capa...
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This document was uploaded on 03/11/2014 for the course PHYSICS 240 at University of Michigan.
 Fall '08
 DaveWinn
 Physics

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