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Unformatted text preview: !1 24.21. 24.22. !1 %d
EXECUTE:! Ceq # ' 1 0 1 ( # ' 1 0 2 ( # 0
. This shows that the combined capacitance for two
C1 C2 *
d1 0 d 2
!0 A !0 A *
capacitors in series is the same as that for a capacitor of area A and separation (d1 0 d 2 ) .
EVALUATE:! Ceq is smaller than either C1 or C2 .
IDENTIFY and SET UP:! C # 0 . For two capacitors in parallel, Ceq # C1 0 C2 .
!0 A1 !0 A2 !0 ( A1 0 A2 )
EXECUTE:! Ceq # C1 0 C2 #
. So the combined capacitance for two capacitors in parallel is
that of a single capacitor of their combined area ( A1 0 A2 ) and common plate separation d.
EVALUATE:! Ceq is larger than either C1 or C2 . IDENTIFY:! Simplify the network by replacing series and parallel combinations of capacitors by their equivalents.
SET UP:! For capacitors in series the voltages add and the charges are the same;
0 % For capacitors
Ceq C1 C2
in parallel the voltages are the same and the charges add; Ceq # C1 0 C2 0 % C # .
EXECUTE:! (a) The equivalent capacitance of the 5.0 $ F and 8.0 $ F capacitors in parallel is 13.0 $ F. When these
two capacitors are replaced by their equivalent we get the network sketched in Figure 24.22. The equivalent
capacitance of these three capacitors in series is 3.47 $ F.
(b) Qtot # CtotV # (3.47 $ F)(50.0 V) # 174 $ C
(c) Qtot is the same as Q for each of the capacitors in the series combination shown in Figure 24.22, so Q for each of
the capacitors is 174 $ C.
EVALUATE:! The voltages across each capacitor in Figure 24.22 are V10 # tot # 17.4 V , V13 # tot # 13.4 V and
# 19.3 V . V10 0 V13 0 V9 # 17.4 V 0 13.4 V 0 19.3 V # 50.1 V . The sum of the voltages equals the applied
voltage, apart from a small difference due to rounding. Figure 24.22 Capacitance and Dielectrics 24.23. 24-7 IDENTIFY:! Refer to Figure 24.10b in the textbook. For capacitors in parallel, Ceq # C1 0 C2 0 %. For capacitors in series, 1
Ceq C1 C2 SET UP:! The 11 $ F , 4 $ F and replacement c...
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This document was uploaded on 03/11/2014 for the course PHYSICS 240 at University of Michigan.
- Fall '08