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Unformatted text preview: !1 24.21. 24.22. !1 %d !A 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 . !A IDENTIFY and SET UP:! C # 0 . For two capacitors in parallel, Ceq # C1 0 C2 . d !0 A1 !0 A2 !0 ( A1 0 A2 ) EXECUTE:! Ceq # C1 0 C2 # . So the combined capacitance for two capacitors in parallel is 0 # d d d 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. 1 1 1 SET UP:! For capacitors in series the voltages add and the charges are the same; #0 0 % For capacitors Ceq C1 C2 Q in parallel the voltages are the same and the charges add; Ceq # C1 0 C2 0 % C # . V 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. Q Q EVALUATE:! The voltages across each capacitor in Figure 24.22 are V10 # tot # 17.4 V , V13 # tot # 13.4 V and C10 C13 Qtot V9 # # 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 C9 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 1 1 #0 0 %. 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.

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