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Unformatted text preview: 9c C1 , C5 and C234 are in series and can be replaced by Ceq (Figure 24.59d): 1 1 1 1 #0 0 Ceq C1 C5 C234 1 2 1 # 0 Ceq 8.4 $ F 6.3 $ F Ceq # 2.5 $ F 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. Qeq # CeqV Qeq # . 2.5 $ F / . 220 V / # 550 $ C Figure 24.59e Q1 # Q5 # Q234 # 550 $ C (capacitors in series have same charge) V1 # Q1 550 $ C # # 65 V C1 8.4 $ F V5 # Q5 550 $ C # # 65 V C5 8.4 $ F V234 # Q234 550 $ C # # 87 V C234 6.3 $ F Capacitance and Dielectrics 24-17 Now draw the network as in Figure 24.59f. V2 # V34 # V234 # 87 V capacitors in parallel have the same potential Figure 24.59f Q2 # C2V2 # . 4.2 $ F /. 87 V / # 370 $ C Q34 # C34V34 # . 2.1 $ F /. 87 V / # 180 $ C Finally, consider the original circuit (Figure 24.59g). Q3 # Q4 # Q34 # 180 $ C capacitors in series have the same charge Figure 24.59g V3 # Q3 180 $ C # # 43 V C3 4.2 $ F V4 # Q4 180 $ C # # 43 V C4 4.2 $ F Summary: Q1 # 550 $ C, V1 # 65 V Q2 # 370 $ C, V2 # 87 V Q3 # 180 $ C, V3 # 43 V Q4 # 180 $ C, V4 # 43 V Q5 # 550 $ C, V5 # 65 V EVALUATE:! V3 0 V4 # V2 and V1 0 V2 0 V5 # 220 V (apart from some small rounding error) 24.60. Q1 # Q2 0 Q3 and Q5 # Q2 0 Q4 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. !1 !1 %% & % && EXECUTE:! (a) With the switch open Ceq...
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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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