726_PartUniversity Physics Solution

726_PartUniversity Physics Solution - 24-16 Chapter 24...

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24-16 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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Capacitance and Dielectrics 24-17 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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726_PartUniversity Physics Solution - 24-16 Chapter 24...

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