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# s41 - Solutions to Homework#4 Picture the Problem Two...

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Unformatted text preview: Solutions to Homework #4 Chapter 21 66. Picture the Problem : Two capacitors are connected in series, and then a third capacitor is connected in series with the original two. Strategy: Recall the characteristics of circuits containing capacitors connected in series. Solution: 1. (a) The equivalent capacitance of a circuit will decrease each time an additional capacitor is connected in series. 2. (b) The best explanation is III . Adding a capacitor in series decreases the equivalent capacitance since each capacitor now has less voltage across it, and hence stores less charge. Statements I and II are each false. Insight: Another way to understand the effect is to realize that adding another capacitor in series increases the effective separation d between the plates, so that the capacitance C A d ε = decreases. 72. Picture the Problem : Three capacitors are connected together as shown in the diagram at the right, and a battery is connected across terminals A and B. Strategy: The voltage drop across C 1 equals the battery emf, so we can find the energy stored by C 1 by using equation 20-17. To find the energy stored by C 2 and C 3 , we must first find the equivalent capacitance C 23 of the two capacitors using equation 21-17. Then use the battery emf, which is the voltage across C 23 , to find the charge Q stored on both C 2 and C 3 . Finally, use equation 20-18 to find the energy stored in C 2 and C 3 . Solution: 1. Apply equation 20-17 to C 1 : ( 29 ( 29 2 2 6 4 1 1 1 2 2 15 10 F 9.0 V 6.1 10 J 0.61 mJ U CV-- = = = = 2. (b) Combine C 2 and C 3 using equation 21- 17: 1 6 eq 1 1 6.0 F 6.0 10 F 8.2 F 22 F C μ μ μ-- = + = = 3. Find the charge stored on C 2 and C 3 : ( 29 ( 29 6 5 eq 6.0 10 F 9.0 V 5.4 10 C Q C V-- = = = 4. Find the energy stored in C 2 : ( 29 ( 29 2 5 2 4 2 6 5.4 10 C 1.8 10 J 0.18 mJ 2 2 8.2 10 F Q U C--- = = = = 5. Find the energy stored in C 3 : ( 29 ( 29 2 5 2 5 3 6 5.4 10 C 6.6 10 J 66 J 2 2 22 10 F Q U C μ--- = = = = Insight: The three capacitors store a total of 0.86 mJ. Verify for yourself that if all three capacitors were connected in parallel and attached to a 9.0-V battery, they would store a total of 1.8 mJ. The 8.2- µ F capacitor connected in series limits the amount of charge that is stored on the 22- µ F capacitor, reducing its ability to store energy. 80. Picture the Problem : Three RC circuits have the emf, resistance, and capacitance given in the accompanying table. Initially, the switch on the circuit is open and the capacitor is uncharged....
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s41 - Solutions to Homework#4 Picture the Problem Two...

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