This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 = 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 2017. 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 2117. 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 2018 to find the energy stored in C 2 and C 3 . Solution: 1. Apply equation 2017 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  = + = = 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  = = = = 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 9.0V battery, they would store a total of 1.8 mJ. The 8.2 F capacitor connected in series limits the amount of charge that is stored on the 22 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....
View
Full
Document
This note was uploaded on 02/10/2012 for the course PHY 102 taught by Professor Korotkova during the Spring '09 term at University of Miami.
 Spring '09
 KOROTKOVA
 Physics, Work

Click to edit the document details