Midterm2 - Version 023 Midterm 02 Yao (59110) 1 This...

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Unformatted text preview: Version 023 Midterm 02 Yao (59110) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points If the plate separation of an isolated parallel plate capacitor is doubled, 1. the potential difference is halved. 2. None of these correct 3. the electric field is doubled. 4. the charge on the each plate is halved. 5. the charge density on each plate is dou- bled. Explanation: Q and A are constant, so E = Q A = constant so that E = 2 Q 2 A and V = Q C = 2 Q C = 2 Q C = 2 V . 002 (part 1 of 2) 10.0 points Consider the system of capacitors connected to a battery as shown below. E B 3 F 3 F 3 F 3 F 3 F 3 F Find the equivalent capacitance of the cir- cuit. 1. C = 4 F 2. C = 3 2 F 3. C = 4 3 F 4. C = 3 F 5. C = 2 F correct 6. C = 1 F 7. C = 2 3 F Explanation: E B C 1 C 2 C 3 C 4 C 5 C 6 c a b c d Let : C 1 = C = 3 F , C 2 = C = 3 F , C 3 = C = 3 F , C 4 = C = 3 F , C 5 = C = 3 F , C 6 = C = 3 F , and E B = 6 V . The basic formulae are C eq = 1 1 C 1 + 1 C 2 , connected in series; C 1 + C 2 , connected parallel. So the equivalent capacitance is C ad = 1 1 C + C + 1 C + C + 1 C + C Version 023 Midterm 02 Yao (59110) 2 = 1 1 2 C + 1 2 C + 1 2 C = 2 3 C = 2 3 (3 F) = 2 F . 003 (part 2 of 2) 10.0 points What potential difference E B must be ap- plied across the capacitor network so that the charge on each plate of each capacitor will have magnitude of 6 C? 1. V ad = 8 V 2. V ad = 6 V correct 3. V ad = 4 3 V 4. V ad = 3 V 5. V ad = 3 2 V 6. V ad = 2 3 V 7. V ad = 4 V 8. V ad = 2 V Explanation: Let : Q = 6 C . Regard the system as an equivalent capacitor with the capacitance C ad = 2 F. The charge on each parallel set of capacitors is the sum of the charges on each of the capacitors ( i.e. , Q 12 = Q 34 = Q 56 = 12 C). The charge on a series set of capacitors is the same ( i.e. , Q total = 12 C). Thus the potential difference between a and d is V ad = Q total C ad = 12 C 2 F = 6 V . 004 10.0 points Consider an RC circuit i C R S E where a battery, a resistor and a capacitor are in series. As the switch is closed, at any instant the current at any part of the circuit is the same. Set the time when we close the switch to t = 0. After the switch is closed the current de- creases exponentially with time according to I ( t ) = I e t/ where I is the initial current at t = 0, and is a constant having dimen- sions of time. Consider a fixed observation point within the conductor. How much charge Q ( ) passes this point between t = 0 and t = ? Notice: The same amount of charge is deposited onto the capacitor plate....
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This note was uploaded on 11/11/2009 for the course PHY 59110 taught by Professor Yao during the Spring '09 term at University of Texas at Austin.

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Midterm2 - Version 023 Midterm 02 Yao (59110) 1 This...

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