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MIDTERM 2 - Version 034/AACAC midterm 02 Turner(59130 This...

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Version 034/AACAC – midterm 02 – Turner – (59130) 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 A parallel-plate capacitor has 2 . 03 cm 2 plates that are separated by 5 . 74 mm with air be- tween them. The permittivity of a vacuum is 8 . 85419 × 10 12 C 2 / N · m 2 . If a 5 . 7 V battery is connected to this ca- pacitor, how much energy does it store? 1. 2.43599e-11 2. 1.91821e-11 3. 1.07309e-11 4. 1.00126e-10 5. 1.42845e-11 6. 5.36657e-12 7. 2.47153e-11 8. 1.16781e-11 9. 1.81619e-11 10. 5.08689e-12 Correct answer: 5 . 08689 × 10 12 J. Explanation: Let : A = 2 . 03 cm 2 = 0 . 000203 m 2 , d = 5 . 74 mm = 0 . 00574 m , V = 5 . 7 V , and ǫ 0 = 8 . 85419 × 10 12 C 2 / N · m 2 . The capacitance is C = ǫ 0 A d , and the stored energy is W = 1 2 C V 2 = ǫ 0 A V 2 2 d = (8 . 85419 × 10 12 C 2 / N · m 2 ) × (0 . 000203 m 2 ) (5 . 7 V) 2 2 (0 . 00574 m) = 5 . 08689 × 10 12 J . 002 (part 1 of 2) 10.0 points Consider the system of capacitors connected to a battery as shown below. E B 3 μ F 3 μ F 3 μ F 3 μ F 3 μ F 3 μ F Find the equivalent capacitance of the cir- cuit. 1. C = 4 3 μ F 2. C = 3 2 μ F 3. C = 2 μ F correct 4. C = 4 μ F 5. C = 2 3 μ F 6. C = 3 μ F 7. C = 1 μ 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 μ F ,
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Version 034/AACAC – midterm 02 – Turner – (59130) 2 C 2 = C = 3 μ F , C 3 = C = 3 μ F , C 4 = C = 3 μ F , C 5 = C = 3 μ F , C 6 = C = 3 μ 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 = 1 1 2 C + 1 2 C + 1 2 C = 2 3 C = 2 3 (3 μ F) = 2 μ 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 μ C? 1. V ad = 4 3 V 2. V ad = 3 2 V 3. V ad = 3 V 4. V ad = 8 V 5. V ad = 2 3 V 6. V ad = 4 V 7. V ad = 2 V 8. V ad = 6 V correct Explanation: Let : Q = 6 μ C . Regard the system as an equivalent capacitor with the capacitance C ad = 2 μ 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 μ C). The charge on a series set of capacitors is the same ( i.e. , Q total = 12 μ C). Thus the potential difference between a and d is V ad = Q total C ad = 12 μ C 2 μ 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 0 e t/τ where I 0 is the initial current at t = 0, and τ is a constant having dimen- sions of time. Consider a fixed observation point within the conductor. How much charge Q ( τ ) passes this point between t = 0 and t = τ ? Notice: The same amount of charge is deposited onto the capacitor plate.
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