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# Midterm2 - Version 023 Midterm 02 Yao(59110 This print-out...

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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 ǫ 0 = constant so that E = 2 Q 2 A ǫ 0 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 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 μ F 2. C = 3 2 μ F 3. C = 4 3 μ F 4. C = 3 μ F 5. C = 2 μ F correct 6. C = 1 μ F 7. C = 2 3 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 , 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

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Version 023 – Midterm 02 – Yao – (59110) 3 Explanation: Current is Q t , where Q is the charge and t is the time. In differential form this gives I ( t ) = dQ dt , which can be integrated as follows Q ( t ) = integraldisplay t 0 I dt = I 0 integraldisplay t 0 e t/τ dt = I 0 τ (1 e t/τ ) and Q ( τ ) = I 0 τ (1 e 1 ) = 0 . 632 I 0 τ .

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