oldmidterm 02-solutions - marout (ssm979) oldmidterm 02...

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Unformatted text preview: marout (ssm979) oldmidterm 02 turner (56725) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A capacitor network is shown in the following figure. 19 . 7 V 4 . 49 F 5 . 3 F 10 . 8 F a b What is the voltage across the 5 . 3 F upper right-hand capacitor? Correct answer: 9 . 03504 V. Explanation: Let : C 1 = 4 . 49 F , C 2 = 5 . 3 F , C 3 = 10 . 8 F , and V = 19 . 7 V . Since C 1 and C 2 are in series they carry the same charge C 1 V 1 = C 2 V 2 , and their voltages add up to V , voltage of the battery V 1 + V 2 = V C 2 V 2 C 1 + V 2 = V C 2 V 2 + C 1 V 2 = V C 1 V 2 = V C 1 C 1 + C 2 = (19 . 7 V)(4 . 49 F) 4 . 49 F + 5 . 3 F = 9 . 03504 V . 002 (part 1 of 2) 10.0 points A coaxial cable with length has an inner conductor that has a radius a and carries a charge of Q . The surrounding conductor has an inner radius b and a charge of- Q . Assume the region between the conductors is air. The linear charge density Q . radius = a + Q radius = b- Q b What is the electric field halfway between the conductors? 1. E = 2 r 2 2. E = Q 4 r 3. E = Q 2 r 4. E = Q 2 r 2 5. E = r 2 6. E = r 7. E = Q r 2 8. E = 2 r correct 9. E = Q r 10. E = 4 r Explanation: Apply Gauss Law to a cylindrical surface of radius r and length , to obtain 2 r E = marout (ssm979) oldmidterm 02 turner (56725) 2 E = 2 r . 003 (part 2 of 2) 10.0 points What is the capacitance C of this coaxial cable? 1. C = 2 k e 2. C = 2 k e ln parenleftbigg b a parenrightbigg correct 3. C = k e ln parenleftbigg b a parenrightbigg 4. C = a 2 k e b 5. C = 2 k e ln parenleftbigg b a parenrightbigg 6. C = k e ln parenleftBig a b parenrightBig 7. C = k e 8. C = k e ln parenleftbigg b a parenrightbigg 9. C = k e 2 ln parenleftbigg b a parenrightbigg 10. C = 2 k e ln parenleftBig a b parenrightBig Explanation: First recall that k e = 1 4 so E = 2 k e r which we can integrate along a radial path from a to b to get the voltage difference, V =- integraldisplay b a E dr = 2 k e integraldisplay a b dr r = 2 k e ln r vextendsingle vextendsingle vextendsingle a b = 2 k e ln parenleftbigg b a parenrightbigg then C = Q V = V = 2 k e ln parenleftbigg b a parenrightbigg . keywords: 004 (part 1 of 4) 10.0 points Four capacitors are connected as shown in the figure. 1 3 F 68 . 8 F 31 . 6 F 7 8 . 1 F 94 . 6 V a b c d Find the capacitance between points a and b of the entire capacitor network....
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oldmidterm 02-solutions - marout (ssm979) oldmidterm 02...

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