# OMT 02 - terry(ect328 – oldmidterm 02 – Turner...

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Unformatted text preview: terry (ect328) – oldmidterm 02 – Turner – (59130) 1 This print-out should have 16 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. 11 . 8 V 4 . 3 μ F 4 . 9 μ F 10 . 5 μ F a b What is the voltage across the 4 . 9 μ F upper right-hand capacitor? Correct answer: 5 . 51522 V. Explanation: Let : C 1 = 4 . 3 μ F , C 2 = 4 . 9 μ F , C 3 = 10 . 5 μ F , and V = 11 . 8 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 = (11 . 8 V)(4 . 3 μ F) 4 . 3 μ F + 4 . 9 μ F = 5 . 51522 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 λ ≡ Q . radius = a + Q radius = b- Q What is the electric field halfway between the conductors? 1. E = λ 2 π r 2 2. E = λ π r 3. E = λ π r 2 4. E = Q π r 5. E = λ 2 π r correct 6. E = Q 2 π r 7. E = Q π r 2 8. E = Q 2 π r 2 9. E = Q 4 π r 10. E = λ 4 π r Explanation: Apply Gauss’ Law to a cylindrical surface of radius r and length , to obtain 2 π r E = λ terry (ect328) – oldmidterm 02 – Turner – (59130) 2 E = λ 2 π r . 003 (part 2 of 2) 10.0 points What is the capacitance C of this coaxial cable? 1. C = k e ln b a 2. C = a 2 k e b 3. C = k e ln b a 4. C = k e 5. C = k e 2 ln b a 6. C = k e ln a b 7. C = 2 k e ln b a 8. C = 2 k e 9. C = 2 k e ln b a correct 10. C = 2 k e ln a b Explanation: First recall that k e = 1 4 π so E = 2 k e λ r which we can integrate along a radial path from a to b to get the voltage difference, V =- b a E dr = 2 k e λ a b dr r = 2 k e λ ln r a b = 2 k e λ ln b a then C = Q V = λ V = 2 k e ln b a . keywords: 004 (part 1 of 4) 10.0 points Four capacitors are connected as shown in the figure. 2 6 . 2 μ F 66 . 9 μ F 38 . 5 μ F 8 7 . 5 μ F 92 . 9 V a b c d Find the capacitance between points a and b of the entire capacitor network. Correct answer: 138 . 137 μ F. Explanation: Let : C 1 = 26 . 2 μ F , C 2 = 38 . 5 μ F , C 3 = 66 . 9 μ F , C 4 = 87 . 5 μ F , and E = 92 . 9 V . C 1 C 3 C 2 C 4 E a b c d A good rule of thumb is to eliminate junc- tions connected by zero capacitance. terry (ect328) – oldmidterm 02 – Turner – (59130) 3 C 2 C 3 C 1 C 4 a b The definition of capacitance is C ≡ Q V . The series connection of C 2 and C 3 gives the equivalent capacitance C 23 = 1 1 C 2 + 1 C 3 = C 2 C 3 C 2 + C 3 = (38 . 5 μ F) (66 . 9 μ F) 38 . 5 μ F + 66 . 9 μ F = 24 . 4369 μ F ....
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OMT 02 - terry(ect328 – oldmidterm 02 – Turner...

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