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# Test - Kapoor(mk9499 oldmidterm 02 Turner(60230 This...

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Kapoor (mk9499) – oldmidterm 02 – Turner – (60230) 1 This print-out should have 21 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. 18 . 2 V 4 . 44 μ F 5 . 5 μ F 13 . 6 μ F a b What is the voltage across the 5 . 5 μ F upper right-hand capacitor? Correct answer: 8 . 12958 V. Explanation: Let : C 1 = 4 . 44 μ F , C 2 = 5 . 5 μ F , C 3 = 13 . 6 μ F , and V = 18 . 2 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 = (18 . 2 V)(4 . 44 μ F) 4 . 44 μ F + 5 . 5 μ F = 8 . 12958 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 π ǫ 0 r 2 2. E = λ 2 π ǫ 0 r 2 3. E = Q π ǫ 0 r 4. E = Q 4 π ǫ 0 r 5. E = Q π ǫ 0 r 2 6. E = λ π ǫ 0 r 7. E = λ 4 π ǫ 0 r 8. E = Q 2 π ǫ 0 r 2 9. E = Q 2 π ǫ 0 r 10. E = λ 2 π ǫ 0 r correct Explanation: The electric field of a cylindrical capacitor is given by E = λ 2 π r ǫ 0 .

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Kapoor (mk9499) – oldmidterm 02 – Turner – (60230) 2 003 (part 2 of 2) 10.0 points What is the capacitance C of this coaxial cable? 1. C = 2 k e ln parenleftBig a b parenrightBig 2. C = 2 k e ln parenleftbigg b a parenrightbigg correct 3. C = k e ln parenleftbigg b a parenrightbigg 4. C = 2 k e ln parenleftbigg b a parenrightbigg 5. C = k e ln parenleftbigg b a parenrightbigg 6. C = k e ln parenleftBig a b parenrightBig 7. C = k e 8. C = k e 2 ln parenleftbigg b a parenrightbigg 9. C = 2 k e 10. C = ℓ a 2 k e b Explanation: C = 2 k e ln parenleftbigg b a parenrightbigg . 004 (part 1 of 4) 10.0 points Four capacitors are connected as shown in the figure. 17 . 5 μ F 55 . 3 μ F 33 . 1 μ F 73 . 1 μ F 93 . 4 V a b c d Find the capacitance between points a and b of the entire capacitor network. Correct answer: 111 . 306 μ F. Explanation: Let : C 1 = 17 . 5 μ F , C 2 = 33 . 1 μ F , C 3 = 55 . 3 μ F , C 4 = 73 . 1 μ F , and E = 93 . 4 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. 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
Kapoor (mk9499) – oldmidterm 02 – Turner – (60230) 3 = (33 . 1 μ F) (55 . 3 μ F) 33 . 1 μ F + 55 . 3 μ F = 20 . 7062 μ F . The total capacitance C ab between a and b can be obtained by calculating the capacitance in the parallel combination of the capacitors C 1 , C 4 , and C 23 ; i.e. , C ab = C 1 + C 4 + C 23 = 17 . 5 μ F + 73 . 1 μ F + 20 . 7062 μ F = 111 . 306 μ F .

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Test - Kapoor(mk9499 oldmidterm 02 Turner(60230 This...

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