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Unformatted text preview: benavides (jjb2356) homework 12 Turner (59130) 1 This printout should have 12 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points A parallelplate capacitor of dimensions 1 . 91 cm 5 . 28 cm is separated by a 1 . 89 mm thickness of paper. Find the capacitance of this device. The dielectric constant for paper is 3.7. Correct answer: 17 . 4806 pF. Explanation: Let : = 3 . 7 , d = 1 . 89 mm = 0 . 00189 m , and A = 1 . 91 cm 5 . 28 cm = 0 . 00100848 m 2 . We apply the equation for the capacitance of a parallelplate capacitor and find C = A d = (3 . 7) (8 . 85419 10 12 C 2 / N m 2 ) parenleftbigg . 00100848 m 2 . 00189 m parenrightbigg 1 10 12 pF 1 F = 17 . 4806 pF . 002 (part 2 of 2) 10.0 points What is the maximum charge that can be placed on the capacitor? The electric strength of paper is 1 . 6 10 7 V / m. Correct answer: 0 . 528613 c. Explanation: Let : E max = 1 . 6 10 7 V / m . Since the thickness of the paper is 0 . 00189 m, the maximum voltage that can be applied before breakdown is V max = E max d. Hence, the maximum charge is Q max = C V max = C E max d = (17 . 4806 pF)(30240 V) 1 10 12 F 1 pF 1 10 6 C 1 C = . 528613 c . 003 (part 1 of 4) 10.0 points Determine the total energy stored in a con ducting sphere with charge Q . Hint: Use the capacitance formula for a spherical capacitor which consists of two spherical shells. Take the inner sphere to have a radius a and the outer shell to have an infinite radius. 1. U = Q 2 16 a 2. U = Q 2 8 a correct 3. U = Q 2 4 a 4. U = Q 2 a 4 5. U = Q 2 a 6. U = Q 8 a 7. U = Q 2 8 a 8. U = Q 2 8 a 2 Explanation: The capacitance formula for a spherical ca pacitor of inner radius a and outer radius b is C = ab k e ( b a ) . If we let b , we find we can neglect a in the denominator compared to b , so C a k e = 4 a....
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 Spring '08
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