47138_EX2 - Version 086 – EX2 – ditmire –(58335 1...

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Unformatted text preview: Version 086 – EX2 – ditmire – (58335) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The current in a resistor decreases by 3 . 5 A when the voltage applied across the resistor decreases from 15 . 9 V to 5 . 29 V. Find the resistance of the resistor. 1. 4.15917 2. 3.03143 3. 2.97519 4. 1.84091 5. 4.48551 6. 2.30201 7. 8.60588 8. 2.77591 9. 4.6943 10. 2.44527 Correct answer: 3 . 03143 Ω. Explanation: Let : Δ I = 3 . 5 A , V i = 15 . 9 V , and V f = 5 . 29 V . V = I R Call the initial voltage and current V i and I , respectively, and the final voltage and current V f and ( I − Δ I ), respectively. R = V I = V i I = V f I − Δ I V i ( I − Δ I ) = V f I ( V i − V f ) I = V i Δ I V i I = V i − V f Δ I , so R = V i I = V i − V f Δ I = 15 . 9 V − 5 . 29 V 3 . 5 A = 3 . 03143 Ω . 002 10.0 points The figure below shows a cylindrical coaxial cable of radii a , b , and c in which equal, uni- formly distributed, but antiparallel currents i exist in the two conductors. O i out ⊙ i in ⊗ F E D C r 1 r 2 r 3 r 4 c b a Which expression gives the magnitude B ( r 3 ) at D of the magnetic field in the re- gion b < r 3 < a ? 1. B ( r 3 ) = μ i ( a 2 − b 2 ) 2 π r 3 ( r 2 3 − b 2 ) 2. B ( r 3 ) = μ i ( r 2 3 − b 2 ) 2 π r 3 ( a 2 − b 2 ) 3. B ( r 3 ) = μ ir 3 2 π a 2 4. B ( r 3 ) = μ i ( a 2 − r 2 3 ) 2 π r 3 ( a 2 − b 2 ) correct 5. B ( r 3 ) = μ i ( a 2 + r 2 3 − 2 b 2 ) 2 π r 3 ( a 2 − b 2 ) 6. B ( r 3 ) = μ ir 3 2 π b 2 7. B ( r 3 ) = μ i 2 π r 3 8. B ( r 3 ) = μ i π r 3 9. B ( r 3 ) = 0 10. B ( r 3 ) = μ ir 3 2 π c 2 Explanation: Ampere’s Law states that the line inte- gral contintegraldisplay vector B · d vector ℓ around any closed path equals Version 086 – EX2 – ditmire – (58335) 2 μ I , where I is the total steady current pass- ing through any surface bounded by the closed path. Considering the symmetry of this problem, we choose a circular path, so Ampere’s Law simplifies to B (2 π r 3 ) = μ I en , where r 3 is the radius of the circle and I en is the current enclosed. Since A en A cylinder = π ( r 2 3 − b 2 ) π ( a 2 − b 2 ) , when b < r 3 < a for the cylinder, B = μ I en 2 π r 3 = μ bracketleftbigg i − i π ( r 2 3 − b 2 ) π ( a 2 − b 2 ) bracketrightbigg 2 π r 3 = μ i parenleftbigg a 2 − r 2 3 a 2 − b 2 parenrightbigg 2 π r 3 = μ i ( a 2 − r 2 3 ) 2 π r 3 ( a 2 − b 2 ) . 003 10.0 points A conductor consists of an infinite number of adjacent wires, each infinitely long and carrying a current I (whose direction is out-of- the-page), thus forming a conducting plane....
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47138_EX2 - Version 086 – EX2 – ditmire –(58335 1...

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