tsl342 - (a) How much energy is stored in the capacitor at...

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Intermediate Exam III: Problem #1 (Spring ’05) An infinitely long straight current of magnitude I = 6 A is directed into the plane ( ) and located a distance d = 0 . 4 m from the coordinate origin (somewhere on the dashed circle). The magnetic field ~ B generated by this current is in the negative y -direction as shown. (a) Find the magnitude B of the magnetic field. (b) Mark the location of the position of the current on the dashed circle. y x B 0.4m Solution: (a) B = μ 0 2 π I d = 3 μ T . (b) Position of current is at y = 0 , x = - 0 . 4 m. tsl342 – p.1/4
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Intermediate Exam III: Problem #2 (Spring ’05) In the circuit shown we close the switch S at time t = 0 . Find the current I through the battery and the voltage V L across the inductor (a) immediately after the switch has been closed, (b) a very long time later. 5H 4 2 2 12V Ι S Solution: (a) I = 12V 2Ω + 4Ω + 2Ω = 1 . 5A , V L = (4Ω)(1 . 5A) = 6V . (b) I = 12V 2Ω + 2Ω = 3A , V L = 0 . tsl343 – p.2/4
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Intermediate Exam III: Problem #3 (Spring ’05) At time t = 0 the capacitor is charged to Q max = 3 μ C and the current is instantaneously zero.
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Unformatted text preview: (a) How much energy is stored in the capacitor at time t = 0 ? (b) At what time t 1 does the current reach its maximum value? (c) How much energy is stored in the inductor at time t 1 ? L = 40mH C = 9 μ F Solution: (a) U C = Q 2 max 2 C = 0 . 5 μ J . (b) T = 2 π ω = 2 π √ LC = 3 . 77ms , t 1 = T 4 = 0 . 942ms . (c) U L = U C = 0 . 5 μ J (energy conservation.) tsl344 – p.3/4 Intermediate Exam III: Problem #4 (Spring ’05) Consider the circuit shown. The ac voltage supplied is E = E max cos( ωt ) with E max = 170 V and ω = 377 rad/s. (a) What is the maximum value I max of the current? (b) What is the emf E ( t ) at t = 0 . 01 s? (c) What is the current I ( t ) at t = 0 . 01 s? ~ 16 μ F . Solution: (a) I max = E max X C = E max ωC = 1 . 03A . (b) E = (170V) cos(3 . 77rad) = (170V)(-. 809) =-138V . (c) I = E max ωC cos(3 . 77rad + π/ 2) = (1 . 03A)(0 . 588) = 0 . 605A . tsl345 – p.4/4...
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This note was uploaded on 04/30/2008 for the course PHYS 204 taught by Professor Andrevantonder during the Spring '07 term at Rhode Island.

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tsl342 - (a) How much energy is stored in the capacitor at...

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