fall_06_exam3_sol_phy2049

fall_06_exam3_sol_phy2049 - PHY2049 Fall 2006 Prof. Yasu...

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PHY2049 Fall 2006 1 Prof. Yasu Takano P r o f . P a u l A v e r y Nov. 20, 2006 Exam 3 Solutions ( First answer is correct ) 1. ( WebAssign 30.15 ) As shown in the figure, a stiff wire bent into a semicircle of radius 5 cm is rotated at constant frequency 55 Hz in a uniform magnetic field of 2.4 T. The resistance R is 16 Ω . What is the amplitude of the emf (in volts) generated in the circuit? (1) 3.26 (2) 0.52 (3) 0.41 (4) 0.20 (5) 6.51 The emf is given by Faraday’s law / B dd t = Φ E . The semicircular area is 2 1 2 r π and, taking into account the rotation of the semicircle, the total flux is 2 1 2 cos B rt ω Φ= . Taking the deriva- tive yields the emf 2 1 2 sin rB t ωω =− E , so the amplitude of the emf is 2 1 2 3.26 m πω == E V. 2. ( WebAssign 31.43 ) Consider an RLC circuit with a driving emf of amplitude E m = 20 V, R = 25 Ω , L = 0.06 H and C = 2.0 μ F. What is the amplitude of the voltage (in volts) across the induc- tor at resonance? (1) 139 (2) 220 (3) 455 (4) 345 (5) 197 At resonance only R contributes to the impedance, so the current amplitude is 20/ 25 0.8 m I A. The voltage amplitude across the inductor can be found from the inductive reactance to be L Lm m VX I L I . Using 1/ LC = at resonance and substituting values yields 139 V. 3. ( Homework 31.24 ) A single loop circuit has R = 9 Ω , C = 16 μ F and L = 4H. Initially, the ca- pacitor has charge 12 μ C and the current is zero. What is the charge (in μ C) on the capacitor 10 complete cycles later? (1) 6.82 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X R B G
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PHY2049 Fall 2006 2 (2) 2.91 (3) 9.92 (4) 4.77 (5) 5.43
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fall_06_exam3_sol_phy2049 - PHY2049 Fall 2006 Prof. Yasu...

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