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Unformatted text preview: benavides (jjb2356) oldmidterm 04 Turner (59130) 1 This printout should have 18 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points In a series RLC AC circuit, the resistance is 24 , the inductance is 15 mH, and the capac itance is 20 F. The maximum potential is 162 V, and the angular frequency is 100 rad / s. Calculate the maximum current in the cir cuit. Correct answer: 0 . 324599 A. Explanation: Let : R = 24 , L = 15 mH = 0 . 015 H , C = 20 F = 2 10 5 F , V max = 162 V , and = 100 rad / s . The capacitive reactance is X C = 1 C = 1 (100 rad / s) (2 10 5 F) = 500 and the inductive reactance is X L = L = (100 rad / s) (0 . 015 H) = 1 . 5 , so the maximum current is I max = V max Z = V max radicalbig R 2 + ( X L X C ) 2 = 162 V radicalbig (24 ) 2 + (1 . 5 500 ) 2 = . 324599 A . 002 10.0 points A certain capacitor in a circuit has a capaci tive reactance of 42 . 7 when the frequency is 150 Hz. What capacitive reactance does the capac itor have at a frequency of 10900 Hz? Correct answer: 0 . 587615 . Explanation: Let : X C = 42 . 7 , f low = 150 Hz , and f high = 10900 Hz . The capacitive reactance is X C = C 2 f , so X C ( high ) X C ( low ) = 2 f low C 2 f high C = f low f high . Thus X C ( high ) = X C ( low ) f low f high = (42 . 7 ) parenleftbigg 150 Hz 10900 Hz parenrightbigg = . 587615 . 003 10.0 points A 93 mH inductor is connected to a outlet where the rms voltage is 78 . 9 V and the fre quency is 79 Hz. Determine the energy stored in the inductor at t = 7 . 8 ms, assuming that this energy is zero at t = 0. Correct answer: 0 . 120849 J. Explanation: Let : t = 7 . 8 ms = 0 . 0078 s , f = 79 Hz , L = 93 mH = 0 . 093 H , and V rms = 78 . 9 V . The inductive reactance is X L = L = 2 f L and the maximum current is I max = 2 V rms X L = 2 V rms 2 f L benavides (jjb2356) oldmidterm 04 Turner (59130) 2 The current at time t is I = I max sin( t ) = 2 V rms 2 f L sin(2 f t ) = 2(78 . 9 V) 2 (79 Hz) (0 . 093 H) sin[(2 (79 Hz) (0 . 0078 s)] = 1 . 61211 A , so the potential energy stored in the inductor is U = 1 2 LI 2 = 1 2 (0 . 093 H) ( 1 . 61211 A) 2 = . 120849 J . 004 10.0 points A ideal transformer shown in the figure below having a primary with 40 turns and secondary with 16 turns. The load resistor is 66 . The source voltage is 140 V rms . 140V rms 40turns 16turns 66 What is the rms electric potential across the 66 load resistor?...
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