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Unformatted text preview: segovia (cs39966) – Homework 7 – Spurlock – (14441) 1 This printout should have 47 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. NOTE TO CLASS: Some of the wording was a little vague on some problems. So I added some (* comments *) at the top of the problems. It’s probably better if you read the problem and then check the comments. 001 10.0 points The output of a generator is given by v ( t ) = a sin( ω t ) , where a = 119 V. Find the rms current in the circuit when this generator is connected to a 249 Ω resistor. Correct answer: 0 . 337935 A. Explanation: Let : R = 249 Ω , and a = 119 V . The general form for the output voltage is v ( t ) = V max sin( ω t ) , so V max = 119 V . Thus, the rms voltage is V rms = V max √ 2 . Ohm’s law gives us the rms current: I rms = V rms R = V max √ 2 R = 119 V √ 2(249 Ω) = . 337935 A . 002 (part 1 of 2) 10.0 points A 12 μ F capacitor is connected to the termi nals of a 18 Hz generator whose rms voltage is 106 V . Find the capacitive reactance. Correct answer: 736 . 828 Ω. Explanation: Let : C = 12 μ F = 1 . 2 × 10 − 5 F , and f = 18 Hz . The angular frequency is ω = 2 π f , so the capacitive reactance is X C = 1 ω C = 1 2 π f C = 1 2 π (18 Hz) (1 . 2 × 10 − 5 F) = 736 . 828 Ω . 003 (part 2 of 2) 10.0 points Find the rms current in the circuit. Correct answer: 0 . 14386 A. Explanation: Let : V rms = 106 V . The rms current in the circuit is I rms = V rms X C = (106 V) (736 . 828 Ω) = . 14386 A . 004 (part 1 of 2) 10.0 points In a purely inductive circuit, the rms voltage is 148 V. If the rms current is 11 . 5 A at a frequency of 72 . 1 Hz, calculate the inductance. Correct answer: 28 . 4085 mH. Explanation: Let : V = 148 V , and I = 11 . 5 A . segovia (cs39966) – Homework 7 – Spurlock – (14441) 2 The inductive resistance is X L = V I and X L = ω L = 2 π f L. Thus, V I = 2 π f suppressL L = X L 2 π f = 12 . 8696 Ω 2 π (72 . 1 Hz) · 10 3 mH 1 H = 28 . 4085 mH . 005 (part 2 of 2) 10.0 points At what frequency is the rms current 3 . 2 A? Correct answer: 259 . 109 Hz. Explanation: Let : I l = 11 . 5 A , f l = 72 . 1 Hz , and I h = 3 . 2 A . The current is I = V X L , so I h I l = V X L ( l ) V X L ( h ) = 2 π f l L 2 π f h L = f l f h . Thus the frequency at rms current is f h = I l f l I h = (11 . 5 A)(72 . 1 Hz) 3 . 2 A = 259 . 109 Hz . 006 10.0 points (* Please note that in this question, ”impedance” refers to the magnitude of the impedance. *) A coil has a DC resistance of 90 Ω and an impedance of 180 Ω at a frequency of 1 kHz. Neglect the wiring capacitance of the coil at this frequency. What is the inductance of the coil?...
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 Fall '11
 HOFFMAN
 Work, Alternating Current, Correct Answer, Inductor, Electrical resistance, Spurlock, Segovia

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