homework 6 - montes(dam2772 Homework6 shih(56310 This...

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montes (dam2772) – Homework6 – shih – (56310) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001(part1of4)10.0points A series RLC circuit has resistance 6 Ω, in- ductance 1 . 7 mH, and capacitance 2 . 1 μ F. Determine the impedance at 45 Hz Correct answer: 1683 . 71 Ω. Explanation: Let : f = 45 Hz , R = 6 Ω , L = 1 . 7 mH = 0 . 0017 H , and C = 2 . 1 μ F = 2 . 1 × 10 6 F . The angular frequency is ω = 2 π f = 282 . 743 rad / s . The impedance is Z = radicalBig R 2 + ( X L - X C ) 2 = radicalBigg R 2 + parenleftbigg ω L - 1 ω C parenrightbigg 2 = braceleftbigg (6 Ω) 2 + bracketleftbigg (282 . 743 rad / s) (0 . 0017 H) - 1 (282 . 743 rad / s) (2 . 1 × 10 6 F) bracketrightbigg 2 bracerightbigg 1 / 2 = 1683 . 71 Ω . 002(part2of4)10.0points Determine the resonant frequency in kHz. Correct answer: 2 . 6637 kHz. Explanation: The frequency at resonance is f 0 = 1 2 π radicalbigg 1 L C = 1 2 π radicalBigg 1 (0 . 0017 H) (2 . 1 × 10 6 F) 1 kHz 1000 Hz = 2 . 6637 kHz . 003(part3of4)10.0points Determine the impedance at resonance. Correct answer: 6 Ω. Explanation: At resonance Z = R = 6 Ω . 004(part4of4)10.0points Determine the impedance at a frequency equal to one-half the resonant frequency. Correct answer: 43 . 0979 Ω. Explanation: The angular frequency is ω = 1 2 radicalbigg 1 L C = 1 2 radicalBigg 1 (0 . 0017 H) (2 . 1 × 10 6 F) = 8368 . 27 rad / s . The impedance is Z = radicalBig R 2 + ( X L - X C ) 2 = radicalBigg R 2 + parenleftbigg ω L - 1 ω C parenrightbigg 2 = braceleftbigg (6 Ω) 2 + bracketleftbigg (8368 . 27 rad / s) (0 . 0017 H) - 1 (8368 . 27 rad / s) (2 . 1 × 10 6 F) bracketrightbigg 2 bracerightbigg 1 / 2 = 43 . 0979 Ω .
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montes (dam2772) – Homework6 – shih – (56310) 2 005(part1of2)10.0points A particular inductor has appreciable resis- tance. When the inductor is connected to a 19 . 3 V battery, the current in the inductor is 3 . 93 A. When it is connected to AC source with an rms output of 19 . 3 V and a frequency of 58 Hz, the current drops to 1 . 8 A. Find the impedance at 58 Hz. Correct answer: 10 . 7222 Ω. Explanation: Let : Δ V rms = 19 . 3 V and I rms = 1 . 8 A .
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