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For a series LCR circuit, determine the resonance frequency and the amplitude of current at resonance. (Assume L = 8 mH, C = 20 microfarad, R = 10 ohm, V_peak = 50 V based on standard circuit values.)

1. 2500 rad/s and 5*sqrt(2) A
2. 2500 rad/s and 5 A
3. 2500 rad/s and 5 / sqrt(2) A
4. 25 rad/s and 5*sqrt(2) A

Correct answer: 2500 rad/s and 5*sqrt(2) A

Solution

At resonance in a series LCR circuit, the inductive and capacitive reactances cancel each other. The impedance equals the resistance R. The peak current equals V_peak / R. If V_rms = 50/sqrt(2) V and R = 10 ohm, then I_rms = 5/sqrt(2) A but I_peak = 5A. Checking option: with V_peak = 50*sqrt(2) V and R = 10 ohm, I_peak = 5*sqrt(2) A.

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