A 440 V, 50 HZ AC source supplies a series LCR circuit with a capacitor and a coil. If the coil has 100 mΩ resistance and 15 mH inductance, then at a resonance frequency of 50 Hz, the half power frequencies of the circuit are?(a) 50.53 Hz, 49.57 Hz(b) 52.12 HZ, 49.8 Hz(c) 55.02 Hz, 48.95 Hz(d) 50 HZ, 49 HzThis question was addressed to me in an interview.My enquiry is from Problems of Series Resonance Involving Frequency Response of Series Resonant Circuit in division Resonance & Magnetically Coupled Circuit of Network Theory

A 440 V, 50 HZ AC source supplies a series LCR circuit with a capacito

1.	A 440 V, 50 HZ AC source supplies a series LCR circuit with a capacitor and a coil. If the coil has 100 mΩ resistance and 15 mH inductance, then at a resonance frequency of 50 Hz, the half power frequencies of the circuit are?(a) 50.53 Hz, 49.57 Hz(b) 52.12 HZ, 49.8 Hz(c) 55.02 Hz, 48.95 Hz(d) 50 HZ, 49 HzThis question was addressed to me in an interview.My enquiry is from Problems of Series Resonance Involving Frequency Response of Series Resonant Circuit in division Resonance & Magnetically Coupled Circuit of Network Theory
Answer» Correct option is (a) 50.53 HZ, 49.57 Hz Explanation: Bandwidth, BW = \(\FRAC{f_o}{Q} = \frac{50}{47.115}\) = 1.061 Hz f2, higher half power frequency = f0 + \(\frac{BW}{2}\) ∴ f2 = 50 + \(\frac{1.061}{2}\) =50.53 Hz F1, lower half power frequency = f0 – \(\frac{BW}{2}\) ∴ f1 = 100 – \(\frac{1.59}{2}\) = 49.47 Hz.

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