Question

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 Hz

This 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 1

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.