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 posed to me in homework.

The query is from Applications of Signals on Circuits topic in chapter Signals and Systems Basics of Signals and Systems

Answer 1

Correct option is (a) 50.53 Hz, 49.57 Hz

To explain I would say: Bandwidth, BW = \(\frac{f_o}{Q} = \frac{50}{47.115}\) = 1.061 Hz

f2, higher half power frequency = f0 + \(\frac{BW}{2}\)

∴ \(f_2 = 50 + \frac{1.061}{2}\) = 50.53 Hz

f1, lower half power frequency = f0 – \(\frac{BW}{2}\)

∴ f1 = 100 – \(\frac{1.59}{2}\) = 49.47 Hz.