Question

A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 50. If R and L are doubled and C is kept same, the new Q of the circuit is ____________

(a) 25.52

(b) 35.35

(c) 45.45

(d) 20.02

The question was asked during an interview for a job.

My question is based upon Applications of Signals on Circuits in portion Signals and Systems Basics of Signals and Systems

Answer 1

Correct choice is (b) 35.35

The explanation: Quality factor Q of the series RLC circuit is given by, \(Q = \frac{1}{R} \sqrt{\frac{L}{C}}\)

Given that Q = 50

Qnew = \(\frac{1}{2R} \sqrt{\frac{2L}{C}}\)

= \(\frac{1}{2} ×  \frac{1}{R} \sqrt{\frac{2L}{C}}\)

= \(\frac{1}{2} × \sqrt{2} × Q \)

= \(\frac{1}{2} × \sqrt{2}\) × 50 = 35.35.