Question

For the circuit given below, what is the value of the Q factor for the inductor?

(a) 4.74

(b) 4.472

(c) 4.358

(d) 4.853

I had been asked this question in an international level competition.

The origin of the question is Problems Involving Dot Conventions in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right choice is (c) 4.358

Easiest explanation: QIN = \(\sqrt{\frac{L}{CR^2} – 1}\)

= \(\sqrt{\frac{1}{2 × 5^2  × 10^{-3} – 1}}\)

= \(\sqrt{\frac{1}{50 × 10^{-3} – 1}}\)

= \(\sqrt{19}\) = 4.358.