Question

In the circuit given below, the resonant frequency is _______________

(a) \(\frac{1}{2\sqrt{2} π}\) Hz

(b) \(\frac{1}{2π}\) Hz

(c) \(\frac{1}{4π}\) Hz

(d) \(\frac{1}{\sqrt{2}2π}\) Hz

I have been asked this question during an interview for a job.

This interesting question is from Problems Involving Dot Conventions topic in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct answer is (c) \(\frac{1}{4π}\) Hz

To explain I would say: IEQ = L1 + L2 + 2M

LEQ = 1 + 2 + 2 × \(\frac{1}{2}\) = 4 H

∴ FO = \(\frac{1}{2π\sqrt{LC}} \)

= \(\frac{1}{2π\sqrt{4 × 1}} \)

= \(\frac{1}{4π}\) Hz.