Question

In the circuit given below, the resonant frequency is ________________

(a) \(\frac{1}{2π\sqrt{3}}\) Hz

(b) \(\frac{1}{4π\sqrt{3}}\) Hz

(c) \(\frac{1}{4π\sqrt{2}}\) Hz

(d) \(\frac{1}{π\sqrt{2}}\) Hz

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

This intriguing question originated from Advanced Problems on Magnetically Coupled Circuits topic in division Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct choice is (b) \(\frac{1}{4π\sqrt{3}}\) Hz

The explanation is: LEFF = L1 + L2 + 2M

= 2 + 2 + 2 × 1

Or, LEFF = 6 H

At resonance, ωL = \(\frac{1}{ωC}\)

Or, ω = \(\frac{1}{\sqrt{L_{EFF} C}} = \frac{1}{\sqrt{12}}\)

Or, I = \(\frac{1}{4π\sqrt{3}}\) Hz.