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) \(\frac{1}{2π\sqrt{6}}\) Hz

The question was asked in a national level competition.

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

Answer 1

Right choice is (d) \(\frac{1}{2π\sqrt{6}}\) Hz

To explain: f = \(\frac{1}{2π\sqrt{L_{EQ} C}} \)

Here, LEQ = 2 + 2 + 2 × 1 = 6

So, C = 1 F

FR = \(\frac{1}{2π\sqrt{6 × 1}} = \frac{1}{2π\sqrt{6}}\) Hz.