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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) \(\frac{1}{2π\sqrt{6}}\) HzThe 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»

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.



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