The frequency for the given circuit when the circuit is in a state of resonance will be?(a) 1 rad/s(b) 2 rad/s(c) 3 rad/s(d) 4 rad/sThis question was addressed to me by my school teacher while I was bunking the class.My query is from Advanced Problems on Resonance in section Resonance & Magnetically Coupled Circuit of Network Theory

The frequency for the given circuit when the circuit is in a state of

1.	The frequency for the given circuit when the circuit is in a state of resonance will be?(a) 1 rad/s(b) 2 rad/s(c) 3 rad/s(d) 4 rad/sThis question was addressed to me by my school teacher while I was bunking the class.My query is from Advanced Problems on Resonance in section Resonance & Magnetically Coupled Circuit of Network Theory
Answer» RIGHT OPTION is (C) 3 rad/s Easy EXPLANATION: Z = jωL + \(\frac{R}{1+jωRC} \) ∴ Z = j0.1ω + \(\frac{1}{1+jω} × \frac{1-jω}{1-jω} \) = j0.1ω + \(\frac{1-jω}{1+ω^2} = \frac{1}{1+ω^2} + j (0.1ω – \frac{ω}{1 + ω^2}) \) At resonance, imaginary part must be zero. 0.1 ω – \(\frac{ω}{ 1+ ω^2}\) = 0 Or, 0.1 = \(\frac{1}{1+ω^2}\) Or, ω^2 + 1 = 10 ∴ ω^2 = 9 Or, ω = 3 rad/s.

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