Question

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/s

This 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 1

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.