7.21 Obtain the resonant frequency and Q-factor of a series LCR circuit with = 3.0 H, = 27µF, and = 7.4 . It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.

 

Given,

Inductance, 𝐿 = 3 H

Capacitance, 𝐶 = 27 μF

Resistance, 𝑅 = 7.4 Ω

Resonant frequency,

ωr=1LC=13×27×106=111rads1Q factor of the circuit, Q=ωrLR=111×37.4=45

For improvement in sharpness of resonance by a factor of 2, 𝑄𝑄 should be doubled. To double 𝑄 without changing frequency 𝑅𝑅 should be reduced to half, i.e., to
3.7 Ω.