Question

Obtain the resonant frequency and Q- factor of a series LCR circuit with
L - 3.0 H, C = 27 (a F, and R = 7.4 Ω 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.

Answer 1

R = 7.4 Ω

L = 3H

C = 27 μF = 27 x 10^-6 F

The resonant angular frequency ω₀ is given by

The simplest way to improve the sharpness of the resonance of the circuit is by reducing its full width at half maximum by a factor of 2 is to reduce the value of R to \(\frac{R}{2}\) i.e. by making
\(R = \frac{7.4}{2}= 3.7\Omega\)