Question

Obtain the resonant frequency and Q – factor of a series LCR circuit with L = 3H, C = 27F, R = 7.4Ω. It is desired to improve the sharpness of resonance of circuit by reducing its full width at half maximum by a factor of 2. Suggest a suitable way

Answer 1

∵ resonant frequency for LCR circuit is given by = v₀ = 1/(2π√(LC)

= 1/ [2 x 3.14√(3 x 27 x 10^-6)]

= 17.69 Hz 

To improve sharpness of resonance circuit by a factor 2, without reducing ω₀ ; reduce R to half of its value i.e. R = 3.7Ω