Question

Obtain the resonant frequency and Q-factor of a series LCR circuit with `L=3.0H, C=27muF, and R=7.4 Omega`. How will you improve the sharpness of resonance of the circuit by a factor of 2 by reducing its full width at half maximum?

Answer 1

Here, `L = 3.0 H, C = 27 mu F = 27 xx 10^(-6) F, R = 7.4 Omega`
Resonace frequency, `omega_(r) = (1)/(sqrt(LC)) = (1)/(sqrt(LC)) = (1)/(sqrt(3 xx 27 xx 10^(-6))) = (10^(3))/(9) = 111.1 rad s^(-1)`
`Q = (omega_(r) L)/(R ) = (111.1 xx 3)/(7.4) = 45.05`
To reduce full width at half max. by a factor of 2 without changing `omega_(r)` we have to reduce the value of R to
`(R)/(2) = (7.4)/(2) = 3.7 ohm`