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

Explanation

`omega_r = (1)/(sqrtLC) = (1)/(sqrt(3 xx 27 xx 10^(-6) ) = 111 rad//s `
`Q = (X_L)/(R ) = (omega_r L)/ ( R) = (111 xx 3)/(7.4) = 45`
For doubling Q for the same `omega_r` , R should be reduced to half and is equal to `3.7 Omega `