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

`f_(0) = ( 1)/( 2pi sqrt( LC))`
`= ( 1)/( 2 xx 3.14 xx sqrt( 3 xx 27 xx 10^(-6)))`
= 17.69 Hz
Q-factor `= ( 1)/( R ) sqrt(( L )/( C ))`
`= ( 1)/( 7.4) sqrt(( 3)/( 27 xx 10^(-6)))`
= 45.04
Q-factor gives measure of sharpness of resonance curve. Henc ein order to double the sharpness,we should make Q-factor doubled. For this , we can make resistance, half of previous value i.e., we should make R = `3.7 Omega` instead of `7.4 Omega`.