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

Explanation

Resonant frequency is given by
`f_(0)=(1)/(2 pi sqrt(LC)) =(1)/(2 pi sqrt(3xx27xx10^(-6)))=17.68 Hz`
Q-factor is given by: `Q=1/R sqrt((L)/(C )) 1/(7.4) sqrt((3)/(27xx10^(-6)))=45`
we know that Q-factor is also given by `Q=(omega_(0))/(2 Delta omega)=(omega_(0))/(omega_(2)-omega_(1))`
Where bandwidth `=(omega_2)-(omega_1)=(R )/(L)`
Now Q-factor can be improved by decreasing bandwidth which in turn can be decreased by decreasing R. So sharpness or Q-factor can be made twice by making the value of R half, i.e. `3.7 Omega`.