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?

Explanation

Inductance, L=3.0H
Capacitance, C=27`muF`=27`xx10^(-6) F`
Resistance, R=`7.4Omega`
at resonance, angular frequency of the source for the given LCR series circuit is given as:
`omega_(r)=(1)/sqrt(LC)`
`=(1)/sqrt(3xx27xx10^(-6))=(10^(3))/(9)=111.11` rad `s^(-1)`
Q-factor of the series:
`Q=(omega_(r)L)/(R)`
`=(111.11xx3)/(7.4)=45.446`
To improve the sharpness of the resonance by reduc ing its full width at half maximum. by a factor of 2 wihtout changing `omega_(r)`, we need to reduce R to half i.e.,
`(R)/(2)=(7.4)/(2)=3.7Omega`
Resistance