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?

Obtain the resonant frequency and Q-factor of a series LCR circuit wit

1.	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» 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

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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?

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