A series LCR circuit contains a pure inductor of inductance 5.0H, a capacitor of capacitance `20mu F` and a resistor `40Omega`. Find the resonant frequency of the circuit. Calculate the quality factor (Q- factor ) of the circuit. What is the impedance at resonant condition?

Explanation

Resonant frequency :`omega_(0)=(1)/(sqrt(LC))`
`=(1)/(sqrt(5xx20xx10)^(-6))=100 rad s^(-1)`
OR
`f_(o)` or `v_(o)=(1)/(2pi sqrt(LC))`
`=(1)/(2(3.14)sqrt(5xx20xx10^(-6)))=15.9 Hz`
(b)Quality factor :Q=`(omega_(0)L)/(R )` OR `Q=(1)/(omega_(0)RC)`
`Q=(100xx5)/(40)=12.5`
OR
`Q=(1)/(R)sqrt((L)/(C))`
`Q=(1)/(40)sqrt((5)/(20xx10^(-6)))=12.5`
(C )Impedance at resonance :Z=R=40 `Omega`