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A series LCR circuit contains a pure ind...

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?

Text Solution

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`L= 5H, C= 20 xx 10^(6)F, R= 40 Omega`
Resonant frequency `f_(0)= (1)/(2pi sqrt(LC))`
`f_(0)= (1)/(2 xx 3.14 sqrt(5 xx 20 xx 10^(-6)))`
`f_(0)= 15.91 Hz or 16Hz`
`Q= (1)/(R )sqrt((L)/(C ))= (1)/(40) sqrt((5)/(20 xx 10^(-6))) = 12.5`
Impedance at resonant Z= R
`Z= 40Omega`
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