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Obtain the resonant frequency omega(r ) ...

Obtain the resonant frequency `omega_(r )` of a series LCR circuit with `L = 2.0H. C = 32 mu F` and `R = 10 Omega`. What is the Q-value of this circuit ?

Text Solution

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Given, inductance, L = 20 H,
Capacitance , C 32 `mu F = 32 xx 10^(-6)` F
resistance , R = 10 `Omega`
Resonant frequency is given by
`omega_(r) = (1)/(sqrt(LC))`
`omega_(r) = (1)/(sqrt(2xx 32 xx 10^(-6)))` = 125 rad `s^(-1)`
Q-value of circuit is
`Q = (1)/(R) sqrt((L)/(C)) = (1)/(10) sqrt((2.0)/(32 xx 10^(-6)) = 25 `
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