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Compute the resonant frequency and the Q...

Compute the resonant frequency and the Q factor of a series LCR circuit having `L = 4.0 H, C = 36 mu F` and `R = (10)/(3) Omega`. How can sharpness of resonance of the circuit be improved by a factor of 2 by reducing its full width at half maximum ?

Text Solution

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Here, `omega_(r) = ? Q = ?, L = 4.0 H`,
`C = 36 mu F = 36 xx 10^(-6) F, R = (10)/(3) Omega`
Resonant frequency.
`omega_(r) = (1)/(sqrt(LC)) = (1)/(sqrt(4.0 xx 36 xx 10^(-6))) = (1000)/(12)`
`= 83.3 rad//s`.
Q factor of the circuit ` = (omega_(r) L)/(R) = (250)/(3) xx (4.0)/(10//3)`
To improve sharpness of resonance by a factor of 2 , Q should be doubled. To double Q. without changing `omega_(r)` resistance R should be reduced to half i.e. R should br `10//6 ohm`
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