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Obtain the resonant frequency and Q fact...

Obtain the resonant frequency and Q factor of a series LCR circuit with L = 3.0 H, `C = 27 mu F` and R = 7.4 ohm.

Text Solution

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Given, inductance, L = 3 H
capacitance, C = 27` mu`F
Resistance, R = 7.4 `Omega`
Resonant frequency is given by
`omega_(0) = (1)/(sqrt(LC))`
` omega_(0) = (1)/(sqrt(3 xx 27 xx 10^(-6))) = 111.1 "rad" s^(-1)`
Q-factor is given by
`Q = (omega_(0)L)/(R) `45.04
To double Q without changing `omega_(0)` reduce R to R/2, i.e, 3.7 `Omega`
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