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Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H,C = 27 uF and R= 7.4 Omega. It is desired to improve the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of 2. Suggest a suitable way. |
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Answer» Solution :It is given that `L= 3.0 H, C = 27 muC = 27 xx 10^(-6) F, R= 7.4 OMEGA` Resonant angular frequency of SERIES LCR circuit is `omega_(r) =1/sqrt(LC) = 1/sqrt(3.0 xx 27 xx 10^(-6)) = 111 RAD s^(-1)` and Q-FACTOR `=(omega_(r)L)/R = (111 xx 3.0)/(7.4) = 45` To improve the sharpness by a factor of 2, Q must be doubled. It is obvious that keeping the resonant frequency the same, the value of R be halved from `R = 7.4 Omega` to `3.7 Omega` |
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