Q30 of 37 Page 1

Obtain the resonant frequency and Q–factor of a series LCR circuit with L= 3H, C = 27

The resonance of the series LCR circuit is that point when the capacitance and inductance of the circuit are equal in magnitude but they are out of phase (180 degree) hence they cancel each other. Q factor is the measure of the sharpness of the resonance.

Inductance, L = 3.0 H


Capacitance, C = 27 μF = 27 × 10−6 F


Resistance, R = 7.4 Ω


At resonance, angular frequency of the source for the given LCR series




Q-factor of the series,




If someone is desired to improve the sharpness of resonance of circuit by reducing its full width at half maximum by a factor of 2, R has to be reduced by the factor of �, i.e.


R= R/2 = 7.4/2= 3.7Ω


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