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InterviewSolution
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What do you understand by "sharpness of resonance" in a series LCR circuit ? Find expression for Q-factor of the circuit. |
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Answer» Solution :We KNOW that current amplitude in a series LCR circuit is maximum when `omega = omega_(0) = 1/sqrt(LC)`. The maximum value of current at resonance is `(I_(m))_(rms) = V_(m)/R`For any other value of `omega` , the current amplitude is less. Choose values of o for which current amplitude is `1/sqrt(2) (I_(m))_(max)` . In Fig. 7.34, these values of WARE represented by POINTS B and C having angular frequencies `omega_(1)` and `omega_(2)`such that `omega_(1) = omega_(2)`and `omega_(2) = omega_(0) + Deltaomega`.The quantity `omega_(0)/(2.Deltaomega)`is regarded as a measure of sharpness of resonance and is also known as the Q-factor of the circuit. Smaller the value of Aw, sharper is the resonance. It can be easily calcualted that `Deltaomega = R/(2L)`  `THEREFORE` Q-factor representing the sharpness of resonance `Q = (omega_(0))/(2Deltaomega) = (omega_(0)L)/R` As, `omega_(0) =1/sqrt(LC)`, hence, `Q = 1/sqrt(LC).1/R = 1/Rsqrt(L/C)` |
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