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Read the following passage and then answer questions on the basis of your under standing of the passage and the related studied concepts. Passage: For an LCR series circuit driven with an alternating voltage of amplitude Vmand angular frequency oo, the current amplitude is given as I_(m) =V_(m)/z = V_(m)/sqrt(R^(2) + (X_(L)-X_(C))^(2)) =V_(m)/sqrt(R^(2) + (Iomega -1/(c omega))^(2)) If omega is varied then for a particular frequency omega_(0), X_( C) = X_(L) and then Z = R and hence, I_(m) = V_(m)/R is maximum. This frequency is called the resonant frequency. The resonant frequency omega_(0) = 1/sqrt(LC) = Resonance of a LCR series a.c. circuit is said to be sharping current amplitude Im falls rapidly on increasing/decreasing the angular frequency from its resonant value 0. Mathematically, sharpness of resonance is measured by the quality factor of the circuit, which is given as: Q = (omega L)/R = 1/R sqrt(L/C) (c) What is the nature of reactance in the circuit when (i) omega lt omega_(0)and (ii) omega gt omega_(0) ? |
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Answer» Solution :(i) For `omega LT omega_(0)`, the net reactance of the circuit is capacitor in nature because for `omega lt omega_(0), X_( C) = (1/(C omega))` is greater than `X_(L) = (L omega)` (II) For `omega gt omega_(0)` , the net reactance is inductance in nature because now `X_(L) gt X_( C)`. |
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