Q21 of 26 Page 1

(a) Show that the average power consumed in an inductor L connected to an a.c. source is zero. (b) In a series LR circuit, and the power factor of the circuit is . When a capacitor with capacitance C such that is put in series, the power factor becomes . Find out .

(a) Let the Potential of the ac source be given by



The current lags in an inductor circuit by a phase of . Therefore, the current is given by



We know that power is given by






(b) Let the total impedance of the circuits be Z.


We know that the power factor is given by



Where,


.


Now, for L-R circuit,



Therefore, power factor


Now, for the LCR circuit,



This is the resonance condition and hence all impedance is due to resistance.



Therefore, power factor


Hence the ratio is given by



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