Answer :

(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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