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In a certain series LCR A. C. circuit it is found that $X_{L} = 2 X_{C}$ and phase difference between the current and voltage is $π / 4$ . If now capacitance is made $1 / 4^{t h}$ & the inductance and resistance are doubled then which are not correct.

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Voltage will lead current by a phase of $\tan^{- 1} (1 / 2)$ .

Voltage will and current will be in same phase.

Voltage will lag behind current by a phase of $π / 4$ .

Voltage will lag behind current by a phase of $\tan^{- 1} (1 / 2)$ .

answer is A, B, C.

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Detailed Solution

$X_{L} = 2 X_{C}$

$X_{C}^{'} = 4 X_{C}$

$X_{L}^{'} = 2 X_{L}$

$\Rightarrow X_{L}^{'} - X_{C}^{'} = 2 X_{L} - 4 X_{C} = 2 [X_{L} - 2 X_{C}] = 0$

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