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Q.

In an L-C-R series circuit, $X_{L} = X_{C} / 2 = R$ . Then the voltage supplied across the combination

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a

must be in phase with the current

b

must lead the current by $45^{o}$

c

must lag the current by $45^{o}$

d

must lead the current by $60^{o}$

answer is C.

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Detailed Solution

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

Since $V_{C} > V_{L}$ , the supply voltage must lag behind the current

$z = \sqrt{{(X_{C} - X_{L})}^{2} + R^{2}} = \sqrt{2} R$

$\cos ϕ = \frac{R}{\sqrt{2} R} = \frac{1}{\sqrt{2}} \Rightarrow ϕ = 45^{o}$

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