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In a series LR circuit X_L = R and power factor of the circuit is P₁. When capacitor with capacitance C such that X_L = X_C is put in series, the power factor becomes P₂. The ratio $\frac{P_{1}}{P_{2}}$ is

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$\frac{1}{2}$

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{\sqrt{2}}$

$2 : 1$

answer is B.

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Detailed Solution

$P_{1} = \cos ϕ = \frac{1}{\sqrt{2}} (X_{L} = R)$
$P_{2} = \cos ϕ^{'} = 1$ (will become resonance circuit)
$So, \frac{P_{1}}{P_{2}} = \frac{1}{\sqrt{2}}$

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