"In a series LR circuit with $\mathrm{X_L=R}$, power factor P1. If a capacitor of capacitance C with $\mathrm{X_C=X_L}$ is added to the circuit the power factor becomes P2. The ratio of P1 to P2 will be :"

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${X_L} = R$

$\Rightarrow {P_1} = {R \over {\sqrt {X_L^2 + {R^2}} }} = {1 \over {\sqrt 2 }}$

Now, ${X_L} = {X_C} = R$

$\Rightarrow {P_2} = {R \over {\sqrt {{R^2} + {{({X_L} - {X_C})}^2}} }} = 1$

$\Rightarrow {{{P_1}} \over {{P_2}}} = {1 \over {\sqrt 2 }}$

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In a series LR circuit with $\mathrm{X_L=R}$, power factor P₁. If a capacitor of capacitance C with $\mathrm{X_C=X_L}$ is added to the circuit the power factor becomes P₂. The ratio of P₁ to P₂ will be :

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In a series LR circuit with $\mathrm{X_L=R}$, power factor P1. If a capacitor of capacitance C with $\mathrm{X_C=X_L}$ is added to the circuit the power factor becomes P2. The ratio of P1 to P2 will be :

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In a series LR circuit with $\mathrm{X_L=R}$, power factor P₁. If a capacitor of capacitance C with $\mathrm{X_C=X_L}$ is added to the circuit the power factor becomes P₂. The ratio of P₁ to P₂ will be :