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 :

Question

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 :

1 : $\sqrt2$