In a series L R circuit with X_L=R, power factor is P_1. If a capacitor of capacitance C with X_C=X_L is added to the circuit the power factor…

In a series $\displaystyle L R$ circuit with $\displaystyle X_L=R$, power factor is $\displaystyle P_1$. If a capacitor of capacitance $\displaystyle C$ with $\displaystyle X_C=X_L$ is added to the circuit the power factor becomes $\displaystyle \mathrm{P}_2$. The ratio of $\displaystyle \mathrm{P}_1$ to $\displaystyle \mathrm{P}_2$ will be :