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 :

For the given figures, choose the correct options :

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $$x$$ times its initial resonant frequency $$\omega_0$$. The value of $$x$$ is :

A circuit element $$\mathrm{X}$$ when connected to an a.c. supply of peak voltage $$100 \mathrm{~V}$$ gives a peak current of $$5 \mathrm{~A}$$ which is in phase with the voltage. A second element $$\mathrm{Y}$$ when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $$\frac{\pi}{2}$$. If $$\mathrm{X}$$ and $$\mathrm{Y}$$ are connected in series to the same supply, what will be the rms value of the current in ampere?