A resistance of $200 \Omega$ and an inductor of $\frac{1}{2 \pi} \mathrm{H}$ are connected in series to a.c. voltage of 40 V and 100 Hz frequency. The phase angle between the voltage and current is

A coil of resistance $450 \Omega$ and self-inductance 1.5 henry is connected to an a.c. source of frequency $\frac{150}{\pi} \mathrm{~Hz}$. The phase difference between voltage and current is

In an $L-R$ circuit, the inductive reactance is equal to $\sqrt{3}$ times the resistance ' $R$ ' of the circuit. An e.1n.f. $\mathrm{E}=\mathrm{E}_0 \sin (\omega \mathrm{t})$ is applied to the circuit. The power consumed in the circuit is

An a.c. source is applied to a series LR circuit with $\mathrm{X}_{\mathrm{L}}=3 \mathrm{R}$ and power factor is $\mathrm{X}_1$. Now a capacitor with $\mathrm{X}_{\mathrm{c}}=\mathrm{R}$ is added in series to LR circuit and the power factor is $\mathrm{X}_2$. The ratio $\mathrm{X}_1$ to $\mathrm{X}_2$ is