When alternating current is passed through $\mathrm{L}-\mathrm{R}$ series circuit, the power factor is $\frac{\sqrt{3}}{2}$ and $\mathrm{R}=50 \Omega$, then the value of L is

$$ \left[\cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}, \sin \frac{\pi}{6}=\frac{1}{2}, \tan \frac{\pi}{6}=\frac{1}{\sqrt{3}}\right] $$

An a.c. e.m.f. of peak value 230 V and frequency 50 Hz is connected to a circuit with $\mathrm{R}=11.5 \Omega, \mathrm{~L}=2.5 \mathrm{H}$ and a capacitor all in series. The value of capacitance is ' $C$ ' for the current in the circuit to be maximum. The value of ' $C$ ' and maximum current are respectively ( $\pi^2=10$ )

An ideal inductor of $\left(\frac{1}{\pi}\right) \mathrm{H}$ is connected in series with a $300 \Omega$ resistor. If a $20 \mathrm{~V}, 200 \mathrm{~Hz}$ alternating source is connected across the combination, the phase difference between the voltage and current is

An alternating e.m.f. having voltage $\mathrm{V}=\mathrm{V}_0 \sin \omega t$ is applied to a series L-C-R circuit. Given : $\left|X_L-X_C\right|=R$. The r.m.s. value of potential difference across capacitor will be