A $20 \Omega$ resistance, 10 mH inductance coil and $15 \mu \mathrm{~F}$ capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made $\frac{1}{3} \mathrm{rd}$, the resonant frequency

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