A group of devices having a total power rating of 500 watt is supplied by an $$\mathrm{AC}$$ voltage $$E=200 \sin \left(3.14 t+\frac{\pi}{4}\right)$$. Then the r.m.s. value of the circuit current is

An AC voltage source of variable angular frequency $$\omega$$ and fixed amplitude $$\mathrm{V}_0$$ is connected in series with a capacitance $$\mathrm{C}$$ and an electric bulb of resistance $$\mathrm{R}$$ (inductance zero). When $$\omega$$ is decreased

A transformer which steps down $$330 \mathrm{~V}$$ to $$33 \mathrm{~V}$$ is to operate a device having impedance $$110 \Omega$$. The current drawn by the primary coil of the transformer is :

A coil of inductance $$1 \mathrm{H}$$ and resistance $$100 \Omega$$ is connected to an alternating current source of frequency $$\frac{50}{\pi} \mathrm{~Hz}$$. What will be the phase difference between the current and voltage?