A capacitor and a resistor of resistance $100 \sqrt{3} \Omega$ are connected in series to an AC source of voltage $100 \sin (200 t) \mathrm{V}$, where ' $t$ ' is time in second. If the phase difference between the voltage and the current in the circuit is $30^{\circ}$, then the capacitance of the capacitor is

An electric bulb, an open coil inductor, an AC source and a key are all connected in series to form a closed circuit. They key is closed and after some time an iron rod is inserted into the interior of the inductor, then

An inductor and a resistor are connected in series to an AC supply. If the potential difference across the inductor and the resistor are 180 V and 240 V respectively, then the voltage of the AC supply is

The frequency of an alternating voltage is 50 Hz . The time taken for instantaneous voltage to increase from zero to half of its peak voltage is