Alternating Current

In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance C \(\mu\)F across a 200 V, 50 Hz supply. The power consumed by the lamp is 500 W while the voltage drop across it is 100 V. Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is \(\varphi\). Assume, \(\pi\)\(\sqrt 3\) \(\approx\) 5.

The value of C is ____________.