In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance \(\mathrm{C} \mu \mathrm{F}\)…

In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance \(\mathrm{C} \mu \mathrm{F}\) across a \(200 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. The power consumed by the lamp is \(500 \mathrm{~W}\) while the voltage drop across it is \(100 \mathrm{~V}\). 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 ...........μF