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A filament lamp is joined in series with a capacitor of capacitance C (in micro-farad) and the combination is connected across a 200 V, 50 Hz AC mains. The lamp dissipates 500 W of power and the rms voltage across it is 100 V. There is no inductance anywhere in the circuit. Using rms values throughout and taking pi*sqrt(3) ~ 5, determine the capacitance C (in micro-farad).

1. 9.2 micro-farad
2. 13.5 micro-farad
3. 115 micro-farad
4. 55 micro-farad

Correct answer: 9.2 micro-farad

Solution

In a series R-C circuit the resistor (lamp) voltage and capacitor voltage are 90 deg out of phase, so they add as a right triangle with the supply voltage as the hypotenuse. The current is fixed by the lamp's resistive behaviour.

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