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A capacitor is used to improve the power factor of the lamp.

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To prevent the lamp from taking too much current a fluorescent lamp has to have a choke, which has magnetic inductance. The inductance has a negative impact on the power factor of the (the ratio between apparent power and real power taken by the lamp) - i.e. the power factor is reduced - so a capacitor is used to compensate for the inductance by improving the power factor so that it is closer to the ideal value of 1.

Basically the inductor with the capacitor smooths out the voltage or current.

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