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  1. Yes but you will not save energy stored in battery as the capacitor gets energy from battery to store

  2. Electrolytic capacitors are generally polarised, meaning they work only when a DC bias is applied..
    The energy stored in an electrolytic capacitor is trivial compared to the energy in a battery also.

    Such a capacitor may be used at the input of a HID lamp inverter to reduce the AC impedance of the supply at the inverter frequency, but it will be internal to the supply. It also helps with suppressing spikes and interference.

    There is no need for an external capacitor. Additionally, as the HID lamp is more efficient, it should actually draw less current than a conventional quartz iodine lamp for the same brightness, reducing the demands on the battery.

Does an ELECTROLYTIC CAPACITOR store electricy when in an DC circuit only?

I have an HID xenon conversion kit installed in my motorcycle.. I hope to save electricity of my battery by having a capacitor. Does it help conserve electricity? I mean the does the capacitor conserve electricity when i’m using my HID Xenon bulb?