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They're charged with power, which is current x voltage. If you have infinite current and zero voltage or vice versa, nothing happens.

They're charged with power, which is current x voltage.

No, they are charged by currents. The normal power source for capacitor charging is a constant current source, one in which the voltage follows the desired current. The least desirable source is a constant-voltage supply, which (in the ideal case) will deliver infinite current at time zero.

The voltage on a capacitor is the time integral of past applied currents. The ideal charging scheme is a constant current source, which cuts off as the capacitor's voltage limit is reached.

Sorry for the late reply, I am traveling.

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