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A charged capacitor has a potential difference when it is just
"sitting around"
A battery has no potential difference unless there is a current
through it.
IF I take a capacitor and drop its temperature to 5 K say, it will
still have a charge to discharge. A battery at 5 K is dead, the
reaction will not happen.
In a capacitor I can discharge as fast as I want depending on the
circuit,
A capacitor's potential difference changes as the the charge changes.
A battery delievers a specific potential difference is a given
circuit as long as there are chemicals left to react.