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Not very well. Cap banks can supply a lot of instant amperage but the voltage drops off quickly at high loads. Think about it like this: Each cap in my 500 farad cap bank (huge; they are 2.7v 3000 farad caps) holds about the same overall energy as a AA battery.
If you need to power something for a long time, you need chemistry. If you want to hit something with a lot of power for a very short time, you need capacitance.
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