Capacitors take time to discharge through resistance. However they do not store enough charge to power a load directly for more than a very brief period of time.
If you want to power something based on the time it takes for a capacitor to discharge, then you could use a transistor to amplify the power.
A very small amount of capacitor discharge current flowing through the base to emitter of a bipolar junction transistor translates into a lot of current flowing through the collector and emitter of the transistor. That current also flows though any load on the collector side of the circuit without affecting the currents involved.
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The 2N3904 is very popular NPN Bipolar Junction Transistor (BJT).
The pin layout and direction of voltage and conventional current flow (positive to negative) is shown in the first diagram.
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