Internal Resistance of a Supercapacitor
This makes little sense.  A power supply plugged into wall power can supply 250 mA indefinitely.  A capacitor has a fixed amount of charge, and a even smaller amount of charge it can deliver usefully.  In addition, the voltage on the capacitor goes down over time, since it is proportional to the charge in the cap at any one time.

You can't just "replace" a power supply with a capacitor.  The two do different things, and are not equivalent.