Powering an Arduino with a Supercapacitor
The voltage on a capacitor is proportional to the charge stored in it.

That means that as the device draws current, the voltage will drop.  You have to decide how low is acceptable.  Do the math.

For example, let's say the device can still run from 4.5 V.  That means the capacitor voltage can drop 500 mV before the system doesn't work anymore.  Let's use a 1 F cap as example.

&nbsp; &nbsp; (500 mV)(1 F) / (35 mA) = 14.3 s

That's how long a 1 F cap charged to 5 V can run your device at the worst case current draw.