Can you use supercapacitor, say 48 V and 165 F, while it is being charged? Can you use the supercapacitor for a much longer or longer duration, or ""infinitely"" if the charging time is a bit faster than the consumption of its energy? Thank you!

 

see this cap as a battery now you couple two things loader and cap.
next step put a load on the cap while loader is connected.
make a drawing and calculate what happens. ( do not forget the internal impedance and serial resistor loading the super cap.)

 

Can you use supercapacitor, say 48 V and 165 F, while it is being charged? Can you use the supercapacitor for a much longer or longer duration, or ""infinitely"" if the charging time is a bit faster than the consumption of its energy? Thank you!

Yes. The capacitor will respond to the net current flow, charging if IN > OUT, discharging if OUT > IN. Once charged or discharged, IN and OUT must be equal since no more charge can go in or out, respectively.

 

Not charging time but charging current.

If the into is less than the outgo the cap voltage falls.

If the into is greater than the outgo the cap voltage rises.

In either case something else may limit the cap voltage from going to zero or infinity, but that depends on the charger and the load.


Only when the into exactly matches the outgo will the cap voltage maintain itself, but that is because the cap is not being charged or discharged.