Charging a supercapacitor through a lamp: A power-law RC decay

A circuit involving a charging supercapacitor in series with a non-Ohmic tungsten lamp displays a wealth of interesting behavior. Most notably, the current through the lamp decreases in time according to a power-law function as opposed to the exponential time dependence observed in RC circuits with Ohmic resistors. We use a combination of computational and analytical techniques to model this power-law behavior as well as the behavior of the filament's temperature and resistance as the supercapacitor charges. Our results agree well with experiment, and the experiment described here can be modified to be appropriate for physics courses at a wide range of levels.