I want to know how to determine the signal sampling rate required to reconstruct electrical signals whose frequency components are unknown, such as, for example, signals of charge/discharge voltage on a capacitor. I want to design a system capable of scanning this type of signal in real time.
Sampling a signal requires that it should be bandlimited. When it's not, you should apply a preprocessing analog bandlimiting (aka anti-aliasing) filter to enable its proper sampling. There are various concerns on how to choose the most practical anti-aliasing filter. The most important concern is the filter cutoff frequency which determines the minimum sampling rate to record the signal.
Your application is about capturing capacitor charge/dischage signals which are of spiky nature and hence posses very large bandwidths; quite large sampling rates might be necessary. In very rough terms, the dischaging signal's bandwidth is inversely proportional to the time-constant of the discharging network, assuming a first order simplified model.
If you know this time constant, then you should select the lowpass filter whose time constant is smaller than that. This will make sure that the anti-aliasing filter's bandwidth will be larger than the signal of interest's bandwidth.
So you should firt determine the time cosntat of your observed network, to predict a first order estimate of the minimum sampling rate required.