Question

How do you get the RC time constant of a charging circuit given by voltages values and time?

Answer 1

Well, if it is a simple RC circuit, then you know that the voltage over the capacitor is of the form
V(t) = V(1-e^(-t/RC)), where V is the voltage difference over the voltage source.

Thus
-t/RC =ln ( 1 - V(t)/V )

Given values of the V(t) at a set of values for t, you can run a simple regression to estimate the value of 1/RC.