Equation For Capacitor Leakage Current

As a first approximation, model the solar cell with a Thevenin equivalent circuit as determined by the open circuit voltage, \$V_{OC}\$, and short circuit current, \$I_{SC}\$, of the cell at a given illumination.

Then, for that fixed illumination, the time constant will be:

$$\tau = \dfrac{V_{OC}}{I_{SC}}C $$

The time required to charge to some fraction \$\chi\$ of the final voltage is:

$$t = -\tau \ln(1 - \chi)$$

I suppose I will answer my own question. There is a constant voltage because you want to observe how the circuit reacts once the capacitor is fully charged. Theoretically there should be no current when the cap is fully charged, but you will observe with enough accuracy there will be a small current. This small current is the leakage current, and the insulation resistance can be calculated using ohm's law.