Modeling Capacitor with Electric Currents

Hi,

So I am trying to model a parallel plate capacitor with a variable overlap between the plates.
Going through the ACDC models in COMSOL, I don't really understand how using electric currents can be accurate.

I have air between the two plates and reading from the forums, everyone says to set the conductivity of it between 1 and 1E-4 but when I am trying to figure out the current traveling between the two plates using a set potential on one side and a ground on the other, the current created is just due to V=IR?

Thanks,
Jeffrey