# Do currents superposition

When you work with an emf of the form:

U(t) = a0 + Ʃaicos($\omega$t)
it desperately cries for using Kirchoffs law for each term in the sum independently. I guess you can do so since Kirchoffs law is linear but then other the hand I get something weird physically when doing so.
In every exercise I am told that the current has been going on forever. Applying Kirchoffs law for the current due to a0 after an infinite amount of time then shows that there is no current due to this. Which I guess makes sense because for a circuit where the only emf is generated by the constant because then after an infinite amount of there is no current because the capacitor is blocking everything because of the charge on it. But on the other hand when you then superposition this situation with a lot of other emfs that are oscillating something is weird physically- because shouldn't the "extra" charge on the capacitor arising from the constant part of the emf not give rise to a different physical situation? I mean even though there is no current due to it has produced some extra charge on the capacitor which generates a potential drop for every electron going towards the - pole. Shouldn't this somehow be accounted for?