I have been reading a bit lately on the basics, but I can't find an answer this question: why does the current to/from (through) a capacitor change?

Here's a little background, first, to help clarify my question. I understand that the instantaneous current through a capacitor is its capacitance multiplied by the rate of change in voltage at that point in time.

I = C dv/dt

But, in a basic circuit I've simulated, it appears that the current itself also changes. For the current to change, and with C being constant, then the rate of change of the voltage must also change, akin to acceleration in physical motion.

This makes me think of "voltage acceleration" but searching for that doesn't turn up anything except for "acceleration voltage" which is related to particle acceleration. I also get no results if I search for something like "capacitor current changes over time"... at least, I get no results going any further than the initial formula above.

Any help?

Thanks!

-Phillip