I understand that a capacitor stores energy on the form of voltage. However, looking at the equations for the current and voltage on the capacitor, we have the following:
I was thinking here that if I connect the capacitor to a DC battery, it is going to charge, right? However, as the voltage is a constant, the current should be 0 according to the second equation. Therefore, according to the first one, the integral value is gonna equal 0, right? If it equals 0, then V(t) = V(t0). Assuming that V(t0) = 0, the voltage is always going to be 0, even though the capacitor charges when you apply a DC voltage to it.
Could someone please explain to me how to link this concept to the mathematical equations?
Thank you very much.