A capacitor opposes a change in?

Capacitors charge by transferring charge from one plate to the other. This is not the same as a battery, though it can seem so. They oppose a change in voltage because the two plates are close to each other, separated by the dielectric, and the transfer of charge requires current. Once charged, however, the current becomes zero. The differential equation describing a capacitor is dv/dt = i/c, or volts per second = current over capacitance.