So what would happen if you magically injected more charge onto the capacitor? Would it flow back to the battery and cause a short circuit?
Q and V have different units, so they can't equal one another per say, but they are proportional and your thinking is right on. The equation you need is Q
stored = V
capacitorC, so V
capacitor = Q
stored/C. If Q
stored increases somehow (like by adding charges to the plate as you suggest), then the voltage across the capacitor would be greater than the voltage across the battery, and the current would need to flow from the capacitor to the battery to balance the voltage difference out.
If you have a system with just a battery and capacitor that is fully charged, you could get backflow from the capacitor to the battery if you (1) moved the two capacitor plates away from one another, (2) removed a dielectric from between the capacitor plates, or (3) added more charge to the capacitor plates. The first two changes reduce C
capacitor while the last change increases Q
stored. All three changes ultimately increase V
capacitor, which in the circuit described above would cause backflow of current to the battery.
