Question

Do the dimensions of the cathode and anode matter in electrochemistry?

Answer 1

YOUR ANSWER BUDDY-

The dimensions of electrodes should not effect the open circuit voltage, since this is determined solely by the identity and concentrations of the redox species.

Once the cell is running, the dimensions may affect how much the voltage drops off as you draw current, known as "overpotential". If your cell is limited by its ability to deliver ions to the surface of the electrode, or to transfer charge into the electrode, then the higher surface area of a large electrode is likely to result in a more efficient battery.