Final answer:
Increasing the surface area of a cathode in an electrochemical cell increases the current by providing more sites for reduction reactions, which in turn allows for a greater flow of electrons and a higher current.
Step-by-step explanation:
The increase in the surface area of the cathode in an electrochemical cell leads to an increase in the current because it allows for more sites for the reduction reaction to occur. As more copper ions are reduced to copper metal at the surface of the cathode, the flow of electrons towards the cathode is facilitated, increasing the overall rate of electron flow or current in the circuit. An increase in the surface area of the cathode means that more ions in solution can come into contact and be reduced at the electrode's surface simultaneously, rather than a smaller area where ions would have to wait for available sites to undergo reduction.
This enhanced electron flow contributes to a higher current because current is defined as the flow of charged particles; in this case, the particles are the electrons moving towards the cathode. Thus, a greater surface area at the cathode provides more opportunities for these charged particles to be transferred, contributing to the increased current in the cell.
Electrochemical cells are systems that allow for the transfer of electrons from the anode to the cathode through an external circuit, thereby creating an electric current that can do useful work. In sum, both increasing the surface area of the anode and cathode enhances the cell's ability to generate current by facilitating the oxidation and reduction reactions, respectively.