The wet cell battery implies that it has an liquid inside.
The Copper and the Zinc are also the compounts that will react in the battery as the semi-reactions implies:
Cu2+(aq) + 2e- --> Cu0
Zn2+(aq) + 2e- --> Zn0
The electrolyte is a substance present in the battery that will help the electricity to flow to the ion of interest and will not participate in the reaction, the acid should work as the electrolyte in this case.
