Step 1: In a dry cell (Leclanché cell), manganese dioxide (\(\text{MnO}_2\)) acts as a depolarizer at the cathode.
Step 2: During the electrochemical reaction, \(\text{MnO}_2\) gets reduced to manganese(III) oxide (\(\text{Mn}_2\text{O}_3\)).
Step 3: The oxidation state of manganese changes from \(+4\) in \(\text{MnO}_2\) to \(+3\) in \(\text{Mn}_2\text{O}_3\).