(a)The carbon electrode acting as anode (positively charged) is burnt away.
(b) In the electrolysis of molten aluminium oxide using carbon electrodes, the pure metal is formed at the cathode (negatively-charged electrode) and oxygen is formed at the anode (positively-charged electrode). This oxygen reacts with positively-charged carbon electrode and produces carbon dioxide gas. Due to this reaction between oxygen and carbon electrode (anode), the carbon electrode burns away gradually and has to be replaced.