An on-board battery charger (OBC) includes first and second rails which generate first and second detection signals based on voltage events, such as zero-crossing or peak voltage events, of input voltages supplied to the rail circuits. The OBC includes a relay switchable between (i) an opened state in which the relay disconnects the rails whereby the rails can respectively receive first and second phase input voltages from a multi-phase mains supply and (ii) a closed state in which the relay connects the rails whereby the rails can both receive a same input voltage from a single-phase mains supply. A controller determines from a comparison of the detection signals at the same time whether input voltages received by the rails from a mains supply are out-of-phase or in-phase to determine therefrom whether the mains supply is multi-phase or single-phase and/or whether the relay is properly or improperly opened or closed.