A battery has some internal resistance.

$($i$)$ Can the potential difference across the terminals of the battery be equal to its emf?

NoYes, if the battery is absorbing energy by electrical transmission.$$Yes$,$ if more than one wire is connected to each terminal.Yes, if the current in the battery is zero.Yes, with no special condition required.

$($ii$)$ A battery has an emf of $12$V and an internal resistance of $2$ohms. What loaded current would cause the terminal voltage to drop to zero?

$12$A$6$A$4$A$2$A$0\mathrm{.}5$A