When a current of $4\,\text{A}$ flows within a battery from its positive to negative terminal, the potential difference across the battery is $12\,\text{V}$. The potential difference across the battery is $9\,\text{V}$ when a current of $2\,\text{A}$ flows within it from its negative to its positive terminal. The internal resistance and the e.m.f. of the battery are: