When a current of $2\, A$ flows in a battery from negative to positive terminal, the potential difference across it is $12\, V$. If a current of $3\, A$ flowing in the opposite direction produces a potential difference of $15\, V$, the $emf$ of the battery is .............. $V$
Diffcult
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Let $\varepsilon$ be emf and $\mathrm{r}$ be intemal resistance of the battery.
In first case, $12=\varepsilon-2 \mathrm{r}$ ..........$(i)$
In second case, $15=\varepsilon+3 \mathrm{r}$ .........$(ii)$
Substract $(ii)$ from $(i),$ we get, $\mathrm{r}=\frac{3}{5}\, \Omega$
Putting this value of $\mathrm{r}$ in equation $(\mathrm{i}),$ we get
$\varepsilon=12+\frac{2 \times 3}{5}=\frac{60+6}{5}=\frac{66}{5}=13.2 \mathrm{\,V}$
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