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 $3 \,A$ flows in the opposite direction potential difference across the terminals of the battery is $15\, V$, the $emf$ of the battery is ................ $\mathrm{V}$
Diffcult
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$\mathrm{T} . \mathrm{P.D.}=\mathrm{E}-\mathrm{I} \mathrm{r} \Rightarrow 12=\mathrm{E}-2 \mathrm{r}$ ..........$(1)$
$\mathrm{T.P.D.}=\mathrm{E}+\mathrm{Ir} \Rightarrow 15=\mathrm{E}+3 \mathrm{r} $ .........$(2)$
Solve ${\rm{e}}{{\rm{q}}^n}$ $(1)$ and $(2)$
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