A battery of $24$ cells, each of emf $1.5\, V$ and internal resistance $2\, \Omega$ is to be connected in order to send the maximum current through a $12 \,\Omega$ resistor. The correct arrangement of cells will be
Medium
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Suppose $m$ rows are connected in parallel and each row contains $n$ identical cells (each cell having $E = 15\, V$ and $r = 2\, \Omega$)
For maximum current in the external resistance $R$, the necessary condition is $R = \frac{{nr}}{m}$
$ \Rightarrow $ $12 = \frac{{n \times 2}}{m}$ $ \Rightarrow $ $n = 6\,m$ ..... $(i)$
Total cells $= 24 = n \times m$ ..... $(ii)$
On solving equations $(i)$ and $(ii)$
$n = 12$ and $m = 2$
i.e. $2$ rows of $12$ cells are connected in parallel.
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