To get maximum current through a resistance of $2.5\Omega$, one can use $‘m’$ rows of cells, each containing $‘n’$ cells connected in series. The internal resistance of each cell is $0.5\Omega$. What are the values of $n$ and $m$ if the total numbers of cells are $45$?

$\begin {array} {1 1} (a)\;3,15 & \quad (b)\;5,9 \\ (c)\;9,5 & \quad (d)\;15,3 \end {array}$

This question requires understanding of the combinations of non-ideal cells and maximum power theorem.
For, current to be maximum, net resistance of the cells must be equal to $2.5\Omega$
i.e. $\large\frac{n(0.5)}{m}$ $= 2.5$
And $n \times m = 45 \Rightarrow n = 15, m = 3$
Ans : (D)
edited Mar 14, 2014