To get maximum current through a resistance of 2.5 , one can use m rows of cells, each row having n cells. The internal resistance of each cell is 0.5 . What are the values of n and m, if the total number of cell is 45?
a)		b)		c)		d)

(a)

If the cells are connected as shown in figure, they are said to be connected in mixed grouping. Let there be cells in series in one row and rows of cells in parallel. Suppose all the cells are identical. Let each cell be of emf E and internal resistance .

In each row, there are n cells in series, therefore their total internal resistance= .

Their total .

Since, there are  rows of cells in parallel therefore, total internal resistance  of all the cells is given by

Total resistance in their circuit

Effective emf of all the cells

The current in the external resistance is given by

The current I will be maximum, if  is minimum.

Mathematically, it can be shown that  is minimum, if

Here,         (given )….(i)

and

Or                    ………..(ii)

From Eqs. (i) and (ii), we have

∴        n=15