## Cells in Mixed Groupings:

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

In each row, there are n cells in series.

Total internal resistance in one row = nr.

There are m rows in parallel. Therefore, the total internal resistance of all the cells is given by

1/r_{p} = 1/nr + 1/nr + 1/nr ——– up to m terms⇒ 1/r _{p} = m/nr⇒ r _{p} = nr/mTotal resistance in the circuit = R + nr/m Total resistance in the circuit = mR+nr/m Total (effective) emf of all the cells = nE The current in external resistance is given by- I = Total EMF/Total resistance = nE/(mR+nR)/m ⇒ I = mnE/mR+nr The current I will be maximum, if (mR+nr) is minimum. It can be shown mathematically that (mR+nr) is minimum. If mR = nr ⇒ R = nr/m i.e. external resistance = Total internal resistance of all the cells |

Thus, we get maximum current in a mixed grouping, if the value of external resistance is equal to the total internal resistance of all the cells.