Cells can be connected in series as shown. When n cells of emf’s E1 E2 ..... En with their internal resistance as r1 r2 , ..... r n are connected in series.
Then
The equivalent e.m.f of a series combinations n cells is just the sum of their individual e.m.f and
The equivalent internal resistance of a series combination of n cells s just the sum of their internal resistance when n cells of e.m.f ε1 ε2 - εn and internal resistances are connected in parallel use these equivalent e.m.f and internal resistance all given by
We can also have a mixed grouping of cells (say N) where we connect n cells in series in row and then connect m such rows in parallel. Assuming each cell has an e.m.f. ε and internal resistance. Assuming each cell has an emf ε and internal resistance r, the equivalent e.m.f. and resistance of n cells in series in a row would be given by nε and nr.
Now there are m rows of cells in parallel therefore total internal resistance of all cells would be given by
Hence, rp = nr/m
Since the parallel combination of rows of cells does not effect the e.m.f. of each row of cells therefore the effective e.m.f. of all cells is nε . If we connect an external resistance R to such as arrangement, the current in the external resistance R is given by
The condition for I to be maximum is given by R = nr/m
