CELLS IN SERIES
Consider two cells which is connected in series. The positive terminal of one cell is connected to negative terminal of the next cell. Here one terminal of two cells are free and the other terminal of two cells are joined together. ε1 and ε2 are the emfs of the cells and r1 and r2 are the internal resistance of the cells respectively. Let I be the current flowing through the cells.
The total internal resistance = nr (since the internal resistances come in series) The total resistance in the circuit = nr+R
The total emf = nE (since the emfs add up in series circuit)
Therefore, the current in the circuit;
Current= Total Emf/Total resistance
PARALLEL COMBINATION OF CELLS
Consider two cells which is connected in parallel. Here the positive terminals of all cells are connected together and negative terminals of all cells are connected together. In parallel connection, the current is divided among the braches. Thus, the current I is split into I1 and I2. I = I1 + I2. Consider the points B1 and B2 and then V (B1) and V (B2) are the potentials respectively. The potential difference across the terminals of the first cell.
The total emf in circuit = E ( Since each cell has the same emf and they are in parallel)
The net internal resistance = r/m (since the cells are in parallel, their resistances are also in parallel. If m identical resistances are in parallel, the effective resistance is r/m)
The total resistance in circuit = R + r/m
Therefore, the current in circuit;
Current= Total EMF/Total Resistance
I=E/mr+R
