Cells in Series

In a SERIES combination of cells, the cells are connected along a single electrical path such that the POSITIVE terminal of one cell is joined to the NEGATIVE terminal of the next, and so on down the chain (Fig. 11.13a). Because of this end-to-end arrangement, the terminal voltage of the overall combination is the SUM of the individual cell voltages -- e.g. two 1.5 V cells in series provide a combined 3.0 V ($1.5\times2$).

More generally, for $n$ cells connected in series, the equivalent emf of the combination is the ALGEBRAIC sum of the individual emfs (respecting each cell's own polarity), and the equivalent internal resistance of the combination is simply the SUM of the individual internal resistances:

(i.e. the combined behaviour is exactly as if a single cell of emf $\sum\varepsilon_i$ and internal resistance $\sum r_i$ were used in its place.) …