Grouping of Cells: Series, Parallel and Mixed

Cells in series. When $n$ identical cells, each of EMF $\varepsilon$ and internal resistance $r$, are connected in series (the positive terminal of each joined to the negative terminal of the next, so they all "aid" each other), their EMFs simply add, and so do their internal resistances, since the same current flows through every cell in turn:

Connected to an external resistance $R$, the current in the circuit is then $I = n\varepsilon/(R+nr)$. Series grouping is used whenever a HIGHER total EMF is needed than a single cell can supply; it is most efficient (gives the largest current) when the external resistance $R$ is large compared with the total internal resistance $nr$.

Cells in parallel. When $m$ identical cells, each of EMF $\varepsilon$ and internal resistance $r$, are connected in parallel (all positive terminals joined together, and all negative terminals joined together), the combination behaves as a single cell of the SAME EMF $\varepsilon$ (since each branch, by itself, is capable of maintaining that potential difference across the common terminals) but with a much SMALLER equivalent internal resistance, since the $m$ internal resistances are themselves effectively in parallel with each other:

Connected to an external resistance $R$, the current is $I = \varepsilon/(R + r/m)$. Parallel grouping is used whenever a LARGER current is needed than a single cell can safely supply, without needing a higher voltage; it is most effective when $R$ is small compared with a single cell's own internal resistance $r$. …