Q.Two cells of emfs $\varepsilon_1$ & $\varepsilon_2$ and internal resistances $r_1$ & $r_2$ respectively are connected in parallel. Obtain expressions for the equivalent.

Cells in series. Several identical cells (each emf $\varepsilon$, internal resistance r) can be chained together, negative terminal to positive terminal, so that n cells in series present a combined emf of $n\varepsilon$ and a combined internal resistance of $nr$ (since the internal resistances, like ordinary series resistors, simply add). Connected to an external resistance R, the current is $I=n\varepsilon/(nr+R)$. If $r\ll R$, this current approaches $n$ times what a single cell alone would supply -- a genuine, worthwhile gain from wiring cells in series. But if $r\gg R$, the current instead approaches just $\varepsilon/r$, essentially the SAME as a single cell alone would supply, meaning there is no real benefit to adding more cells in series in that regime. Series wiring is therefore advantageous specifically when the cells' combined internal resistance is small compared with the external load R. …