9.2 Electromotive force: terminal voltage  (Page 5/12)

But if the cells oppose one another, such as when one is put into an appliance backward, the total emf is less, since it is the algebraic sum of the individual emfs.

A battery is a multiple connection of voltaic cells, as shown in [link] . The disadvantage of series connections of cells is that their internal resistances add. One of the authors once owned a 1957 MGA that had two 6-V batteries in series, rather than a single 12-V battery. This arrangement produced a large internal resistance that caused him many problems in starting the engine.

If the series connection of two voltage sources is made into a complete circuit with the emfs in opposition, then a current of magnitude $I=\frac{\left({\text{emf}}_1–{\text{emf}}_2\right)}{r_1+r_2}$ flows. See [link] , for example, which shows a circuit exactly analogous to the battery charger discussed above. If two voltage sources in series with emfs in the same sense are connected to a load $R_{\text{load}}$ , as in [link] , then $I=\frac{\left({\text{emf}}_1+{\text{emf}}_2\right)}{r_1+r_2+R_{\text{load}}}$ flows.

[link] shows two voltage sources with identical emfs in parallel and connected to a load resistance. In this simple case, the total emf is the same as the individual emfs. But the total internal resistance is reduced, since the internal resistances are in parallel. The parallel connection thus can produce a larger current.