Multiple Voltage Sources

When batteries are connected in series, the overall electromotive force (EMF) is the sum of individual batteries' EMFs. Each battery boosts the electrons flowing through it, resulting in increased total voltage. For example, two 1.5 V batteries in series produce 3.0 V. However, the total internal resistance also increases because internal resistances are additive in series configurations.

In parallel connection, positive terminals connect together and negative terminals connect together, maintaining the same EMF as individual batteries. Parallel configuration reduces equivalent internal resistance, allowing larger current delivery to the load. This setup is ideal for high-current applications like diesel truck engines, where two 12 V batteries in parallel provide 12 V but deliver greater current capacity.

Internal resistance affects the terminal voltage available to the load. In series, internal resistances add, reducing efficiency. In parallel, internal resistance decreases, enabling higher current output. Terminal voltage equals EMF minus the product of equivalent internal resistance and current. Lower internal resistance in parallel configurations allows batteries to deliver more power to devices requiring high current.

Kirchhoff's loop rule determines the current in series circuits. The same current flows through each battery because they are connected in series. The current is calculated using the total EMF divided by the total resistance, which includes both the load resistor and the sum of all internal resistances from each battery.

Terminal voltage for parallel batteries equals the EMF minus the equivalent internal resistance multiplied by the load current. Applying Kirchhoff's junction and loop rules at common nodes determines the load current through equivalent resistance. Since parallel connection reduces internal resistance compared to individual batteries, the terminal voltage remains close to the EMF even under load.

Connect batteries in series to increase voltage for devices requiring higher voltage, like flashlights needing 3.0 V from two 1.5 V cells. Connect batteries in parallel to increase current capacity and runtime for high-power devices like diesel engines. Series increases voltage but internal resistance; parallel maintains voltage while reducing internal resistance and enabling larger current delivery.

For N batteries in series, total EMF is the sum of all individual EMFs, and total internal resistance is the sum of all individual internal resistances. For N identical batteries in parallel, total EMF equals one battery's EMF, while equivalent internal resistance is one battery's internal resistance divided by N. These generalizations allow prediction of voltage and current for any number of combined batteries.