27.8:
Multiple Voltage Sources
When two batteries are connected in series with a load resistor, the overall emf is the sum of the individual batteries' emfs. The total internal resistance is the sum of the individual internal resistances. The same current flows through each battery.
The terminal voltage is the sum of the individual terminal voltages. Kirchhoff's loop rule gives the current.
Although the series connection increases the supplied voltage, it also increases the equivalent internal resistance.
The equivalent terminal voltage can be generalized for N batteries in series.
When two batteries with identical emfs are connected in parallel to a load resistor, the total emf is the same as the individual batteries' emfs.
Applying Kirchhoff's junction rule at the common node, Kirchhoff's loop rule for loop 1, and for loop 2, the equations are solved to determine the load current via the equivalent resistance. Thus, the terminal voltage is obtained.
The parallel connection reduces the internal resistance and can produce a large current.
The equivalent terminal voltage expression can be generalized for N batteries in parallel.
27.8:
Multiple Voltage Sources
Generally, a single battery is not enough to power some devices. In such cases, batteries can be combined in two ways: in series or in parallel.
In series, the positive terminal of one battery is connected to the negative terminal of another battery. Hence, the voltage of each battery is added to give the net voltage, which is increased because each battery boosts the electrons that enter it. The same current flows through each battery because they are connected in series.
Batteries are connected in series to increase the terminal voltage of the load. For instance, an LED flashlight may have two AAA cell batteries, each with a terminal voltage of 1.5 V, to provide 3.0 V to the flashlight. The disadvantage of series connections of cells is that their internal resistances are additive.
If the batteries are connected in parallel, the positive terminals are connected to each other, the negative terminals are connected to each other, and the load resistance is connected across those terminals. Voltage sources in parallel are chosen so that they have identical EMFs. The total EMF is the same as the individual EMFs of each battery. This configuration provides more current and has a larger capacity, thus powering the device for longer.
The parallel connection reduces the internal resistance and, thus, can produce a larger current. For example, some diesel trucks use two 12 V batteries in parallel. They produce a total EMF of 12 V but can deliver the larger current needed to start a diesel engine.
When batteries are connected in parallel, they usually have equal EMFs. The terminal voltage is equal to the EMF minus the equivalent internal resistance multiplied by the current. Since the equivalent internal resistance is smaller than the individual internal resistances, batteries are connected in parallel to increase the current to the load.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules; section 10.3; pages 463–465.