# Q & A: Teaching about Batteries in Series

Q:
I am taking a basic electricity class and I am trying to find a good analogy to explain why the voltage of batteries in series are added together. What is the reason that the voltage is added together instead of staying the same as just one of the batteries?
- Chris (age 24)
Westwood College of Aviation Technology, Broomfield, CO, USA
A:
Chris -

I'm assuming you know this already, but I'm going to try to give you the simplest explanation possible.

Charges in different parts of a circuit have varying levels of electrostatic potential energy (voltage). Any parts of the circuit connected just by wires (ok, pretend we're using ideal wires with no resistance) have the same level of potential energy. What a battery does (by using the chemical energy stored inside of it) is to take electrons from one side of the battery with a certain amount of electrostatic potential energy and move them to the other side, giving them more electrostatic potential energy. There's a limit to how big this electrical potential difference can be, because it can't get bigger than the drop in chemical potential made when each electron goes from one side to the other. Otherwise it would be as if water flowed uphill. That limit is the battery voltage. So long as the current flow is low enough, each electron sees nearly the same chemistry as when there's no flow, and the voltage will be nearly the same as when there's no flow. Of course, when the flow gets very large (say if you accidentally short the battery) the chemical composition of the battery changes and the voltage drops, so each battery has a maximum current it can supply at nearly its rated voltage.

If you put the batteries in series, then the electrons pick up more potential energy as they go through each battery. For example, pretend you had three 9V batteries lined up in series. If we say that our electrons have 0V of potential energy at the beginning, then they have 9V after the first battery, 18V after the second, and 27V after the third - they gain more energy at each step.

If you put the 3 batteries in parallel, a third of the electrons goes through each battery. But like I said before, it doesn't matter how many electrons go through a battery (so long as it's not too much) - it treats them all the same way. Since each electron only goes through one battery, its potential energy is only increased by 9V (not 27V).

A nice analogy to this is a grain elevator. Imagine that a bunch of grain is moving along a conveyor belt and it comes to a grain elevator that moves it up 9 feet. This gives it more (gravitational) potential energy - it has further that it could fall. Then it comes to another 9 foot elevator and another. At the end it's all 27 feet up. The flow of grain up the elevators would be just the same as for one elevator, but it would go higher., just as batteries in series can't supply more current than ones in parallel, but they do supply more voltage. But if the grain went up 3 elevators placed in parallel then after the 3 elevators, all of the grain would only have gone up 9 feet. Of course, the 3 elevators in parallel could carry more grain, just as batteries in parallel can supply more current. But the height it was carried to would be just the same as for one elevator, just like the voltage of batteries in parallel.

Hope this helps.

-Tamara (w. mike)

(published on 10/22/2007)

## Follow-Up #1: Changing the voltage on an electric toothbrush

Q:
If I were to connect two 9V batteries in series to a small DC motor (electric tooth Brush) would I increase the rounds per minute of the motor or would it remain the same?
- Brendon
New Zealand
A:

I'm guessing that you mean a toothbrush designed to work with a single 9V battery. If you apply 18 V to it with your series batteries, about twice as much current will flow. The power input (voltage times current) is then four times larger than normal. Most of that power turns to thermal energy, heating up the motor. My guess is that the motor will overheat and burn out quickly. Probably it will turn faster briefly first.

Mike W.

You can try this with less risk to your electric toothbrush by lowering the voltage instead of raising it.  Use 1.5V batteries in series to add up to combinations less than 9V and see how your toothbrush behaves.  I’ll bet it’ll still work, but be slower.

Some equipment has voltage regulators on it, and possibly also frequency generators to ensure stable operation even when the input power supply varies in voltage over time, or isn’t quite what’s expected when the device was designed.  Many devices you can plug into the wall can handle 120V and also 240V electricity automatically.  I’ll bet your 9V battery-powered electric toothbrush isn’t anywhere near this sophisticated, and will respond to a different power supply voltage by speeding up or slowing down.  Don’t plug it into the wall -- you might get hurt.

Tom

(published on 10/22/2007)

## Follow-Up #2: How does a moving electron carry energy?

Q:
How does an electron carry the energy? Is it energized somehow? Thanks
- barry coe (age 58)