If you have kids, you probably know this already, but lots of stuff needs batteries. Remote control toys, Wii remotes, laser pointers (well, that is for me), flash lights, even Nerf guns. For me, I have found the best place to pick up batteries is at one of these “dollar” stores. Sure the batteries are cheaper, but are they any good? Who knows. Let’s find out.
The first way to look at the quality of a battery is to see how much stored energy is in it. How could you measure this? Well, here is how I did it. I took a battery and connected to a light bulb and let it run for as long as it could. Like this:
With this setup, I can measure both the current ( I ) from the battery and the electric potential ( ΔV ) across the battery. At any given instant in time, the power from the battery will be:
Power tells me how fast the energy is changing, but not the total energy in the battery. In order to find the total energy, I can write the power like this:
If the current and the change in potential were constant for the whole time interval (Δt), this would be a fairly straightforward calculation. Alas, these are not constant. So what do I do? I cheat. If I instead look at a very short time interval, the current and potential do not really change too much. This means that I can reasonably calculate the energy during this short time. Then I just need to do this a whole bunch of times to get the total energy.
Adding up a whole bunch of small pieces is called “an integral”. In this case, I won’t use calculus to evaluate an integral since I don’t know a mathematical function for the power. Instead I will do it numerically with the following formula (by “I will do” I really mean “make a computer do”):
And that is it. The total energy that the battery produced.Measuring Energy
Vernier makes both a current and voltage probe for the LabQuest system. Collecting data was fairly simple (even though each battery would take quite some time). Here is the data from LoggerPro (Vernier’s software):