Additional Math Pages & Resources

Thursday, September 29, 2011

Battery Math, Part III

Yesterday we looked at common, household batteries. Today we will investigate rechargeable batteries and learn how they differ from regular cells. We'll keep our analysis at the elementary math level, which is all that most of us possess. I think the math we teach in Excel Math curriculum gives most people all the skills they need for life's math challenges.

A rechargeable battery means the chemical changes that occur during use (discharge) can be be readily reversed when electrical power (charge) is applied. In contrast, regular batteries involve irreversible chemical changes.
  • In rechargeable NiCad batteries, Cd(OH)2 and Ni(OH)2 formed when the cell is working are converted back to Cd and NiOOH when the cell is recharged.
  • Regular Carbon-Fluoride-Lithium batteries (used in cameras) generate energy by converting (CF)n and Li metal to Carbon and LiF. The (CF)n is not recreated when the battery is charged, but the cell decomposes, creating fluorine gas (unsafe and unusable).
  • Every battery variation uses different chemistry, and these are readily available if you search the web. As I'm not a chemist, we will stop with just the two examples above.

A rechargeable battery should be able to discharge and charge thousands of times without degrading, overheating or short-circuiting. Developing these batteries is much more difficult than creating a regular battery, and the quality of the materials is more important. That's why they cost so much to purchase! However, your overall cost of operation should be lower IF you use your battery-powered device regularly.

Another factor in the cost of batteries is the capacity (or current-generating ability). That is measured using a unit called milliamp hours. This is partially dependent on the quality of the chemistry of the battery, and also on the quantity of materials inside. If you weigh batteries with different ratings, you will find that the highest-rated models weigh the most. Some battery cases are half-empty.

The capacity and quality of rechargeable batteries affect the price in unpredictable ways. I just compared about 20 different brands of batteries, all from the same Internet vendor, all in 4-packs. After checking some reviews, I decided to stick with brand-name batteries in my comparison.

The range of capacity on rechargeable AA batteries runs from under 1200 up to 3100 milliamp hours. The weights ranged from 15 to 30 grams. The power voltage varies from 1.25 to 1.65 volts depending on the chemistry.

When you see the chart below, it is readily apparent to you which is the best deal? Does my display present the relevant information in a clear and understandable fashion? [click on image to enlarge]

Despite the ratings printed on the side, many batteries cannot be charged to their full rated capacity, nor do they hold the charge and provide power to your camera, flashlight, etc. in the same way. For this reason, you should use matching sets (age, brand) when powering a device.

There are many different sorts of battery chargers, and they are evolving with battery chemistry. If you have a 10-year-old charger, it might be time to look into a new one. Maybe we will do that in tomorrow's blog post.

Or in English, Let the buyer beware! I suggest that you read reviews on Amazon or your favorite rating site BEFORE you buy a load of expensive rechargeable batteries. There are many disappointed customers of bargain-price batteries.