## Wednesday, September 28, 2011

### Battery Math, Part II

DISPOSABLE BATTERIES
Batteries are tiny chemical generating plants that produce electrical current at a given voltage while they proceed to consume themselves via chemical reactions. Yesterday I reviewed a battery tester that might help me save money on replacement batteries. I'm thinking that our elementary math skills are more than enough to tackle the intellectual challenges posed by "dry cells."

We consume and discard hundreds of millions of batteries a year without thinking too much about them, except "Didn't I just replace these recently?" If we get fed up and decide to switch to rechargeables (Tomorrow's blog!) we will be thinking "Boy, these rechargeable batteries are expensive!"

These are the most common battery sizes in the US.

(For a full discussion and range of battery data, refer to the battery manufacturer's web pages or this Wikipedia article.)

BATTERY CELLS
Batteries are usually made up of one or more generating units, known as cells. Each cell produces between 1.25-3.0 volts, depending upon their chemistry. These cells can be stacked inside a larger case, or inside the user's device if more power is required. The full battery designation identifies the size, shape and terminal layout of the battery and its chemistry.

For example, a CR2032 battery is always LiMnO2 chemistry, 20mm in diameter, 3.2mm in thickness and always produces 3 volts. I know from physical inspection that a CR2016 battery is thinner (1.6mm) but it's the same diameter and produces the same voltage.

CHEMISTRY (NOT SIZE) DETERMINES VOLTAGE
The voltage produced by a battery cell depends on its chemical makeup, not its size.
• NiCd (nickel cadmium) and NiMH (nickel metal hydride) produce about 1.25 volts per cell
• Mercury batteries produced about 1.35 volts
• Zinc-air batteries produce about 1.4 volts
• Carbon-zinc "regular" batteries produce about 1.5 volts
• Alkaline batteries produce about 1.5 volts
• Zinc-manganese dioxide produce 1.5 volts
• Zinc-silver dioxide produce about 1.55 volts
• LiMnO2 (lithium manganese dioxide) produce about 3 volts per cell
• 9 volt LiMnO2 (lithium manganese dioxide) produce about 10-11 volts when new
NOTE: This might be more clearly displayed in a table. I'll let you do that on your own.

SIZE DETERMINES CURRENT
If you put multiple batteries + end to - end (in series), as in a flashlight) you get higher voltage. This will give you a brighter flashlight.

If you use larger batteries (or put several in parallel) they can produce more current. This will allow a flashlight to run for a longer period of time.

• D cells produce about 16500mAh on a load of 4.7Ω resistance, at 70°F
• C cells produce about 7800mAh on a load of 10Ω resistance, at 70°F
• AA cells produce about 2450mAh on a load of 24Ω resistance, at 70°F
• AAA cells produce about 1120mAh on a load of 160Ω resistance, at 70°F
• CR2032 cells produce about 200mAh on a load of 15,000Ω resistance, at 70°F
• LR44 cells produce about 150mAh on a load of 625Ω resistance, at 70°F
• 9 Volt cells produce about 565mAh on a load of 510Ω resistance, at 70°F
Notice that the specifications imply that each battery is happiest with a different kind of load. The battery is chosen to suit the device it's powering!

I found an elaborate discussion about battery life with two similar (but unequal) devices using the same battery. Here's a simplified, elementary-math version of the discussion:

An SR44 cell has a 150 milliamp/hour rating. If we assume we can use up 90% of its working life, we get 150 x  90% = 135 milliamp/hours. That's equal to 135,000 microamps.

Well-designed Device A draws 4 microamps when working and 2 when resting. If used 1 hour/day and resting 23 hours/day, the calculation for battery life is:

(1 hour x 4 microamps) + (23 hours x 2 microamps) = 50 microamp hours/day. Battery life is 135,000 ÷ 50 = 2700 days = 7.39 years

Poorly-designed Device B draws 18 microamps when working and 17.5 when resting. If used 1 hour/day and resting 23 hours/day, the calculation is:

(1 hour x 18 microamps) + (23 hours x 17.5 microamps) = 420.5 microamps per day. Battery life is 135000 ÷ 420.5 = 321days = .87 years