The Amp Hours confusion

When it comes to batteries, the energy capacity is often given as Amp-Hours. For smaller batteries like those used in portable devices, this often shows up as milliamp-hours. This can be misleading because a proper measure of energy needs volts as well as amps over time. An example is the auxiliary batteries available for charging cell phones. Here’s an example: iXCC 8000mAh Compact Power Bank – Portable External Backup Charger Battery Pack for Smartphones, MP3 Players, Tablets and Other Devices(Silver) that Amazon had as a lightening deal until 2/22 at 1300z.

This example does specify “8000 mAh external Li-polymer rechargeable battery” which means that the voltage in question is 3.7 nominal so the actual energy capacity is 8*3.7 or 29.6 watt hours. A low end phone has an internal battery listed as 2100 mAh or 8.0 Wh. That means this particular power bank has enough energy to recharge the cell phone about 3 times before it is depleted.

What confuses things? Both the power bank and the cell phone charge at 5 volts. If you use the rather unusual watt hours rather than the mAh there’s no confusion but the power bank is rated in mAh and you have to look close to realize that that rating is for an assumed battery voltage that is 26% less than the voltage the power bank provides for charging.

This measurement confusion can get even more interesting when talking about battery banks or about batteries that have significant voltage changes over their useful discharge cycle. This can complicate the analysis about replacing lead acid batteries with lithium batteries in a car or RV, for instance. Lead acid cells are nominally 2 volts. Lithium cells are 3.7v unless they are LiFePO4 which operate at 3.2v. Then you can look at the discharge curves and get an insight into why calculus and integration might be useful ….

Fun stuff. The lesson is to use proper units and don’t confuse current, power, and energy.