Rechargeable battery technology is familiar to most people with phones and other portable devices. But larger batteries to power cars and homes are less well understood.

A rechargeable battery can be modelled as an ideal rechargeable battery in series with a parasitic resistance. This resistance dissipates power dependent on the square of the charging current. Now given that electric cars typically have a range of only 200 miles, it is quite tiresome to stop every 150 miles and recharge it for 300 minutes (5 hours). It would be much nicer to charge it in 30 minutes, or even 3 minutes, to make it more like a gasoline (petrol) powered car. But is there a downside to this?

We are going to assume for simplicity that a rechargeable battery is charged by a certain number of ampere-hours. If you double the current (measured in amperes) you halve the charging time.

Consider what happens to the energy loss in the parasitic resistance in the battery if instead of charging in 300 minutes you use a hyper-charger and do it in 3 minutes (for the same battery type).

Author: Leslie Green