Lee Hart on High Current Battery Use
Peukert and internal resistance are separate phenomena. Each has its own causes and effects on battery capacity under high current load.

Internal resistance: Internal resistance causes heating inside the battery. Higher currents cause more heating according to power = I^2 x R. The energy converted to heat is lost, and unavailable to the outside load.

In a lead battery, the internal resistance increases as the acid in the electrolyte gets used up (this occurs as the battery discharges). The resistance is low at full charge, and rises considerably as it discharges. It becomes almost an open circuit if 100% of the acid is used up.

The designer can vary the amount of excess acid in the electrolyte to use this effect to advantage.

With too little acid, the battery is acid starved and it approaches an open circuit when dead. This serves to automatically disconnect it from the load. If the battery is promptly recharged, no harm is done; but it may take an exceptionally long time, or exceptionally high charging voltage, to recover. You tend to see this with gel cells.

With too much acid, the internal resistance is extremely low, and stays reasonably low even when the battery is almost dead. This is good for starting batteries and other applications that require high peak currents. But the stronger acid when fully charged attacks the plates, causing grid corrosion and shortening life.

Interestingly, heat causes an increase in amphour capacity in many types of batteries (including lead-acid). There are atypical situations where shorting a cold battery battery to self-heat it will actually yield an increase in the current you can draw, even though fewer amphours are left.

Peukert effect: The Peukert effect is a consequence of the rate at which the chemical reactions can occur, to convert the battery's active materials into electricity. The reactants need to physically move together to react. In the case of a lead acid battery, one of the reactants is the sulfuric acid in the electrolyte. The acid molecules need to migrate to the surface of the plate to react with the lead. At high currents, the acid can't move fast enough, and the surface of the plate temporarily "runs out of electrolyte." So, the voltage falls, and the battery appears to be prematurely flat.

But it isn't! If you wait, or discharge at a slower rate, the remaining acid has time to move to the plate, and the reaction can continue. All the acid is still there, and all of it can react -- if given enough time.

The Peukert effect doesn't cause energy to be lost as heat, except indirectly by causing a higher voltage drop if you force a high current anyway.

An interesting way to demonstrate the Peukert Effect is to test a battery with two different loads. Let's say you have a 20ah (at the 20 hour rate) battery:

  1. Connect a 1 amp load for 20 hours. You obviously get 20 amp hours before the battery falls to 1.75v/cell (the definition of "dead").

  2. Connect a 20 amp load with a timer that cycles on 1 for second, and off for 19 seconds, over and over again. The average load is still 1 amp, so it still takes 20 hours to reach "dead." You still get the whole 20ah, even though you're discharging the battery at 20a.

  3. Connect a 20 amp load continuously. If this battery has a Peukert exponent of 1.23, it will fall to 1.75v/cell in about 30 minutes (Peukert's equation says 20ah = 0.5 hours x 20a^1.23).

    But that is only 20a x 0.5h == 10ah. There is still another 10ah left in the battery -- it's just that you can't withdraw it at the same 20 amps. Instead, connect a 0.5 amp load. It will take about 20 hours to reach 1.75v/cell again (0.5a x 20h = 10ah). You've gotten the full 20 amp hour capacity of the battery.

In this experiment, the time you can operate the battery at the 0.5 amp load will actually fall a bit short of the theoretical 20 hours. This is because the initial high current will have produced some I^2R heating, which will have been dissipated and lost over the 20-hour discharge.