I start by showing a typical discharge curve of a 20Ah LiFePO4 battery. Then I build a test set-up with an 8 meter cable between the battery and a CBA IV battery tester. I use alligator clips and undersized wire to push the current draw to the maximum it can handle with that mess in between. It could pull 8A and the voltage at the tester dropped to 0.5/0.6V (the lowest the CBA IV will allow) and ran this for almost 2.5 hours until the battery was depleted. I then show the results of the amount of Ah and Wh drawn at the end of the test.
In the end, this shows that even with massive losses in the wires and connections (80%!) the Ah rating at the end remains the same and is a good indicator for the capacity of the battery. In other words: voltage, losses, etc. don’t matter when you test Amp-Hour capacity – the current flowing is the same everywhere in the circuit. Naturally, the measured Watt-Hour (Wh) at the end of the test are not, because of the losses in the set-up – if you want to measure Watt-Hours, you need to account for losses. This is one of the reasons why battery capacity is given in Amp-Hours: the amount of current a battery can push in a circuit for a given amount of time.
Remember that Wh is a measure of energy, Ah is a measure of charge. Batteries are specified at both these days, but Ah is easier to test because of the above.