I found this

[Burgerman]

Which is a great way to graphically display the all important battery or cell resistance. And why it matters.

[Burgerman]

Which, means the size of that "resistor" (the batteries own resistance) determines the actual current the battery can produce and the amount that the voltage drops at a given current (load) or given charge rate. Even ignoring the chemical "surface charge" changes.

It is also why when charging some power is wasted as heat, and the real battery voltage is less than we measure while charging. And the reason that the battery isnt charged as soon as it reaches the set voltage, and why we have a CV stage that takes a further 8 hours. Because while theres still some current flowing, the real battery voltage is less than we measure at the terminals or charger. And why we have to wait till current falls (very very slowly) to almost zero. Or around 1/500th to 1/1000th of the Ah capacity.

[Burgerman]

The surface charge (the Peukert effect) is in addition to the resistance and far worse!

A lead battery is just some lead plates sat in an electrolyte. All the electricity generated comes from the bit where the water/acid elecrolyte contacts the lead plates. This interface is literally a few atoms thick. As you draw out power, the electrolyte in this few atom thick area is used up! The acid in this tiny area has its acid turn to lead dioxide and lead sulphate that coats the plates with a microscopically thin coating. The electrolyte in this super thin area is now just water. Which doesent conduct.