Think of the energy in the battery as a thick, viscous fluid, like honey.
When you draw power from the battery, you siphon honey from the sides.
When the battery is full of honey, the big mound of honey quickly flows to touch the edges as you take honey away.
When the battery is nearly empty, the shallow film of honey takes a long time to spread out thin enough to touch the edges of the battery.
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[But instead of honey, it is more details, like “a degree of charge separation in an ionic solution separated by a semi-permable membrane” or something like that.]
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