When it is connected to its maximum load. Or perhaps I don't understand the question. What type of battery (flashlight, emergency light, car, boat, UPS storage, etc.)?
Charles E. Beck, P.E., Seattle
Comments based on 2017 NEC unless otherwise noted.
In car batteries I was told the produce their most power in the summer when it's hot and you don't need that cranking power. And they produce the least power when it is cold and you do need it to turn over a cold engine.
In general chemical reactions happen faster when things are warmer. So an electrochemical cell (in a battery) will have lower internal resistance, and can deliver higher current when warm.
There are second order changes in battery voltage versus temperature, but the big one is the change in rate that current can be delivered.
The maximum power that a battery can deliver is when it is connected to a load that has the same resistance as the internal resistance. The output voltage is half the open circuit voltage, and the product of voltage and current is maximum.
If you do not have knowledge of calculus, then a way to see how power in the load varies as load resistance varies with constant source voltage and constant source internal resistance is to perform calcultations for incremental load resistance changes and calculate the load power. You will find that this maximum power transfer occurs at Rload = Rinternal.
Edison understood that a practical power distribution system could not be based on maximum power transfer as many others thought in 1879. Rather Edison understood that a low source impedance and moderately constant voltage distribution system was required.
If you do not have knowledge of calculus, then a way to see how power in the load varies as load resistance varies with constant source voltage and constant source internal resistance is to perform calcultations for incremental load resistance changes and calculate the load power. You will find that this maximum power transfer occurs at Rload = Rinternal.
Edison understood that a practical power distribution system could not be based on maximum power transfer as many others thought in 1879. Rather Edison understood that a low source impedance and moderately constant voltage distribution system was required.
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For practical distribution, the goal has to be not to transfer the highest possible amount of power, regardless of the fact that it wastes half of the available energy, but instead to go for a combination of high efficiency and reasonable power.
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