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In my question I'm neglecting the impact of discharging.

I'm trying to make sense of Watt's law: $$P=IV.$$ I always thought that the voltage and the power of a battery were constant features that reflected the strength of the chemical forces inside the battery. As for the current, I thought that it was determined by the voltage as well as the arrangement of the circuit. Now, from Watt's law, something about this view must be wrong, as according to it current varies from one circuit to another, whereas voltage and power don't. I suspect that it must be something about my understanding of what the power of a battery is. So could someone explain to me what the power of a battery is and what it tells me about the circuit and the battery? Is it constant for a given battery, or does it vary from one circuit to another? Thank you all!

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  • $\begingroup$ This may help. $\endgroup$
    – Stuti
    Commented Jan 18 at 18:11
  • $\begingroup$ Some people call this a battery: amazon.com/dp/B091BSG9GS But, it actually is much more. It is a combination of a battery, and a "smart" charger for the battery, and a switch-mode power supply that provides a regulated (constant) 5V to an external device, even as the voltage of its internal battery decreases with the state-of-charge. "Batteries" like that sometimes are labelled with a capacity in Watt hours. Is that the kind of battery you meant? Or, did you mean something more like this? amazon.com/dp/B00MH4QKP6 $\endgroup$ Commented Jan 18 at 22:40

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If a battery has a power specification, it's a maximum rating. The maximum power the battery can supply without overheating or otherwise being damaged and without its output voltage dropping below specifications.

The actual power it supplies in use depends on the current drawn by the circuit, which is, as you say, "determined by ... the arrangement of the circuit."

That said, batteries are usually characterized by an equivalent series resistance (aka internal resistance) and possibly a discharge curve that shows how the terminal voltage will drop when the battery is discharged at different current loads. Power as such is not usually specified.

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    $\begingroup$ To this (otherwise correct answer), I would add a temperature dependence tied to the particulars of the chemical reaction powering the battery. $\endgroup$
    – user121330
    Commented Jan 19 at 5:35

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