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This is a very trivial question in my opinion, but I was thinking about what a battery would be classified as. In the physics world, batteries are often used to represent a voltage source.

I feel like that a battery should be considered a dependent voltage source since a batteries voltage is dependent on the amount of current the load draws within a certain amount of time. An ideal battery wouldn't have this issue. But to me, batteries aren't independent sources like power supplies, which will always supply a fixed voltage (as long as it is CV mode).

The question is do you think batteries are independent voltage sources or dependent voltage sources?

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there are many different battery models some can be as simple as a voltage source with series resistance some are more complicated.

You're correct in thinking that there is a dependent source in more complicated battery models the lifetime is dependent on the current that has already been discharge through the battery. Such as shown in the circuit below:

enter image description here.
Source: https://www.edaboard.com/showthread.php?214394-how-to-make-a-battery-model-of-NiMH-on-HSPICE

The model uses in RC circuit to model the capacity of the battery and the current withdrawn from the circuit.

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