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I recently discovered this answer which explains how batteries maintain a constant potential difference. So what I understood was that batteries spew out electrons on the cathode, and by doing this they create an electrical field. When this field becomes strong enough, it stops the redox reactions occurring in the battery. This causes the potential difference to become constant as there is no more charge accumulation.

The last part didn't really make sense to me, I thought voltage had nothing to do with the charge density. I thought some amount of energy is taken from the electron during the reactions occurring in the battery, creating a potential difference (aka voltage). It wouldn't be too far-fetched to make some connection to charge density as well, but I don't have the knowledge to make such conclusions. So is my original understanding of how a potential difference is generated correct or does charge density also play a role?

Kryptic Coconut
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    Your title says, "...in a circuit," but your question seems to be specifically about how batteries work. Maybe you could change the title to make it more clear. On the other hand, that change might get your question kicked over to the chemistry Stack Exchange. On the gripping hand, you might get a more comprehensive answer from chemists anyway. – Solomon Slow Mar 02 '23 at 17:24

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Charge density plays an indirect role and can be calculated once the size, geometry, and materials that encompass the charge are specified. Once you specify the geometry (e.g. parallel fixed metallic plates), the size (e.g. area A, separated by distance d), and the materials (e.g. air) then charge density can be related to voltage. In the example of a parallel metallic plates $$V= \frac{Q}{C} = \frac{Q}{\epsilon A/d} = \frac{Q}{A} \frac{d}{\epsilon}$$once the material (given by it's permittivity $\epsilon$) and geometry are known, V is proportional to charge density (Q/A) on the plates.

Once the voltage due to charge accumulation reaches a certain level, the electrochemical reaction is incapable of supplying enough energy to an electron to increase this voltage, and the reaction mostly stops. The reaction must stop, because if it didn't, charge accummulation would continue and the voltage would increase without bound.

A battery cell maximum voltage is dependent on the specific electrochemical reaction driving it, because that specific reaction determines the amount of energy supplied to each electron. But the reaction is started and stopped by voltage which is a product (literally) of geometry and charge density.

AndyW
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  • So voltage is only created by charge densities and is not a result of energy being taken out of electrons? In which case how does it make sense that voltage (a product of charge density) drops in a circuit with resistance, as the charge density (amperage) stays the same throughout a circuit? – Kryptic Coconut Mar 02 '23 at 17:28
  • Yes. Voltage in a battery cell is created by charge density.Current (measured in amperes) is not the same as charge density. Current is charge per unit time (Q/t). And voltage dropping in a circuit is a verbal shorthand for a variety of unrelated phenomena, and not necessarily even always true. The entire explanation requires more characters than available in a comment. – AndyW Mar 02 '23 at 17:39
  • Thanks, can you point me toward any resources that can help me understand this further? – Kryptic Coconut Mar 03 '23 at 02:38