I was sent here by the folks on the physics stack exchange as they thought my question was more chemistry-related, but I am only a 10th grader and don't have a very strong chemistry background, so please be patient if I am not very proficient in expressing my question.
I was trying to figure out why parallel connected batteries don't add voltages, and the exceedingly common answer was that batteries act as sources of fixed potentials, not fixed fields. So my next step was to figure how they maintained a fixed potential - I discovered this answer which explains how batteries maintain a constant potential difference.
So what I understood was the field created by the batteries grows in strength as more charges are spewed out of the cathode. 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.
I have my doubts about this explanation - I thought potential difference had nothing to do with how many charges there were present, but rather that the battery added some amount of energy into electrons coming out of the cathode which created a potential difference that was used to do work in a circuit.
At this point I am confused about how a potential difference is created by a battery - is my past understanding correct or does charge density truly create voltage? If charge density does create voltage, what is the point of adding energy to electrons inside a battery (if the chemical reactions in a battery even "add" energy to the electrons)?
If charge density does indeed create voltage, how would that explain stuff like voltage drops accross resistance?
Note: I want to know what happens at the atomic level, not analogies.