# Why do batteries in series add up in voltage? (real explanation requested)

This has been asked before but I need to be clear on what kind of answer I'm looking for. All the other posts are just water analogies.

I get it, you add the voltages together. And there's a magical unicorn pumping it aka the water pump and hill-tilts on hill-tilts with meatballs rolling on meatballs.

Seriously though, how does it REALLY work? I don't need any analogies to tell me WHAT it does, because I can sum that up in a simple formula. And I really really do not want any false quasi-explanations.

If you must use analogies to convince yourself of its workings, you simply do not understand it. Electricity is NOT water.

So if we have two batteries of the same chemistry in series, why do we get higher Fermi levels? The chemistry shouldn't support that, the chemistry has a set Fermi level: you get 1.5V of some materials. But somehow, by having them in series you get e.g. 6V. How does that work in terms of particle physics? That is very crucial here: how do we chemically and electrically get that higher fermi level.

• The Fermi levels are relative so just because you set the potential of the negative terminal at +200 V relative to the ground that does not affect the potential difference across positive and negative terminal of the cell. The work done in taking charge between the negative and the positive terminal stays the same. If you have cells in series then each cell does its bit in producing a potential difference across its terminal which overall will lead to a larger potential difference across all the cells. – Farcher Jun 5 '17 at 7:29
• en.wikipedia.org/wiki/Fermi_level – user126422 Jun 5 '17 at 7:46
• Yes, that's what I said. I mentioned that 1.5V+1.5V+1.5V+1.5V=6V. You just repeated that by saying that "they add up". That's not explaining anything. Yes, I'm assuming that Fermi levels are relative already, that's a premise of my question, and I'm saying that that the potential difference is adding up, we have established that. But how is it getting there physically? That's the question. – PhysicsLady2013 Jun 5 '17 at 8:00
• I don't really understand the need to ask questions in such an aggressive way... – valerio Jun 5 '17 at 9:10
• -1. I think your question is not clear. @Farcher points out that each cell produces a PD across its own terminals. You agree with this. It follows that in a series connection of cells the PDs will add up. I do not understand why you find this explanation unsatisfactory, or why you think the 'real' explanation is related to Fermi levels. ... As Toby's answer shows, the addition of potential differences in series is fundamental to physics, not only to batteries, and is a consequence of the conservation of energy. You cannot get more fundamental than that. – sammy gerbil Jun 5 '17 at 9:25

## 2 Answers

Voltage is a potential difference. The difference here is important.

Firstly ill explain potential energy in general. Lets look at gravitational potential (which is behaves in the exact same way). It is given by $mgh$. But what is $h$, is it measured from the centre of the Earth, the surface, the floor, the shelf? The truth is, it doesn't matter. When you use it, all that matters is the difference in potential energy, not the actual value. This means that energy is only defined up to a constant: $mgh$ will work just as well as $mgh+392.5$, the constant doesn't matter.

I know you said not to use analogies but gravity and electro-statics are very similar (look at coulombs law and newtons law).

A potential is just defined as the potential energy per unit charge (for electrostatics) or mass (for gravity). So almost anything I say about potential energy will be true for potentials in general.

So the battery doesn't create 1.5v, there is no such this as a set potential of 1.5 volts. What it does create is a potential difference of 1.5 volts.

Lets say I have a pole of 1.5m. The potential difference between the ends, if held vertically, is $1.5gh$. If I move that up or down the potential difference doesn't change. I can stack several on top of each other and we can, quite obviously, just add the lengths.

batteries are no different - mathematically a battery is just the same as holding a ball slightly higher up.

In short, potentials/energy is only ever a difference, there is no universal 1.5v.

Really good question by the way. If you want to know more, look at an a-level physics book on gravity and electro-statics. It should also have a section on the similarities and differences and you will see then how energy really works.

Here's my hypothesis. Assume batteries A->B. Orientation: + -

The drain from A to B is no mystery. A- and +B gets into equilibrium, both change by a half in potential. That does something chemically (which I'm curious about) which drops +A 1/2 in potential to have some kind of chemical balance with A- (that just dropped). Same happens for B, and you get an extra 2*(1/2)=1 (battery "unit") potential difference.

To clarify, the chemistry of the battery is such that there's a set (e.g. 1.5) potential difference as a minimum; anything less and it's imbalanced and reacts and creates a 1.5 difference.

I will have to verify this theory.