# What is the theoretical reasoning behind calculating emfs in series or parallel?

First off, I did some research on my own but the answers weren't satisfactory. The analogy of the water pump makes zero sense as I see no way how "Potential" is even comparable with "Dynamic Pressure". This seemed plainly improvised.

So I have my own ideas but I don't know how much accurate it is.

Let's talk about these two simple circuits:

A. 3 cells of equal emf $\epsilon$ connected in series, and discharging through a resistor with resistance $R$. (Note: I am not using any values. I'm interested in the theory not the math.)

B. 3 cells of equal emf $\epsilon$ connected in parallel, and discharging through a resistor with resistance $R$.

My Current Ideas. As far as I have found, the reason is more chemical than physical. Inside the cells, spontaneous redox reactions are happening, which are in equilibrium. A cell dies out when the rate of oxidation equal the rate of reduction. Hence the potential is somehow proportional to the difference of the rates of oxidation and reduction.

In case A, we have the batteries like this: [+ P -][+ Q -][+ R -], where P,Q & R have the same emf $\epsilon$. Electrons get transferred between P-Q and Q-R, which would cause a lack of anions in P and hence a drop in the rate of oxidation. So this shifts the equilibrium and causes more cations to form at a faster rate. Vice versa in R. So probably that's how the emf increases and it turns out to be the algebraic sum (internal resistance negligible). Using the same thoughts on B, I found that the arrangement does not allow the equilibrium in the cell to shift in any way so overall emf remains same.

The Kinds of Answers I need. I'm looking for a better explanation than mine, maybe something related to electric and potential fields in wires would be better, or how my idea is correct or wrong? Will two A.C. supplies in series behave similarly? You get it right? I'm requesting an existing theory on this matter. Thanks in Advance. :)

• Are you interested in electrochemistry or physics of electrostatic potentials? The latter does not depend on the former, only the other way round. Commented Apr 26, 2015 at 22:45
• I'd definitely be more interested in a physics-based answer. I brought in chemistry cause I didn't find much physical reasoning. Well I know potentials linearly add up in classical electrostatics, and it'd be great if the case was this simple.
– Foon
Commented Apr 27, 2015 at 5:53