# Why does voltage increase in a series circuit?

I'm just starting electronics and I find myself not understanding voltage at all. In a simple circuit, let's say a 1.5V battery connected end to end it's easy to see how there's a 1.5V drop.

However what I don't understand is how a series of say 2 batteries, each 1.5V results in a 3V drop. My understanding is that a voltage of 1.5V pushes electrons out of the first batteries negative terminal and towards the positive of the 2nd battery. Then inside the 2nd battery there is no physical interaction between the anode and cathode. Otherwise batteries would be complete circuits in and of themselves. So how is the 1.5V carrying over to the 2nd batteries negative terminal to result in a combined 3V push?

Think of a water pump which can lift water to a height between inlet and outlet of $$1.5\,\rm m$$.
Putting two of these pumps in series results in the total lift height of $$1.5\,\rm m$$ (pump $$1$$ ground level to $$1.5\,\rm m$$) $$\bf \large +$$ $$1.5\,\rm m$$ (pump $$2$$ height $$1.5\,\rm m$$ to height $$3.0\,\rm m)$$ $${\bf \large =}\, 3.0\,\rm m$$.

And so it is with batteries in which an electrochemical reaction maintains a constant potential difference across the terminals of the battery.
Thus, battery $$1$$ raises the potential from $$0\,\rm V$$ to $$1.5\,\rm V$$ and battery $$2$$ raises the potential from $$1.5\,\rm V$$ to $$3.0\,\rm V$$, a total of $$3.0\,\rm V$$

• Good explanation! Commented Jun 8, 2023 at 0:02
• The water pipe analogy never fails! Commented Jun 8, 2023 at 20:06

Then inside the 2nd battery there is no physical interaction between the anode and cathode.

I don't know what you mean by "no physical interaction", but inside the battery there is a chemical reaction going on that maintains a 1.5 V difference between the anode and the cathode (provided the current flow through the battery is not too great).

This isn't any different for the first battery or the second battery.

And the second battery doesn't "know" what the first battery is connected to. It can only maintain a relationship (1.5 V difference) between its anode and its cathode.

• by no physical interaction I meant that there's a separator between the cathode and the anode so the electrons from one can't directly flow to the other. right?
– KAT
Commented Jun 7, 2023 at 3:55
• @KAT, they are connected through the cell itself, but that won't allow current to flow from cathode to anode unless there's an external voltage applied that exceeds the battery voltage. Commented Jun 7, 2023 at 5:21

You are correct that electrons can't flow between cathode and anode: the electrolyte contains no free electrons. Instead, the electrical current in the battery is carried by ions, usually positive ions moving with the current, rather than negative electrons moving against the current. In an electric circuit, the current is the thing you should track, not electrons, since electrons are not always the current carriers.

Yeah, cations and anions moving opposite each other like cars on an electric freeway.

Simply put, though, voltage is measured in potential difference which is additive in series. Easily provable mathematically as well experimentally as your voltmeter will tell you so. As apples roll down a hill at a particular incline, when you double the inclined angle or add the same amount again of voltage, you are doubling the potential difference. So the increase of potential difference in a linear fashion gives you a proportional increase in voltage that turns out to be additive since get proportional voltage and velocity in that metaphor. There is an energy gradient in the case of voltage and an gravity gradient (potential energy - PE) in the case of the apple since falling bodies have a propensity to go from high PE to low PE.

Because potential makes all the difference in the world, it even makes the world go round! That's why! I'm here all week!