# How do the voltage of DC voltage sources and capacitors add up in series

I can't quite get my head around how the voltage adds up in a series circuit. Not the mathematics, I mean, but the reason down to the charge on plates and the actions inside the battery. Also, if I were to charge two capacitors separately from a same 1.5 V battery (first charging the first, then removing it, then charging the other). And then combine them in series (like ---| |-----| |---- ). Would the charge across them be 3.0 V (ideally speaking)? If so, what would happen on the plates before and after combining them? Thanks.

I can't quite get my head around how the voltage adds up in a series circuit.

Voltage is always a difference between the potential at two points.

If the difference in potential between point a and point b is +10 V, and the difference between point b and point c is +5 V, then the difference between point a and point c is +15 V. It makes absolutely no difference what kind of components are connected between points a, b, and c.

Just like if a hilltop nearby is 100 feet above where I'm standing, and another larger hilltop is 200 feet above the first hilltop, then I know the second hilltop is 300 feet above me. It doesn't matter what kind of roads or stairways or rope-slides are forming a path between me and either of the hilltops, or between the two hilltops.

if I were to charge two capacitors separately from a same 1.5 V battery (first charging the first, then removing it, then charging the other). And then combine them in series (like ---| |-----| |---- ). Would the charge across them be 3.0 V (ideally speaking)?

Yes. You don't even have to charge them one after the other; you can charge them at the same time. That's the principle behind a switched capacitor voltage converter circuit.

If so, what would happen on the plates before and after combining them?

Nothing in particular happens. Each individual capacitor still has the same 1.5 V across it that it had before, so it has the same charge on its plates.

• But what happens "inside" the batteries when they are in series? And what happens between the two capacitor plates connected with each other end to end with the small wire, when capacitors are being discharged? Oct 7, 2015 at 20:35
• The same as what happens when current flows through those devices and they aren't connected in series. For capacitors, some electrons build up on one plate and repel electrons from the other plate, which is a microscopic view of a current (in the opposite direction of the electron flow). For batteries, a chemical reaction occurs which produces excess electrons on one plate and an electron deficit on the other (relative to the fixed positive charge in the metal). Oct 7, 2015 at 21:10