How does the voltage source provide energy in a circuit?

I understand that a voltage source drives the current to flow from the terminal with lower potential to the terminal with higher potential. However, if the electrons are gaining potential energy then how can it also be supplying energy to the circuit?

• Does it make sense to you that if the battery provides high energy electrons into the circuit, and collects low energy electrons on the other side, that energy must have gone into the circuit? – Cort Ammon Aug 1 '17 at 23:54
• Yes! So what I'm confused about then is what that potential is referring to? Is it not potential energy? – Annie Aug 1 '17 at 23:57
• Yes, it is potential energy. The electrons entering the circuit have more potential energy than those leaving. It's like the electrons entering the circuit are at the top of a hill, and roll down to the bottom of the hill, doing work along the way. Except in this case, instead of a hill and a gravitational field, we have an eletromagnetic field which causes electrons near one terminal of the battery to have more electromagnetic potential than ones near the other end. – Cort Ammon Aug 1 '17 at 23:58
• Ahh, that might be the source of confusion, and I may have worded my comment imprecisely. The numbers we use for electromagnetic fields are all based around positive charges. We would say that the EMF near the source of the electrons has the "lowest" value, but because electrons have a negative charge, that is the highest potential energy for the electron. They then move towards the point where the EMF is "highest," which because the electron is negative, is actually the lowest potential energy. – Cort Ammon Aug 2 '17 at 0:05
• Glad you got Cort's explanation. It took me a long time to understand the positive charge CONVENTION thing when I first met this idea. My first science books were all worded in terms of electron flow, so it really threw me when I learnt about the mysterious "conventional current" notion. Our wording is back to front because the language developed in the 18th and 19th centuries, I think, but it was certainly well before we knew that current in circuits was carried by electrons with negative charge. So we only had 50% chance of "getting it right". – WetSavannaAnimal Aug 2 '17 at 1:08

However, if the electrons are gaining potential energy [...]

Actually, they are not.

[...] then how can it also be supplying energy to the circuit?

There indeed is a reduction in potential energy, transformed into kinetic energy.