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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?

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    $\begingroup$ 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? $\endgroup$ – Cort Ammon Aug 1 '17 at 23:54
  • $\begingroup$ Yes! So what I'm confused about then is what that potential is referring to? Is it not potential energy? $\endgroup$ – Annie Aug 1 '17 at 23:57
  • $\begingroup$ 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. $\endgroup$ – Cort Ammon Aug 1 '17 at 23:58
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    $\begingroup$ 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. $\endgroup$ – Cort Ammon Aug 2 '17 at 0:05
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    $\begingroup$ 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". $\endgroup$ – WetSavannaAnimal Aug 2 '17 at 1:08
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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.

It all comes down to the answer to your first line:

I understand that a voltage source drives the current to flow from the terminal with lower potential to the terminal with higher potential.

This is correct. But. Two types of charges exist. A positive and a negative. What would happen if you suddenly replaced all negative charge-carriers with positive charge-carriers?

The flow will be opposite. The battery is creating a high negative net charge at one terminal, which is the reason that electrons are repelled and want to move away from this end towards the other end. Had they been positive, then they would be attracted to this terminal instead. The current flow would be opposite. In some circuits (most common ones with metallic wiring) the current flow is made from electrons. In others (semiconductors, ionic solutions, etc.) it is made from positive charges (or a mix). So it is not an irrelevant consideration.

So, which terminal is the "high-potential" one and which is the "low-potential" one? You are thinking, that a charge flowing from a low to a high potential must gain energy - but clearly, electrons moving one way or positive charges moving the other way, gives the same final result - energy will be spent as they move through the circuit in the same manner. They are two equivalent ways of thinking of the circuit.

Which do we call high and which low potential? People in the past have made the decision to always name it as if the charge-carrier was positive. The terminal (or point in the circuit) of higher potential is thus the terminal positive charges will move away from - and a "lower potential" point is a point that attracts positive charges. Regardless of what the actual sign of the charge is. This is a convention, so we didn't have to think in charge-carriers all the time.

So it is correct to think that the "high potential" battery terminal actually is a "low potential" point for the electrons. Because they loose energy on their way to that point. Like a ball falling from high potential on a shelf to low potential on the flow. We just don't say this conventionally. But keep it in mind, and then you always understand what potentials mean.

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