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According to what I have learnt, there is always a potential difference across a resistor in a circuit (having a battery).

Considering a simple 'resistor' circuit, when we apply an e.m.f in the circuit, we know that electrons that have yet to pass the resistor are at high potential, and electrons in the resistor are losing energy in the form of heat. What happens to the electrons that are already away from the resistor (i.e. their path starts after the resistor, hence they never encounter any resistance)? They cannot be having the same energy as the electrons that are to meet the resistance, i.e. at a high potential.

I may be wrong in some of the ideas I have developed, any help would be generously appreciated.

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    $\begingroup$ The potential is defined at a point in space, not for each individual electron. $\endgroup$
    – The Photon
    Commented May 9, 2022 at 5:49
  • $\begingroup$ People tend to characterize the voltage as the pressure/height and the current as the velocity $\endgroup$
    – ChemEng
    Commented May 14, 2022 at 16:44
  • $\begingroup$ It seems I had wrongly understood the concept of potential and potential difference in a circuit (the 'pressure/height' model is misguiding). Thanks! $\endgroup$
    – Tanish Desai
    Commented Dec 19, 2022 at 4:43

2 Answers 2

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It is not the electrons themselves that carry the energy in the circuit. They do not gain any energy overall in the battery, and nor do they lose any in the resistor, overall.
The electrons undergo random motion, with a net "drift" opposite the direction of the electric field (set up by the battery in the circuit) described by the drift velocity.

The energy flows outward into the electromagnetic field from the battery, and energy flows into the resistor from the field. The direction of the flow of energy is best described by the Poynting vector $\overrightarrow{S} = \frac{\overrightarrow{E}\times\overrightarrow{B}}{\mu_0}$.

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The free electrons in a circuit distribute themselves to give a large charge density gradient (and strong electric field) in regions of high resistance and low gradient in regions of low resistance. This produces the required continuity of current flow.

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