# Why does a resistive wire heat up from current flow?

The kinetic energy of electrons in a conductor is roughly 9 orders of magnitude greater than the kinetic energy from the drift velocity of the electrons. It seems that the kinetic energy from the drift velocity is not enough to account for the heating, where does the heat energy come from?

Cheers

anorlunda
Staff Emeritus
Charged particles create fields. The fields of each particle interact with all the other charged particles simultaneously. That makes them behave very differently than uncharged particles. The energy of an electric current is carried in the fields. See Poynting's Theorem. Therefore you should not equate mechanical kinetic and potential energies with electric energy; they are very different.

If you are really interested in the fine details of conduction and resistance and electric energy read these articles
https://en.wikipedia.org/wiki/Drude_model
https://en.wikipedia.org/wiki/Poynting's_theorem.

• davenn
Dale
Mentor
2021 Award
It seems that the kinetic energy from the drift velocity is not enough to account for the heating, where does the heat energy come from?
Yes the KE is largely irrelevant. The energy comes from the fields. This is what Poynting’s theorem describes

In an analogy, although a bicycle chain is moving, the KE in the chain is largely irrelevant to the amount of energy transferred along the chain.

• davenn and berkeman
anorlunda
Staff Emeritus
On second thought, it is a bit more nuanced. While electric energy is carried outside the conductor (Poynting Vector), resistive heating losses occur within the conductor.

A pop sci type of explanation comes from this image from The Drude Model Wikipedia article. As electrons accelerate in the field and collide with atoms from all directions, they convey thermal energy to the atoms. The kinetic energy of electrons in a conductor is roughly 9 orders of magnitude greater than the kinetic energy from the drift velocity of the electrons. It seems that the kinetic energy from the drift velocity is not enough to account for the heating, where does the heat energy come from?

Cheers

Well, if the electron-gas has a very small amount of kinetic energy, then it must lose that kinetic energy very quickly, in order to provide a significant amount of heating energy. So there must be a large friction force.

Now as we know that the electron-gas does not stop despite of the huge friction, we conclude that there is a large force F pushing the electron-gas.

Heating power = drift velocity * F
or:
Heating power = drift velocity * friction force

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sophiecentaur
Gold Member
it must lose that kinetic energy very quickly,
A 'mechanical' reason for losing KE and never gaining much is the interaction of the electrons with the positive ion cores of the conductor.
If you allow electrons and unobstructed path through a vacuum, they gain loads of KE. In fact each electron gains eV Joules and electrons can easily reach speeds where Special Relativity starts to have an effect. A beam of electrons can be considered as having a Resistance which is equal to the PD / the beam current

russ_watters
Mentor
The kinetic energy of electrons in a conductor is roughly 9 orders of magnitude greater than the kinetic energy from the drift velocity of the electrons. It seems that the kinetic energy from the drift velocity is not enough to account for the heating, where does the heat energy come from?
Even if you could compare this to fluids where the energy was mechanical and not electrical, it still wouldn't be kinetic energy that is lost. Conservation of mass (continuity) demands that the velocity and therefore kinetic energy of a fluid in a pipe be constant, since otherwise mass would have to be lost somewhere. A fluid in a pipe works similar to sliding a block across the floor: the loss is work due to friction; simple force times distance in the case of the block.

Switching back to electricity, the principle is basically the same. You have a resistance to the motion of the electrons that applies a force against their motion. The nuts and bolts of what causes the force is different in the three cases, so the loss is a different function of flow rate for each (linear, square and cube function), but the idea is otherwise similar.

So maybe the next question is on a nuts and bolts level what causes resistance? Googling (or reading @anorlunda's post) gives me high school class notes that talk about electrons bouncing off of ions when traveling through the matrix, but that feels overly mechanical to me (even if it is electromagnetic "bouncing"). Maybe someone else can provide a deeper dive if indeed there is more to it...

sophiecentaur
Gold Member
high school class notes
I think that says it all. What a high school teacher / text book tells a student about something as sophisticated at this topic is guaranteed to be far too simple.
I am so pleased that, when I was at School, they rapped our knuckles if we asked for the 'electron' description of electricity. It was not until my first year at Uni, in a solid state Physics intro course that the transfer of energy by electrons was actually presented to us. (decades later) The utter nonsense that my teacher friends were expected to teach about 'Modern Physics' to kids at school (up to 16 years) was positively embarrassing. It made it all far too simple.

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thanks for all your answers, I should have remembered the Drude model.

Cheers