# Joule's first law - kinetic energy of electrical current

Abimbola1987
Dear Sirs,

If I take this explanation as being true "The heat is generated on the microscale when the conduction electrons transfer energy to the conductor's atoms by way of collisions."

So a "current" must have a quantum of kinetic energy going into the conductor (resistive element) and a lesser quantum of kinetic energy coming out the other end.

So first, how do I quantify the kinetic energy of a electrical current? And where can I find the correct formulae that describes the relationship between drift velocity and the kinetic energy?

Thank you very much on beforehand.
Abim.

Abimbola1987
Dear anorlunda

Thank you for the wiki articles, if I sum them up I get (no disrespect intended): "it's mostly based on assumptions and mathematical simplifications, thus making it very laborious to obtain a precise result"

Then I might as well assume that P α I2 R from a practical point of view.

But logically that bothers me because the current (which is proportional to the drift velocity) is the same on both sides of the conductor in electric theory. Unless the collisions are elastic, in which case it shouldn't generate heat.

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Mentor
So a "current" must have a quantum of kinetic energy going into the conductor (resistive element) and a lesser quantum of kinetic energy coming out the other end.
This is not correct. The KE is generally the same at each end of the resistor.

Abimbola1987
This is not correct. The KE is generally the same at each end of the resistor.

So what you are saying is that the collisions are elastic?

Mentor
So what you are saying is that the collisions are elastic?
No, but I don’t think that the collisions are useful for gaining understanding about circuits.

Abimbola1987
No, but I don’t think that the collisions are useful for gaining understanding about circuits.

I can agree with you, however I'm trying to gain an understanding for the process of joule heating, and if the kinetic energy and drift velocity is the same at each end of the resistor, then where does the heat come from?

jartsa
If I take this explanation as being true "The heat is generated on the microscale when the conduction electrons transfer energy to the conductor's atoms by way of collisions."

An electron tube is a device where electrons are emitted from the cathode, then they accelerate until they hit the anode.

Now let's connect million electron tubes in series.

Well, that device that we just made is supposed to be a model of a resistor.

So when an electron goes through said device it accelerates, stops, accelerates stops ... more or less like an electron that goes through a resistor.

Mentor
if the kinetic energy and drift velocity is the same at each end of the resistor, then where does the heat come from?
You can forget the KE and the drift velocity entirely. They are not necessary at all. You have an E field and a current density, so by Poynting’s theorem there is work being done. Since the resistor is not gaining mechanical or chemical or any other form of energy, all that is left is thermal energy.

• Abimbola1987
Abimbola1987

Thank you very much, that is such a nice and informative book in every sense.

Abimbola1987
You can forget the KE and the drift velocity entirely. They are not necessary at all. You have an E field and a current density, so by Poynting’s theorem there is work being done. Since the resistor is not gaining mechanical or chemical or any other form of energy, all that is left is thermal energy.

Thank you for poynting to Poynting’s theorem (bad pun intended) - that was the thing I missed.

• Dale
Abimbola1987
An electron tube is a device where electrons are emitted from the cathode, then they accelerate until they hit the anode.

Now let's connect million electron tubes in series.

Well, that device that we just made is supposed to be a model of a resistor.

So when an electron goes through said device it accelerates, stops, accelerates stops ... more or less like an electron that goes through a resistor.

Thank you for the analogy, it's pretty much what is described in the book suggested by "Lord Jestocost".