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

• Abimbola1987
In summary, the process of joule heating is when conduction electrons transfer energy to the conductor's atoms through collisions, which results in the generation of heat on the microscale. This heat is caused by work being done by the electric field and current density, as explained by Poynting's theorem. The kinetic energy and drift velocity of the electrons are not necessary to understand this process. The analogy of connecting millions of electron tubes in series helps to visualize the concept of a resistor.
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.

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.

Last edited:
Abimbola1987 said:
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.

Dale said:
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?

Abimbola1987 said:
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.

Dale said:
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?

Abimbola1987 said:
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.

Abimbola1987 said:
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
Lord Jestocost said:

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

Dale said:
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
jartsa said:
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".

## 1. What is Joule's first law?

Joule's first law states that the amount of heat produced by an electrical current is directly proportional to the square of the current and the resistance of the material through which the current is passing.

## 2. How does Joule's first law relate to kinetic energy?

Joule's first law relates to kinetic energy because the heat produced by an electrical current is the result of the kinetic energy of the moving electrons in the current. This kinetic energy is transferred to the material and causes it to heat up.

## 3. What is the formula for calculating the kinetic energy of an electrical current?

The formula for calculating the kinetic energy of an electrical current is E = I^2R, where E is the heat produced, I is the current, and R is the resistance of the material.

## 4. How is Joule's first law used in practical applications?

Joule's first law is used in practical applications such as electric heaters, toasters, and electric stoves, where the heat produced by the electrical current is used to generate heat for cooking or warming up a space.

## 5. What is the significance of Joule's first law in the field of thermodynamics?

Joule's first law is significant in the field of thermodynamics because it is a fundamental law that explains the relationship between electrical energy and heat energy. It also helps to understand the efficiency of energy conversion in electrical systems.

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