Energy transfer in electricity conduction

[loom91]

Hi,

I was wondering something. What is the mechanism of energy transport when electricity is conducted through a conductor? The continuity equation requires current to be constant in a circuit, which means the expectation velocity of the electrons in the conduction bands must be constant throughout the circuit, no kinetic energy is lost. Yet resistances in the circuit get heated. Where does this energy come from?

Thanks.

Molu

 

[andrevdh]

I am not on your level, but it might be helpfull to compare the situation with its gravitational equivalent. The source of gravitational potential energy is our planet (power supply). It generates a force (electric) field that causes the object (electric charge) to do work when moved by the field. The resulting energy can be converted to other forms (heat), depending on what the object encounters on its way through the field.

Having said that I must confess that logic brought me to the conclusion at some stage that there should not be an electric field in a good conductor.

 

[loom91]

But under a gravitational field changes in kinetic energy occur. Also, why do electrons have constant velocity in a conductor? Should not they be accelerated? Thanks.

 

[andrevdh]

In a conductor the free electrons do collide with the ions (that lost the electrons) in the crystal lattice at regular intervals on the average. When an electric field is applied the electron paths become slightly curved between the collisions, that is the electrons are pushed sideways a bit. This means that the electrons do accelerate between collisions, but they lose their gained speed again due to the collisions. So on the average all that happens to the path of the electrons due to the applied electric field is that they drift sideways a bit under its influence.

 

[loom91]

But where does the energy released in conduction come from? The average kinetic energy of the electrons is staying the same, so what energy translates into the vibrational energy of the resistance? Thanks.

Molu

 

[loom91]

Can anyone help me?

 

[SGT]

But where does the energy released in conduction come from? The average kinetic energy of the electrons is staying the same, so what energy translates into the vibrational energy of the resistance? Thanks.

Molu

The energy comes from the field. If there were no collisions with the ions, the electrons would accelerate indefinitely. In the collisions they lose their kinectic energy that is transferred to the ions, which vibrate with higher amplitude. In the steady state, all the energy provided by the field is absorbed by the material.
The gravitational analogy is valid if there is air present. A body under the influence of the gravitational field accelerates until it reaches terminal velocity. Then the velocity is constant and all the energy provided by the gravitational field is used to heat the body and the air.

 

[loom91]

But what of the theorem that electric field is zero inside conductor? Thank you.

Molu

 

[SGT]

But what of the theorem that electric field is zero inside conductor? Thank you.

Molu

The electric field is zero inside an ideal conductor. In this case there is no resistance and no dissipated power and the voltage at the extremes of the conductor is zero.
In a real conductor you need a potential difference at the extremes of the conductor in order to establish a current, so there is a nonzero field.