Is there microscopic version of general Ohm's law of V=IZ?

[goodphy]

Hello.

Resistive Ohm's law is famously known as V = IR. We can derive its microscopic version as being followed.

V = El, where E and l are, respectively, an electric field and a resistive load length over which a voltage drop V is developed.

I = JS, J and S are a current density and a cross-sectional area of the load (uniform cross-section is assumed).

Substituting these expressions into the Ohm's law gives El = JSR → J = σE where σ = l/(SR) or R = l/(σS).

It is very obvious that J = σE is the microscopic version of the Ohm's law of V = IR. It looks that J = σE is only true for resistive load and DC.

I would like to know if there is any microscopic version of generalized Ohm's law of V = IZ where Z is an impedance.

Could we find this?

 

[anorlunda]

You may be asking for the Drude model (which I'm not fond of) Read about it at https://en.wikipedia.org/wiki/Drude_model

 

[Baluncore]

An impedance is a complex number that includes resistive and reactive components.

If the impedance was a series connection of RLC, then how could you map a length onto the impedance in the same way that you can with a linear potentiometer ?

 

[dlgoff]

It is very obvious that J = σE is the microscopic version of the Ohm's law of V = IR. ...

Just in case other readers would like to see how this applies to "ohmic" materials:

http://hyperphysics.phy-astr.gsu.edu/]When[/PLAIN] a microscopic view of Ohm's law is taken, it is found to depend upon the fact that the drift velocity of charges through the material is proportional to the electric field in the conductor.