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

  1. Feb 23, 2017 #1

    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?
  2. jcsd
  3. Feb 23, 2017 #2


    Staff: Mentor

  4. Feb 23, 2017 #3


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    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 ?
  5. Feb 23, 2017 #4


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    Just in case other readers would like to see how this applies to "ohmic" materials:
    Last edited by a moderator: May 8, 2017
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