Non-Ohmic Materials: Learn About Vanishingly Small Terms

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Discussion Overview

The discussion revolves around the characteristics of non-Ohmic materials, particularly focusing on the "vanishingly small" extra terms in the context of Ohm's law, and the nature of slight non-linearities in Ohmic materials. Participants explore examples of non-Ohmic behavior and seek information on the magnitude of non-linear terms in Ohmic conductors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes the existence of "vanishingly small" extra terms in the context of Ohm's law for non-Ohmic materials like superconductors.
  • Another participant mentions that traditional non-Ohmic materials include semiconductors, highlighting the exponential nature of the V-I curve in p-n junction diodes.
  • A participant suggests that high current density in Ohmic materials could lead to transient heating effects, which might introduce non-linearity, while still maintaining Ohmic behavior by using temperature-dependent resistivity.
  • Examples of Voltage Dependent Resistors (VDRs) and Negative Temperature Coefficient Resistors (NTCs) are provided, illustrating how these components exhibit non-linear behavior under certain conditions.
  • The Positive Temperature Coefficient Resistor (PTC) is also mentioned, with its behavior of increasing resistance with temperature being discussed in the context of controlling startup currents.

Areas of Agreement / Disagreement

Participants present multiple viewpoints regarding the nature of non-linearities in Ohmic materials and the characteristics of non-Ohmic materials. There is no consensus on the specific magnitude of the "vanishingly small" terms or the conditions under which non-linearities occur.

Contextual Notes

Some claims depend on specific definitions of Ohmic and non-Ohmic behavior, and the discussion does not resolve the extent to which transient effects impact the linearity of Ohmic materials.

snatchingthepi
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So I learned today about the version of Ohm's law where

[tex]J = \sigma E[/tex]

and my professor mentioned that some materials (non-Ohmic materials like superconductors) have "vanishingly small" extra terms that are quadratic or cubic. I'm wondering if anyone can direct me to a source (or even just tell me) where I can find out just how small these terms are for Ohmic (linearly conducting) materials.
 
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snatchingthepi said:
So I learned today about the version of Ohm's law where

[tex]J = \sigma E[/tex]

and my professor mentioned that some materials (non-Ohmic materials like superconductors) have "vanishingly small" extra terms that are quadratic or cubic. I'm wondering if anyone can direct me to a source (or even just tell me) where I can find out just how small these terms are for Ohmic (linearly conducting) materials.

The traditional example of non-ohmic materials are semiconductors and semiconductor junctions. The V-I curve of a p-n junction diode is exponential in nature.

But it sounds like you are asking for examples of slight non-linearities in simple conductors? I suppose if the current density is high enough, the transient heating effects might be considered a non-linearity. But the material is still Ohmic, if you use the resistivity for the temperature at each point in the conductor...
 
For example, the Voltage Dependent Resistor that we use for damping voltage spikes.
220px-Typische_Varistorkennlinien.gif

Or the Negative Temperature Coefficient Resistor (NTC)- the resistance decreases when the temperature increases. Since the current through the NTC will generate heat, it can be used to limit "inrush current".
A244Fig01.gif

You also have the Positive Temperature Coefficient Resistor (PTC)- the resistance increases when the temperature increases. Since the current through the PTC will generate heat, it can be used to generate a startup-current that gradually decreases (for example if you want to demagnetize an instrument when you turn it on).
http://www9.dw-world.de/rtc/infotheque/electronic_components/fig1521.gif
 
Last edited by a moderator:
Thank you both.
 

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