Non-Ohmic Materials: Learn About Vanishingly Small Terms

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Non-Ohmic materials, such as superconductors and semiconductors, exhibit "vanishingly small" extra terms in their conductivity equations, which can be quadratic or cubic. In contrast, traditional Ohmic materials maintain linearity, although slight non-linearities can occur under high current densities due to transient heating effects. Examples of these non-linear behaviors include Voltage Dependent Resistors (VDRs) and Negative Temperature Coefficient Resistors (NTCs), which adjust resistance based on temperature changes. Positive Temperature Coefficient Resistors (PTCs) also demonstrate non-linear characteristics by increasing resistance with temperature. Understanding these nuances in conductivity can enhance the application of materials in electronic components.
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So I learned today about the version of Ohm's law where

J = \sigma E

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

J = \sigma E

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
 
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Thank you both.
 

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