# Non-Ohmic Materials: Learn About Vanishingly Small Terms

• snatchingthepi
In summary, the extra terms in Ohmic materials are quadratic or cubic, and can be found by doing resistivity measurements at different temperatures. There are also negative and positive temperature coefficient resistors that can be used to generate startup current or limit inrush current.
snatchingthepi
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.

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.

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".

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.

Hello,

Thank you for sharing your interest in non-Ohmic materials and their vanishingly small terms.

The extra terms that you mentioned are called nonlinear terms and they represent the non-Ohmic behavior of certain materials. These terms can arise due to various factors such as temperature, pressure, and electric field strength.

To answer your question, the size of these nonlinear terms can vary greatly depending on the material and the conditions under which it is being tested. For Ohmic materials, these terms are usually very small and can be neglected in most cases. However, for non-Ohmic materials such as superconductors, these terms can be significant and cannot be ignored.

The exact values of these nonlinear terms can be found in research papers and textbooks on the specific materials you are interested in. You can also consult with experts in the field or conduct your own experiments to determine the magnitude of these terms.

I hope this helps to answer your question. Keep exploring and learning about non-Ohmic materials, as they are a fascinating and important aspect of science and technology.

Best regards,

## What are non-Ohmic materials?

Non-Ohmic materials are materials that do not follow Ohm's law, which states that the current through a conductor is directly proportional to the voltage applied, as long as the temperature and other physical conditions remain constant.

## How do non-Ohmic materials differ from Ohmic materials?

Non-Ohmic materials have a non-linear relationship between current and voltage, meaning that the resistance of the material changes as the voltage applied changes. Ohmic materials, on the other hand, have a constant resistance regardless of the voltage applied.

## What causes the non-Ohmic behavior in materials?

Non-Ohmic behavior in materials can be caused by a variety of factors, such as temperature changes, changes in the material's structure, or the presence of impurities or defects in the material.

## What are some common examples of non-Ohmic materials?

Some common examples of non-Ohmic materials include semiconductors, diodes, and thermistors. These materials have varying resistance depending on the voltage applied, making them useful for electronic devices such as transistors and temperature sensors.

## How do scientists study non-Ohmic materials?

Scientists use a variety of techniques, such as measuring current-voltage relationships and using specialized equipment like scanning tunneling microscopes, to study the behavior of non-Ohmic materials. They also use mathematical models to understand and predict the behavior of these materials.

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