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Resistivity

Resistivity

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Summary

Resistivity

In a nutshell

Resistivity is defined as the resistance of a unit length and unit cross sectional area of a material. Conductors have a very low resistivity, insulators have a very high resistivity and semiconductors have a resistivity in between them.



Equations

Description

equation

Resistivity
​ρ=RAL\rho=\dfrac{RA}{L}ρ=LRA​​​

​


Variable definitions

quantity name

symbol

derived units

alternate units

si base units

​resistivityresistivityresistivity​​
​ρ\rhoρ​​
​Ω m\Omega\ mΩ m​​

​kg m3 s−3 A−2kg\ m^3\ s^{-3}\ A^{-2}kg m3 s−3 A−2​​
​resistanceresistanceresistance​​
​RRR​​
​Ω\OmegaΩ​​
​V A−1V\ A^{-1}V A−1​​
​kg m2 s−3 A−2kg\ m^2\ s^{-3}\ A^{-2}kg m2 s−3 A−2​​
​cross−sectional areacross-sectional\ areacross−sectional area​​
​AAA​​
​m2m^2m2​​

​m2m^2m2​​
​legnthlegnthlegnth​​
​LLL​​
​mmm​​

​mmm​​

​


Resistivity

Resistance is a term that defines the opposition of current flow of a specific component. It can change depending on the size of the component; if the component is longer the resistance will increase since there is more material to get through and thus more collisions for the electrons, if the component has a larger cross-sectional area the resistance will decrease since more electrons can pass through. One can therefore write:


​R∝LAR\propto\dfrac{L}{A}R∝AL​​​


The constant of proportionality of this equation is known as the resistivity. It is defined as the resistance of a unit length and unit cross-sectional area of a material or in other words, it is a measure of how much a material opposes current flow. Resistivity is an electrical property specific to every material no matter the size and is symbolised by the greek letter ρ\rhoρ. Its unit is the ohm-meter Ω m\Omega\ mΩ m, and can be calculated with the equation:


​ρ=RAL\rho=\dfrac{RA}{L}ρ=LRA​​​


Note: The symbol for resistivity ρ\rhoρ is also often used for density, be careful not to get confused!


Physics; Electrical circuits; KS5 Year 12; Resistivity



Resistivity in conductors, semiconductors and insulators

Resistivity varies vastly depending on the type of material and its temperature:

  • Conductors have a very low resistivity of about 10−8 Ω m10^{-8}\ \Omega\ m10−8 Ω m. When the temperature increases so does their resistivity since ions vibrate more increasing the chance of collision with electrons.
  • Semiconductors have a moderate resistivity that vary greatly but hover around 1 Ω m1\ \Omega\ m1 Ω m. They have very different properties within each other, for example in some semiconductors a rise in temperature releases more charge carriers decreasing the resistance.
  • Insulators have a very high resistivity of about 1016 Ω m10^{16}\ \Omega\ m1016 Ω m.


Example

A metal wire is 2 m2\ m2 m long, has a cross-sectional of 5×10−5 m25\times10^{-5}\ m^25×10−5 m2 and a resistance of 5×10−3 Ω5\times10^{-3}\ \Omega5×10−3 Ω. What is the resistivity if this metal?


Firstly, write down all the known values:


L=2 mA=5×10−5 m2R=5×10−3 Ω\begin{aligned}L&=2\ m \\A&=5\times10^{-5}\ m^2\\R&=5\times10^{-3}\ \Omega\end{aligned}LAR​=2 m=5×10−5 m2=5×10−3 Ω​​​


Next, write down the equation for resistivity:


ρ=RAL\rho=\dfrac{RA}{L}ρ=LRA​​​


Substitute all the values into the equation:


ρ=5×10−3×5×10−52\rho=\dfrac{5\times10^{-3}\times5\times10^{-5}}{2}ρ=25×10−3×5×10−5​​​


Calculate the resistivity:


ρ=1.25×10−7 Ω m\rho=1.25\times10^{-7}\ \Omega\ mρ=1.25×10−7 Ω m​​


The resistivity of the metal is 1.25×10−7 Ω m‾\underline{1.25\times10^{-7}\ \Omega\ m}1.25×10−7 Ω m​.

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Resistivity

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FAQs - Frequently Asked Questions

How does the resistivity change depending on the type of material?

Conductors have a very low resistivity, semiconductors have a moderate resistivity and insulators have a very high resistivity.

How does the size of a component affect its resistance?

If a component is longer its resistance will increase and if it has a larger cross-sectional area its resistance will decrease.

What is resistivity?

Resistivity is defined as the resistance of unit length and unit cross-sectional area of a material.

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