Let’s Get Physics-l: Resistivity

In the past few Electricity posts we have taken a look at Resistance which we have learnt is dependent on a number of factors such as length and cross-sectional area. Resistivity, on the other hand, is a property unaffected by physical changes in a material. It is a fixed value which we refer to as an intrinsic or natural property.

Resistivity is, in affect, the ratio of the product of resistance and cross-sectional area of a component over its length (See the equation below).

Now, we an calculate resistivity relatively easily when we take into consideration two properties of resistance:

  • The resistance of a wire is directly proportional to its length provided other factors are constant. This means that as the length of a wire increases the resistance of it increases. This is because if we were to go subatomic (Not that you should, Scott Lang got lucky) we would see a higher number of collisions between conduction electrons as they move through the wire.
IMG_4124
Despite Warnings from Hank, Scott saw fit to go subatomic – The blue bricks represent electrons which are colliding with metal atoms.
  • The resistance of a wire is inversely proportional to the wire’s cross sectional area meaning that as the area increases resistance decreases. This is because the electrons have more “paths” to travel through so collisions are less frequent.
IMG_4123
The area is now wider so the electrons collide far less frequently.

We can combine these two principles into an equation:

R = kl

+

R = k(1/A)

=

R = pl/A

(I’ve skipped a step simply because I don’t have a proportional sign on my keyboard. p represents the constant of proportionality)

Where:

  • R = Resistance in Ohms
  • p = Resistivity in Ohm metres
  • k = Constant of Proportionality
  • l = length in metres
  • A = Cross-sectional area in metres squared

You may be wondering what Resistivity is actually used for. Archaeologists use resistivity meters as the data they collect can be used to determine what structures are present underground as well as the nature of any erosion that has occurred in underground rocks. Stonehenge was originally believed to be just a single, isolated structure but it has since been revealed that is was part of a bigger structure.

Whilst Resistivity is a fixed property of all metals, it isn’t completely impervious to change. Temperature causes resistivity to increase for most metals but there are a few exceptions.

Germanium’s resistivity decreases as it gets hotter. This comes in handy when we want to create components known as negative temperature coefficient thermistors. As temperature increases the component’s resistance decreases. They are used in numerous household appliances such as fridges, toasters and coffee makers to regulate temperature. Basically, they are very useful.

In terms of equations, we do have one that we can use to demonstrate the relationship between temperature and resistivity:

pT = p0[1 + a(T – T0)]

Where:

  • pT – The Resistivity at temperature, T
  • p0 – The resistivity value of the material at T0 (Often room temperature)
  • a – Temperature coefficient
  • T – The Temperature of the material
  • T0 – The reference temperature, often room temperature when we talk about it so 20 degrees Celsius

Summary

  • Resistivity – An intrinsic property unaffected by physical changes in a wire
  • R = pl/A
    • R directly proportional to l
    • R inversely proportional to A
  • Uses – Archaeology
  • Temperature
    • Most metals – As temperature increases the resistivity increases
    • Exceptions – Temperature increases cause resistivity to drop (e.g. Germanium)
    • pT = p0[1+a(T – T0)]
  • NTCT
    • Resistance decreases as Temperature increases
    • Uses – Common appliances reliant on temperature control

That concludes Resistivity. If you have any thoughts or questions please feel free to leave them in the comments and I will do my best to answer them. Thank you.

(The Character referenced is property of Marvel comics. I in no way lay claim to him, he has simply been used to help convey a concept)

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