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# Resistivity and Conductivity

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## Resistivity and Conductivity

**What factors affect the resistance of a material?**

**a) Length **- the further electrons have to travel through material, the more collisions they will have so the higher the value of resistance.

**b) Area** - a bigger area means that in any 1 second more electrons will be able to travel through a piece of wire. More electrons means more current which means less resistance.

**c) Material** - if you swapped all the copper wire in a circuit for wood you'd notice a lot less current and a lot more resistance in the circuit. The ability of a material to resist a current is called its **resistivity**, ρ. Resistivity is measured in ohm-metres ( Ω m).

**d) Temperature** - but we've covered that in 'current-voltage graphs'.

* So:*.

R ∝ l

R ∝ l/A

R ∝ ρ

**These can be combined to give:**

R = *ρl/A*

* Where:*.

R = resistance (Ω)

ρ = resitivity of the material (Ω m)

I = length of wire (m)

A = cross-sectional area of the wire (m^{2})

**Here's one for you to try:**

A 20 cm long metal wire has a cross-sectional area of 1 mm^{2}.

**As conductance is the reverse of resistance, so conductivity is the reverse of resistivity.**

So conductivity,

Conductivity is measured in Sm^{-1}