Question

Aluminium wire has radius 0.25 mm and length or 75 m. If the resistance of the wire is 10Ω, calculate the resistivity of aluminium.

Answer 1

The formula of resistance is: R = \(\frac{ρ\,\times\,I}{A}\)

Where, ρ = resistivity 

I = Length of the conductor 

A = Area of the conductor 

∴ ρ = \(\frac{R\,\times\,A}{I}\)

Here: R = 10 Ω 

r = 0.25mm l = 75m  We know that the area of the wire will be: A = πr²

∴ A = 3.14 x (0.25 x 10^-3)²

A = 0.196 x 10^-6 m²

Putting the given values in the above formula

ρ = \(\frac{10\,\times\,0.196\,\times\,10^{-6}}{75}\)

ρ = 26.133 x 10^-6 Am