Question

Calculate the resistance of an aluminium cable of length 10 km and diameter 2.0 mm if the resistivity of aluminium is 27 × 10⁻⁸ Ωm. 

Answer 1

Length of the cable wire, l = 10 km = 10000 m

Diameter of the cable wire, d = 2.0 mm

Radius of the cable wire, r = 0.1 mm = 0.0001 m = 10^-4 m

Area of cross-section, `A=Api^2` 3.14 × 10^-8 m²

Resistivity of the aluminium cable wire = 27 × 10⁻⁸ Ω m.

Let the resistance of the aluminium cable be R.

We know that `R=l/A` 

R=P/A 

`R=27xx10-8xx103.14xx10-8`   

`R=(27xx10^-8xx10000)/(3.14xx10^-8)`

R = 86 Ω