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 = 1.0 mm = 1.0 × 10⁻³ m

Area of cross-section, A = πr²

= π(1.0 × 10⁻³)²

= π × 1.0 × 10⁻⁶

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

Let the resistance of the aluminium cable be R.

We know that `R = (rho l)/A` 

`R = (27 xx 10^-8 xx 10^3 xx 10)/(pi xx 10^-6)`   

`R = (27 xx 10^-8 xx 10^4)/(3.14xx10^-6)`

`R = (27 xx 10^2)/pi`

R = 86 Ω