Question

(a) Give one example to show how the resistance depends on the nature of material of the conductor.
(b) 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

(a) If we take two similar wires with equal length and diameter, one made of copper (metal) and the other made of nichrome (alloy), we will find that the resistance of the nichrome wire is about 60 times more than that of the copper wire. This shows that the resistance of a conductor depends on the nature of the material of the conductor.

(b) 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, $A=\mathrm{\pi }{r}^2$ = 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 $R=\frac{\mathrm{\rho }l}{A}$

$R=\frac{27\times {10}^{-8}\times 10000}{3.14\times {10}^{-8}}$

R = 86 Ω