Question

(a) Write down an expression for the resistance of a metallic wire in terms of the resistivity.
(b) What will be the resistance of a metal wire of length 2 metres and area of cross-section 1.55 × 10⁻⁶ m² if the resistivity of the metal be 2.8 × 10⁻⁸ Ω m?

Answer 1

(a) Length of the cable wire = l

Area of cross-section = A

Resistivity of the aluminium cable wire = $\mathrm{\rho }$

Resistance of the wire = R

Then, $R=\frac{\mathrm{\rho }l}{A}$

(b) Length of the cable wire, l = 2 m
Area of cross-section, A = 1.55 × 10⁻⁶ m²

Resistivity of the aluminium cable wire, $\mathrm{\rho }$ = 2.8 × 10⁻⁸ Ωm

We know that:

$R=\frac{\mathrm{\rho }l}{A}$

$R=\frac{2.8\times {10}^{-8}\times 2}{1.55\times {10}^{-6}}$

R = 0.036 Ω

Thus, the resistance of the metal wire, R = 0.036 Ω