Question

A current of 4.0 A flows through a wire of length 1 m and cross-sectional area 1.0 mm², when potential difference of 2 V is applied across its ends.

Calculate the resistivity of the material of the wire.

Answer 1

Given: Area (A) = 1 mm² = 1 × 10⁻⁶ m²

Current (I) = 4.0 A

Potential difference (V) = 2 V

Length (L) = 1 m

Resistivity of a material is given by:

By using Ohm’s law:

R = `V/I`

= `2/4.0`

= 0.5 Ω

Resistivity of a material (ρ) = `(R A)/L`

= `(0.5 xx 1 xx 10^-6)/1`

= 0.5 × 10⁻⁶

= 5 × 10⁻⁷ Ω . m

∴ The resistivity of the material of the wire is 5 × 10⁻⁷ Ω . m.