Question

A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6.0 × 10⁻⁷ m², and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?

Answer 1

Length of the wire, l = 15 m

Area of cross-section of the wire, a = 6.0 × 10⁻⁷ m²

Resistance of the material of the wire, R = 5.0 Ω

Resistivity of the material of the wire = ρ

Resistance is related to resistivity as

R = `ρ "l"/"A"`

ρ = `("RA")/"l"`

= `(5 xx 6 xx 10^-7)/15`

= 2 × 10⁻⁷ Ω m

Therefore, the resistivity of the material is 2 × 10⁻⁷ Ω m.