Question

A negligibly small current is passed through a wire of length 15 m and uniform cross-section $6.0 × 10^{−7} m^{2},$ 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, $a = 6.0 × 10^{−7} m^{2}$
Resistance of the material of the wire, R = 5.0 Ω
Resistivity of the material of the wire = ρ
Resistance is related with the resistivity as
$R = ρ\frac{l}{A}$
$ρ =\frac{ RA}{l}$
$ρ = \frac{5 \times 6 \times 10^{-7}}{15}$
$ρ = 2 \times 10^{-7} Ωm$
Therefore, the resistivity of the material is $2 \times 10^{−7} Ω m.$