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?
Solution:
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 with the resistivity as
$R=\rho \frac{l}{A}$
$\rho=\frac{R A}{l}$
$=\frac{5 \times 6 \times 10^{-7}}{15}=2 \times 10^{-7} \Omega \mathrm{m}$
Therefore, the resistivity of the material is $2 \times 10^{-7} \Omega \mathrm{m}$.