Question

A wire of length 1 m and radius 0.1 mm has a resistance of 100 Ω. Find the resistivity of the material.

Answer 1

Let ρ be the resistivity of the wire.
Given:
Length, l = 1 m
Radius, r = 0.1 × 10^–3 m
Area, A = $\mathrm{\pi }{r}^2$
Resistance, R = 1000 Ω
We know:
$$\begin{gathered} R=\rho \frac{l}{A} \\ \Rightarrow \rho =\frac{RA}{l} \\ =\frac{1000\times \mathrm{\pi }\times 0.1\times 0.1\times {10}^{-6}}{1} \\ =\mathrm{\pi }\times {10}^{-6}\mathrm{\Omega m} \end{gathered}$$