Resistance of a wire of length 1 m, diameter 1 mm is 2.2 Ω. Calculate its resistivity and conductivity.

Resistance of a wire of length 1 m, diameter 1 mm is 2.2 Ω. Calculate its resistivity and conductivity.
Solution:
Given,
resistance , \(R\) = 2.2 \(\Omega\)
length, \(l\) = 1 m
diameter, \(d\) = 1 mm
radius, \(r\) = \(\frac{d}{2}\) = 0.5 \(\times\) 10\(^{-3}\) m
resistivity, \(\rho\) = ?
conductivity, \(\sigma\) = ?
Now,
\[\begin{align*} R&=\frac{\rho l}{A}\\ 2.2 &= \frac{\rho \times 1}{\pi \times (0.5 \times 10^{-3})^2}\\ \rho&=2.2 \times \pi \times (0.5 \times 10^{-3})^2\\ \therefore \rho &= 1.73 \times 10^{-6} \hspace{0.1cm} \Omega m\\ \end{align*}\] Again,
\[\begin{align*} \sigma&= \frac{1}{\rho}\\ &=\frac{1}{1.73 \times 10^{-6}}\\ \therefore \sigma&=5.78 \times 10^5 \hspace{0.1cm} \Omega^{-1} m^{-1}\\ \end{align*}\] Hence, the resistivity is \(1.73 \times 10^{-6}\) \(\Omega m \) and conductivity is \(5.78 \times 10^{5}\) \(\Omega^{-1} m^{-1}\).