Question

The resistance of a metallic wire of 100 m is 20 \(\Omega\). If the radius of the wire is 5 mm, find the resistivity of the metal of the wire.

Answer 1

Resistivity calculation:

Given: \(R = 20 \, \Omega\), \(l = 100 \, \text{m}\), radius (\(r\)) = 5 mm = 0.005 m

First, we calculate the area of cross-section (\(A\)) of the wire:

\[ A = \pi r^2 = \pi (0.005 \, \text{m})^2 = 2.5\pi \times 10^{-5} \, \text{m}^2 \]

Now, we can use the formula for resistivity:

\[ \rho = \frac{RA}{l} = \frac{20 \, \Omega \times 2.5\pi \times 10^{-5} \, \text{m}^2}{100 \, \text{m}} = 5\pi \times 10^{-6} \, \Omega \text{m} \]

Therefore, the resistivity of the metal is approximately \(5\pi \times 10^{-6} \, \Omega \text{m}\).