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

To find the resistivity §,

We know that R = pl/ A

p = R x A / L

= 100 x 0.22 / 7 / 1000

= 0.22 / 7 x 10 = 0.22 / 70 = 0.022 / 7 = 0.0031429 Ω-m

Area of the cross-section of the wire = $\pi $ ${{r}^{2}}$

= 22/7 x x 0.1 x 0.1 = 22.7 x 0.01 = 0.22 / 7

l = 1m = 1000mm