Question

A wire of a length 1m and radius 0.1 nm has a resistance 100 $\Omega$ Find the resistivity of the material.

Answer 1

Given: A wire of a length, $L=1m$ and radius, $r=0.1nm=0.1\times {10}^{-9}m$ has a resistance, $R=100\Omega$

To find the resistivity of the material

Solution:

We know,

$R=\rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $A=\pi r^2$ is the area of cross-section.

By substituting the given values,

$100=\rho \frac{1}{\pi \times r^2}⟹100=\rho \frac{1}{3.14\times (0.1\times {10}^{-9}{)}^2}⟹\rho =100\times 3.14\times {10}^{-20}=3.14\times {10}^{-18}\Omega m$

is the required resistivity of the material.