Question

A material of diameter 4mm and length of 14cm offers a resistance of 30Ω.

Calculate the resistivity offered by the material.​

Answer 1

Answer:-

• Diameter of wire=4mm=4×10^-3m
• Length=l=14cm=1.4m
• Resistance=R=30ohm

We know

$\boxed{\sf Surface\:Area\:of\:wire=A=\dfrac{\pi d^2}{4}}$

Now

$\boxed{\star\sf R=\rho\dfrac{\ell}{A}}$

$\\ \sf\longmapsto \rho=R\dfrac{A}{\ell}$

$\\ \sf\longmapsto \rho=\dfrac{R\pi d^2}{4\ell}$

$\\ \sf\longmapsto \rho=\dfrac{30\times 22\times 16\times 10^{-6}}{7\times 4\times 1.4}$

$\\ \sf\longmapsto \rho=\dfrac{660\times 16\times 10^{-6}}{28\times 1.4}$

$\\ \sf\longmapsto \rho=\dfrac{10560\times 10^{-6}}{39.2}$

$\\ \sf\longmapsto \rho=269.3\times 10^{-6}$

$\\ \sf\longmapsto \rho=2.7\times 10^{-4}\Omega m$