Question

A wire of 1m long has an area of cross section of $2\times {10}^{-3}c{m}^2$ and has a resistance of 10 ohm. The resistivity of the material of the wire is:

• A. $2\times {10}^{-6}\Omega cm$
• B. $2\times {10}^{-4}\Omega cm$
• C. $2\times {10}^{-2}\Omega cm$
• D. $2\times {10}^{-8}\Omega cm$

Answer 1

The correct option is B $2\times {10}^{-4}\Omega cm$

Given:-
$L=1m=100cm$
$A=2\times {10}^{-3}c{m}^2$
$R=10\Omega$
$\Rightarrow R=\frac{\rho L}{A}$
$\Rightarrow \rho =\frac{RA}{L}$
$=\frac{10\times 2\times {10}^{-3}}{100}$
$\Rightarrow \rho =2\times {10}^{-4}\Omega cm$