Question

A certain electrical conductor has a square cross-section, 2.0 mm on a side and is 12 m long. The resistance between its ends is $0.072\Omega .$ The resistivity of its material is equal to :

• A. $2.4\times {10}^{-6}\Omega m$
• B. $1.2\times {10}^{-5}\Omega m$
• C. $1.2\times {10}^{-8}\Omega m$
• D. $2.4\times {10}^{-8}\Omega m$

Answer 1

Answer: (D)

$2.4\times {10}^{-8}\Omega m$

Resistance of a conductor is given by

$R=\frac{\rho A}{l}$ ..(i)

When $l$ is the length of conductor. A its area of cross-section and $\rho$ its resistivity

$\rho =\frac{RA}{l}$ ...(i)

Given $R=0.072\Omega$

$A=(2\times 2)m{m}^2$

$l=12m$

Substituting the given values is Eq. (i) we get

$\rho =\frac{0.072\times 4\times {19}^{-6}}{12}=2.4\times {10}^{-18}\Omega m$