Question

Calculate the resistivity of the material of a wire 1 m long , 0.4 mm in diameter and having a resistance $2\Omega$.

• A. $300\Omega$m
• B. $2.514\times {10}^{-7}\Omega m$
• C. $2\times {10}^7\Omega m$
• D. $1\times {10}^{-15}\Omega m$

Answer 1

The correct option is B $2.514\times {10}^{-7}\Omega m$

Given : $R=2\Omega$ $l=1$ m $d=0.4$ mm $=0.0004$ m

Cross section area of wire $A=\frac{\pi d^2}{4}=\frac{\pi \times (0.0004{)}^2}{4}=1.256\times {10}^{-7}$ $m^2$

Resistivity of the material $\rho =\frac{RA}{l}$

$\therefore$ $\rho =\frac{2\times 1.256\times {10}^{-7}}{1}=2.514\times {10}^{-7}$ $\Omega m$