Question

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

• A. $1\times {10}^{-7}\Omega -m$
• B. $2.5\times {10}^{-7}\Omega -m$
• C. $1.25\times {10}^{-7}\Omega -m$
• D. $2.5\times {10}^7\Omega -m$

Answer 1

The correct option is C $1.25\times {10}^{-7}\Omega -m$

Given:
Length of the wire, L $=2m$
Diameter, $d=0.4mm=4\times {10}^{-4}m$
Resistance, $R=2\Omega$
Cross section area of wire: $=\frac{\pi d^2}{2}=\pi \times \frac{(0.0004{)}^2}{4}=1.256\times {10}^{-7}{m}^2$
Resistivity, $\rho =\frac{RA}{L}=\frac{2\times 1.256\times {10}^{-7}}{2}$
Or, $\rho =\frac{RA}{L}=1.256\times {10}^{-7}\Omega -m$