Question

The resistance of a metal wire of length $1m$ is $25\Omega$ at ${20}^{\circ }$ Celsius. If the diameter of the wire is $0.3mm,$ then the resistivity of the wire at that temperature is

• A. $4.96\times {10}^{-6}\Omega m$
• B. $3.96\times {10}^{-6}\Omega m$
• C. $2.96\times {10}^{-6}\Omega m$
• D. $1.76\times {10}^{-6}\Omega m$

Answer 1

The correct option is D. $1.76\times {10}^{-6}\Omega m$.

Given: Length of metal wire, $l=1m$
Diameter of the wire, $d=0.3mm$
Radius $r=\frac{0.3}{2}=0.15mm=0.15\times {10}^{-3}m$
Resistance of the metal, $R=25\Omega$

Area of the wire $A=\pi r^2=\pi \times (0.15\times {10}^{-3}{)}^2$

We know that Resistance, $R=\rho \frac{l}{A}$

where $\rho$ is the resistivity of the wire.

$\Rightarrow$ $\rho =\frac{RA}{l}=\frac{25\times \pi \times (0.15\times {10}^{-3}{)}^2}{1}=1.76\times {10}^{-6}\Omega m$.