Question

A wire is 1.0 m long , 0.2 mm in diameter and has a resistance of 10 $\Omega$. Calculate the resistivity of its material.

Answer 1

Given,

$l=0.1m=1000mm$

$d=0.2mm\therefore radius\left(r\right)=\frac{0.2}{2}=0.1mm$

$R=10\Omega$

To find,

Resistivity$\left(\rho \right)$

$\rho =R\frac{A}{l}$

where,

$R=$ Resistance

$l=$ Length of wire

$A=$ Cross sectional area of wire

Cross sectional area of cylinder $\left(A\right)=\Pi r^2$

$\Rightarrow A=\pi \times {\left(0.1\right)}^2$

$\Rightarrow A=0.0314{mm}^2$

$\therefore \rho =10\left(\frac{0.0341}{1000}\right)$

$\Rightarrow \rho =0.000314\Omega -mm$

$\Rightarrow \rho \simeq 3.14\times {10}^{-7}\Omega -m$

So, the resistivity of the material is equal to $3.14\times {10}^{-7}\Omega -m$