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.
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.
Given $L =1.0 m , D =0.2 mm$
Or $r=0.1 mm =0.1 \times 10^{-3} m$
$R=10 \Omega, \rho=?$
Using the relation
$R =\frac{\rho L }{ A }=\frac{\rho L }{\pi r^{2}}$
or $\rho=\frac{R A}{L}=\frac{10 \times 3.14 \times\left(0.1 \times 10^{-3}\right)^{2}}{1.0}$
$=3.14 \times 10^{-7} \Omega m$
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