A wire of length 1m and radius 0.1mm has a resistance of $100\Omega.$ Find the resistivity of the material.
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$\ell=1\text{m},\text{r}=0.1\text{mm}=0.1\times10^{-3}\text{m}$
$\text{R}=100\Omega,\text{f}=?$
$\Rightarrow\text{R}=\frac{\text{f}\ell}{\text{a}}$
$\Rightarrow\text{f}=\frac{\text{Ra}}{\ell}=\frac{100\times3.14\times0.1\times0.1\times10^{-6}}{1}$
$=3.14\times10^{-6}=\pi\times10^{-6}\Omega\text{-m}.$
$\text{R}=100\Omega,\text{f}=?$
$\Rightarrow\text{R}=\frac{\text{f}\ell}{\text{a}}$
$\Rightarrow\text{f}=\frac{\text{Ra}}{\ell}=\frac{100\times3.14\times0.1\times0.1\times10^{-6}}{1}$
$=3.14\times10^{-6}=\pi\times10^{-6}\Omega\text{-m}.$
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