A hollow cylindrical conductor has length of $3.14\,m$, while its inner and outer diameters are $4\,mm$ and $8\,mm$ respectively. The resistance of the conductor is $n \times 10^{-3}\,\Omega$.If the resistivity of the material is $2.4 \times 10^{-8}\,\Omega\,m$. The value of $n$ is $..........$
JEE MAIN 2023, Medium
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$R =\rho \frac{\ell}{ A }$, the cross-sectional area is $\pi\left( b ^2- a ^2\right)$
$R =\rho \frac{\ell}{\pi\left( b ^2- a ^2\right)}=\frac{2.4 \times 10^{-8} \times 3.14}{3.14 \times\left(4^2-2^2\right) \times 10^{-6}}$
$=2 \times 10^{-3}\,\Omega$
$\rightarrow n =2$
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