Question

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 ___

Answer 1

$R =\rho \frac{\ell}{ A }$, 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$
$\rightarrow n =2$