Question

A hollow cylindrical conductor has length of $3.14m$, while its inner and outer diameters are $4mm$ and $8mm$ 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

Answer: 2

$R=\rho \frac{\ell }{A}$, the cross-sectional area is $\pi \left(b^2-a^2\right)$
$R=\rho \frac{\ell }{\pi \left(b^2-a^2\right)}=\frac{2.4\times 10^{-8}\times 3.14}{3.14\times \left(4^2-2^2\right)\times 10^{-6}}$
$=2\times 10^{-3}\Omega$
$\to n=2$