Question: A hollow aluminum cylinder is 2.50 mlong and has an inner radius of 2.75 cmand an outer radius of 4.60 cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface. At room temperature, what will an ohmmeter read if it is connected between (a) the opposite faces and (b) the inner and outer surfaces?

Now, we know the formula

$R=\frac{\rho L}{A}$

Substitute the given values

Therefore, the ohmmeter reading if the ohmmeter is connected between the opposite faces is

Let us assume a thin cylindrical shell of length L, radius r, and thickness dr(the outer radius is approximately equal to inner radius)

We know, the current moves radially, so, the current moves along a distance L = dr and through a cross-sectional area .

Now, the resistance of this conductor is

The current that flows radially from , the resistance is

Use the formula found above,

$R=\frac{\rho }{2\mathrm{\pi L}}\ln \left(\frac{r_{out}}{r_{in}}\right)$

Substitute the given values

Therefore, when the ohmmeter is placed between the inner and outer surfaces, the ohmmeter reading is found to be