Chapter 25 Problem 93

Problem

The cross-section of a portion of a wire increases uniformly as shown, so it has the shape of a truncated cone. The diameter at one end is $a$ and at the other it is $b$, and the total length along the axis is $l$. If the material has resistivity $\rho$ determine the resistance $R$ between the two ends in terms of $a$, $b$, $l$, and $\rho$. Assume that the current flows uniformly through each section, and that the taper is small, i.e. $(b-a)\ll l$,