A common textbook problem asks you to calculate the resistance of a cone-shaped object, of resistivity p, with length L, radius a at one end, and radius b at the other (Fig. 7.50). The two ends are flat, and are taken to be equipotentials. The suggested method is to slice it into circular disks of width dz, find the resistance of each disk, and integrate to get the total.

(a) Calculate R thisway.

(b) Explain why this method is fundamentally flawed.

(c) Suppose the ends are, instead, spherical surfaces, centered at the apex of the cone. Calculate he resistance in that case. (Let L be the distance between the centers of the circular perimeter, of the end caps.)

CEPE dz b N