Question

2. Consider a conical conductor of length L, radius a at one end and b at the other end, as shown to the right. The material has conductivity σ. We want to find the total resisitance R V/I of the conductor, when a voltage V is applied between the two ends. (a) A common approach is to slice the conductor into (infinitesimal) disks of thickness dz and add up the (infinitesimal) resistance of each disk. Evaluate R in this manner. dz (a) Explain why the above approach is fundamentally fawed. [See J. D. Romano and R. H. Price, Am. J. Phys. 64, 1150 (1996); you may also ask the first author in person.] (b) Alternatively, consider the case where the ends of the conductor are spherical caps centred on the apex of the cone, and L is the distance between the centres of the circular perimeters of the end caps. Compute the resistance in this case. (c) Compare the two calculations in the limit where the slope of the cone is very shallow: b-a< L

Answer 1