Question

A 200 W resistor is made by filling the region between two concentric conducting cylinders 10 cm long and 1.0 and 2.0 cm radius respectively with a resistive material. What is the resistivity, ρ, of this material? (Method 1: Use the fact that E=ρJ, and that the total current, I, through a cylindrical shell at radius r is always the same. Method 2: Add up the delta-R’s for each cylindrical shell between r₁ and r₂.)

Answer 1

This problem is from topic resistivity and resitance of material having variable cross section.

Here we will proceed by method 2.We will go fo integration by choosing an element of type cylindrical shell located at a distance r from the axis .