A conductor having resistivity ρ is bent in the shape of a half cylinder as shown in the figure. The inner and outer radii of the cylinder are a and b respectively and the height of the cylinder is h. A potential difference is applied across the two rectangular faces of the conductor. Calculate the resistance offered by the conductor.

Question

G1 Physics · Accepted Answer

Image Consider concentric strips of radius r and thickness dr conducting along semicircular paths. Path length = πr and cross-section = h dr. These strips are in parallel: dG = h dr/(ρπr). Integrating a to b gives G = h ln(b/a)/(ρπ). Hence R = πρ/[h ln(b/a)].