A conducting plate of thickness t is in the shape of an arc. Its inner and outer rim form a 30° arc of radius r and 2r respectively at point O (see Figure). Electric current flows through the strip along circular arcs as indicated in the diagram. Find resistance of the plate if its material has conductivity σ.

Question

G1 Physics · Accepted Answer

Image Take a radial strip of width dρ. Current flows along arc length L = ρθ with θ = π/6. Cross-section normal to current is t dρ. Differential conductance dG = σt dρ/(ρθ). Integrating from r to 2r: G = (σt/θ)ln2. Thus R = θ/(σt ln2) = π/[6σt ln2]. Use the exact derived expression; the listed options should be adjusted if strict answer matching is required.