Question

The hollow cylinder of length l and inner and Outer radius R1 and R2 respectively find the resistance of the cylinder if the current flows radially outward in the cylinder. The resistivity of the material of the cylinder is p​

Answer 1

The hollow cylinder of length l and inner and Outer radius R1 and R2 respectively. The resistivity of the material of the cylinder is ρ.

We have to find the resistance of the cylinder if the current flows radially outward in the cylinder.

solution : cut an element of thickness dx , at x distance from the centre of cylinder where R₁ < x < R₂.

now, area of infinitesimal thickness cylinder , dA = 2πxl

now using formula, ∫dR = ρ ∫dx/dA

⇒R = ρ ∫dx/2πxl

= ρ/2πl ∫dx/x

= ρ/2πl ln[x]

now putting upper limit = R₂ and lower limit = R₁

= ρ/2πl ln[R₂/R₁]

Therefore the resistance of the cylinder is ρ/2πl ln[R₂/R₁]