Question

A hollow cylinder of length 'l'and radii a and b is filled with a material of resistivity 'ρ' and is connected to a battery of emf ‘E’ through an ammeter, the reading of ammeter will be

(1) \(\frac{E2\pi l}{ρ\,log_e (b/a)}\)

(2) \(\frac{E2\pi l}{ρ\,log_e (a/b)}\)

(3) infinite

(4) zero

Answer 1

 (1) \(\frac{E2\pi l}{ρ\,log_e (b/a)}\)

Resistance of an imaginary cylinder of radius x, thickness dx, dR = ρdx/2πxl

So the resistance of given cylinder (R)

Hence reading of ammeter I