A hollow cylinder of length `l` and of radii a and b is filled with a material of resistivity `rho` and is connected to a battery of emf `E` through an ammeter. Find the current through ammeter

Answer

`p log_(e)((b)/(a))

Explanation

Consider an imaginary cylinder of radius x and thickness dx of the given cylinder. Its resistance is
`dR = (rho dx)/(2pi x l)`
Total resistance, `R=underset(a)overset(b)(int)(rho dx)/(2pixxl)=(rho log_(e)((b)/(a)))/(2pil)`
Current, `I=(E)/(R)=(Exx2pil)/(rho log_(e)((b)/(a)))`.