Determine the resistance between concentric spherical surfac

Determine the resistance between concentric spherical surfaces of radii R₁ and R₂ (R₁<R₂), assuming that a material of conductivity =₀(l +k/R) fills the space between them.

Solution

you know that Capacitance between these two sphere will be

C = 4*pi*e/(1/R1 - 1/R2)

Also you know

R = V/I

C = Q/V

RC = Q/I

Which gives us

RC = e/sigma

R = e/(C*sigma)

R = [(1/R1 - 1/R2)]/(4*pi*sigma)

given that sigma = sigma0*(1 + k/R)

R =[(1/R1 - 1/R2)]/(4*pi*sigma0*(1 + k/R))

Let me know if you have any doubt.