Two identical conducting plates, each having area A, are located at z = 0 and z = d. The region between plates is filled with a material having z-dependent conductivity, σ(z) = σ₀e^−z/d, where σ0 is a constant. Voltage V₀ is applied to the plate at z = d; the plate at z = 0 is at zero potential. Find, in terms of the given parameters,

(a) The resistance of the material;

(b) The total current flowing between plates;

(c) The electric field intensity E within the material.