Find the electric potential V(x) in the rod as a function of x.

The resistivity of a semiconductor can be modified by adding different amounts of impurities. A rod of semiconducting material of length L and cross-section area A lies along the x-axis between x = 0 and x = L. The material obeys Ohm’s law, and its resistivity varies along the rod according to ρ (x) = ρ0 exp (-x/L).

Find the electric potential V(x) in the rod as a function of x.

so, The resistance is R= ρ0L(1- exp-1)/A and the current is: I= VoA/ ρ0L(1- exp-1)