A rod 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 `rho(x) = rho_0 epsilon^(-x//L)`. The end of the rod `x=0` is at a potential `V_0` and it is zero at `x=L`.
(a) Find the total resistance of the rod and the current in the wire.
(b) Find the electric potential in the rod as a function of `x`.

Answer

(a)`R=rho_(0)L/A((e-1)/e),i=V_(0)/R,`
(b)`V_((X))=(V_(o)(e^(-X//L)))/(1-e^(-1))`