The resistivity of a semi conductor can be modified by adding different amounts of impurities. A rod of semi conducting material of length L and cross-sectional 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 p(x) = P0 exp (-x/L). The end of the rod at x = 0 is at a potential V0 greater than the end at x = L.
a) Find the total resistance of the rod and the current in the rod.
b) Find the electric-field magnitude E(x) in the rod as a function of x.
c) Find the electric potential v(x) in the rod as a function of x.
d) Graph the functions p(x). E(x), and V(x) for values of x between x = 0 and x = L