The resistivity of a semiconductor can be modified by adding different amounts of impurities. A rod of semiconducting 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 ?(x)=?0exp(?x/L). The end of the rod at x=0 is at a potential V0 greater than the end at x=L.

Find the total resistance of the rod.

Express your answer in terms of the given quantities and appropriate constants.

R =
.632L?0A

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Part B

Find the current in the rod.

Express your answer in terms of the given quantities and appropriate constants.

I =
V0A?0L(1?e?1)

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Part C

Find the electric-field magnitude E(x) in the rod as a function of x.

Express your answer in terms of the given quantities and appropriate constants.

E(x) =
V0e?xLL(1?e?1)

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Part D

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

Express your answer in terms of the given quantities and appropriate constants.

V(x) =
V0e?xL?e?11?e?1

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Part E

Graph the function ?(x) for values of x between x=0 and x=L.

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Part F

Graph the function E(x) for values of x between x=0 and x=L.

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Part G

Graph the function V0(x) for values of x between x=0 and x=L.