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# Current Electricity: A Rod with Variable Resistivity

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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 p(x)= p0exp(-x/L). The end of the rod at x=0 is at a potential Vo greater than the end at x=L.

1.)Find the total resistance of the rod.
Express your answer in terms of the given quantities and appropriate constants.

2.)Find the current in the rod.
Express your answer in terms of the given quantities and appropriate constants.

3.)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.

4.)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.