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A rod of length L and cross-section area...

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`.

Text Solution

Verified by Experts

`R=(rho_(0)L)/(A)(1-(1)/(e)),I=(V_(0)A)/(rho_(0)L)((e)/(e-1)),V=(V_(0)(e^(-X//L)-e^(-1)))/(1-e^(-1))`
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