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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

(i) `E =(V_(0))/(L)((e)/(e-1))e^(-x//L)`
(ii) `-(dV)/(dx)=(V_(0))/(L)((e)/(e-1))e^(-x//L)`
(iii) `R = (p_(0)L)/(A)[1-(1)/(e)]`
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