Physics

Problem

A cylindrical wire of length

L = 1.0\,\text{m}

and constant cross-sectional area

A = 1.0\,\text{mm}^{2}

is manufactured such that its resistivity is not constant. The resistivity varies linearly with position

x

from the left end, given by the function

\rho(x) = \rho_{0} (1 + x)

, where

\rho_{0} = 1.0 \times 10^{-6}\,\Omega\cdot\text{m}

and

x

is in meters. Determine the total resistance of the wire.