Physics

Problem

A specialized sensor wire of length

L = 1.0\,\text{m}

has a circular cross-section where the radius decreases exponentially with distance

x

from the source end:

r(x) = r_{0} e^{-x}

. Given

r_{0} = 1.0\,\text{mm}

and material resistivity

\rho = 3.14 \times 10^{-7}\,\Omega\cdot\text{m}

, find the total resistance of the wire. (Use

e^{-2} \approx 0.135

if needed, take

\pi = 3.14