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Cheap resistors are fabricated by depositing a thin
layer of carbon onto a nonconducting cylindrical substrate. If such a cylinder has radius a and length d, determine the thickness of the film required for a resistance R if
a = 1 mm R = 33 k
σ = 1
ρ = 2.9 MS/m
d = 9 mm
Neglect the end surfaces of the cylinder and assume
that the thickness is much smaller than the radius.

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