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If the resistance of a wire 1200ft long with a diameter of 0.28 inches is 16279 ohms, what is the resistance of 2600ft of the same type of wire with a diameter of 0.18 inches? (Leave k in fraction form or round to at least 3 decimal places. Round off your final answer to the nearest hundredth.)
Solution
The Resistance of a (conducting) material is defined by R = ρL/A,
where ρ = resistivity of the material
L = length of material
A = cross-sectional area = πD2/4 [ with D = diameter]
Solve for the resistivity using the first part of the known quantities,
==> ρ = RA/L =…
with this resistivity value solve for the new resistance using Rnew = ρLnew/Anew,
NB: remember to convert the units: 1 ft = 12 in