The Resistance R Of A Wire Varies Directly As Its Length And Inversely As T

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