The resistance, R, of a wire varies directly as its length and inversely as the square of its diameter.

Question

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.)

Answer 1

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 R_new = ρL_new/A_new,

NB: remember to convert the units: 1 ft = 12 in

Answer 2

The relation to work with for resistance (R) proportional to lenght (L) but inversely proportional to diameter squared (D²) is

RD² / L = k = constant ⇒

R = k (L/D²)

Get the value of k from the first set of R, L, and D values. Then plug in the second set of L and D values to get the new value of R.