A 10-gauge copper wire (diameter = 2.588 mm,$\rho$ = 1.7 $\times$ 10^-8 $\Omega$ · m)has a total resistance of 0.32 $\Omega$.How long is the wire?

Question

Quizplus · Accepted Answer

The formula for the resistance of a wire is R = (ρL)/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area. Rearranging the formula, we get:
L = (RA)/ρ
Substituting the given values, we get:
L = (0.32 x π x (0.002588/2)^2)/1.7x10^-8
L = 99.2 meters or 99 m (rounded to two significant figures) 
Therefore, the best choice is C.

A 10-Gauge Copper Wire (Diameter = 2 ρ\rhoρ = 17 ×\times× 10-8 Ω\OmegaΩ

A 10-Gauge Copper Wire (Diameter = 2 $\rho$ = 17 $\times$ 10^-8 $\Omega$