The resistivity of copper at 20ºC is 1.7 $\times$ 10^-8 $\Omega$ · m.You have copper wire whose diameter is 2.00 mm and need a resistance of 1.00 $\Omega$.How long would a piece of this wire need to be to provide this resistance? A)19.6 m B)49.1 m C)185 m D)317 m E)542 m

Question

Quizplus · Accepted Answer

The formula for resistance of a wire is:

R = (ρL)/A

where:
R = resistance
ρ = resistivity
L = length of wire
A = cross-sectional area of wire

We are given:
ρ = 1.7 x 10^-8 Ω·m
diameter of wire = 2.00 mm = 0.002 m
We need to find L such that R = 1.00 Ω

The cross-sectional area of the wire can be calculated as:

A = πr^2 = π(d/2)^2
where d = diameter and r = radius

A = π(0.002/2)^2 = 3.14 x 10^-6 m^2

Now we can rearrange the formula for resistance to solve for L:

L = (RA)/ρ

L = (1.00 Ω x 3.14 x 10^-6 m^2) / (1.7 x 10^-8 Ω·m)

L = 185.3 m

Therefore, the length of wire needed to provide a resistance of 1.00 Ω is 185 m (to three significant figures). The correct answer choice is C.

The Resistivity of Copper at 20ºC Is 1 ×\times× 10-8 Ω\OmegaΩ · MYou Have Copper Wire Whose Diameter Is 2

The Resistivity of Copper at 20ºC Is 1 $\times$ 10^-8 $\Omega$ · MYou Have Copper Wire Whose Diameter Is 2