Question

Suppose that you wish to fabricate a uniform wire out of 1.05 g of copper. Assume the wire has a resistance R = 0.800 ohm, and all of the copper is used. What will be the length of the wire? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m What will be the diameter of the wire? mu m

Answer 1

(a).

density of copper is ρ = 8.94 grams/cm³ and its resistivity σ = 16.78 * 10^(-9) Ω·m

V = m/ρ

AL = m/ρ

A = m/(ρL)

R = σL/A

R = σL²ρ/m

0.8 = 16.78 * 10^(-9) L²(8.94 * 1000)/(1.05*10^-3)

L = 2.3663 m




(b).

AL = m/ρ

(¼ π d²)L = m/ρ

(¼ π d²)(2.3663) = (1.05 * 10^(-3))/(8.94 * 1000)

d = 2.5138887x10^-4 m

d =251.3887xu m