Question

You've made the finals of the Science Olympics! As one of your tasks, you're given 2.0 g of copper and asked to make a cylindrical wire, using all the metal, with a resistance of 1.8 Ω .

Part A

What length ℓ will you choose for your wire?

Express your answer in meters to two significant figures.

**** the answer is NOT 16m or 24m!!!!!

Part B

What diameter d will you choose for your wire?

Express your answers in millimeters to two significant figures.

Answer 1

R = rho*l/A

where "R" is the resistance, "rho" is the resistivity of copper, and "A" is the cross-sectional area of the wire.

l = R*A/rho = R*(pi*r^2)/rho

mass

m = D*v = D*A*l = D*(π*r^2)*R*(π*r^2)/ρ

where "D" is the density of copper.

r^4 = m*rho/( D*(pi^2)*R )

D = 8.94 g/cm^3 = 8.94*10^3 kg/m^3

rho = 16.8 n ohm = 16.8*10^-9 ohm*m

r^4 = (.002)*( 16.8*10^-9 )/( ( 8.94*10^3 )*(pi^2)*1.8 ) = 2.12 x 10^-16 m

r = 1.21*10^-4 m = .12 mm, or the diameter = .24 mm

l = R*(pi*r^2)/rho = 1.8*(pi*( .121*10^-3 )^2/16.8*10^-9 = 4.9 m