Question

You've made the finals of the Science Olympics! As one of your tasks, you're given 1.5 g of copper and asked to make a cylindrical wire, using all the metal, with a resistance of 1.0 Ω . What length ℓ will you choose for your wire? What diameter d will you choose for your wire?

Answer 1

Mass of copper = m = 1.5 gm = 1.5 x 10^-3 kg

Density of copper = _c = 8960 kg/m³

Resistivity of copper = = 1.72 x 10^-8m

Resistance of wire = R = 1

Length of copper wire = L

Diameter of copper wire = d

Area of cross section = A = d²/4

Volume of copper wire = V = AL

m = _cV

1.5 x 10^-3 = 8960 x V

V = 1.674 x 10^-7 m³

AL = 1.674x10^-7

A = (1.674x10^-7)/L

L² = 9.732

L = 3.12 m

A = (1.674x10^-7)/L

d²/4 = (1.674x10^-7)/3.12

d² = 6.831 x 10^-8

d = 2.613 x 10^-4 m

Length and diameter of the wire are 3.12m and 2.613x10^-4m respectively.