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 1.1 Ω .

What length ℓ will you choose for your wire?

What diameter d will you choose for your wire?

Answer 1

we know the resistivity of copper is = 1.72*10^-8 ohm m

and density of copper d= 8940 kg/m³

so we know

  

on combining these equations

L = (mR/(ρ*d)) ^1/2

= [1.5*10^-3*1.1/(1.72*10^-8 *8940 )]^1/2

= 3.275 m

and

  

so diameter = 2r = 0.255 mm