physics question

Question

A 1.0 kg bar of copper is drawn into 0.50 mm diameter wire. Calculate

a) The length of the wire

 b) The electrical resistance of the wire.

 • Density of copper = 8.96 x 103 kg m-3

• Resistivity of copper = 1.68 x 10-8 Ω m

Answer 1

You need to find the length and the cross sectional area of the wire in order to calculate the resistance.

 

A = πr² = π(0.25 x 10^-3 m)² ≅ 1.963 x 10^-7 m²

 

(a)

 

L = V/A

 

V = m/density = (1.0 kg) / (8.96 x 10³ kg/m³) ≅ 1.116 x 10^-4 m³

 

L = (1.116 x 10^-4 m³)/(1.963 x 10^-7 m²) ≅ 568.5 m

 

(b)

 

R = ρL/A = (1.68 x 10^-8 Ωm)(568.5 m) / (1.963 x 10^-7 m²) ≅ 48.65 Ω