Question

A copper wire 225m long must experience a voltage drop of less than 2.0v when a current of 3.5 a passes through it. compute the minimum diameter of the wire in millimeters (mm) if the electrical conductivity of copper is 60.0 x106 (ohm-m)-1 . answer should be in millimetres and carried out 2 decimal places (x.xx mm)

Answer 1

V = I * R

R = 2 / 3.5 = .571 ohms maximum resistance of wire

R = ρ L / A where R is proportional to L and inversely proportional to A

A = ρ L / R minimum area of wire

ρ = 1 / μ = 1.67E-8 ohm-m resistivity inverse of conductivity

A = 1.67E-8 ohm-m * 225 m / .571 ohm = 6.68E-6 m^2

A = 6.68 mm^2 since 1 mm^2 = 10-6 m^2 or 1 mm = 10-3 m

A = Π r^2 = 6.68 mm^2

r = (6.68 / 3.14)^1/2 mm = 2.13 mm radius of wire

d = 2 * r = 4.26 mm