Question

5 (17 points)). Calculate the dift velocity of electrons in a copper wire (which has a ia o 6.053 mm) carrying a 209-A current, given that there is one free electron per copper atom Density ofcopper = 8.80x10° kg/m, Molar mass of copper = 63.549 gmimo)

Answer 1

Given

copper wire of diameter d = 6.053 mm , radius r =3.0265 mm

current I = 20.9 A

and one free electron per copper atom

density of copper d = m/v = 8.80*10^3 kg/m3

molar mass of copper MW=63.549 gm/mol

and avagadro number is NA = 6*10^23 ,

we know that the drift speed the averave speed with which the electrons can move in the conductor

given by Vd = J/N*e where J is current density J = I/A

A = area of cross section A = pi*r^2 = pi*(3.0265*10^-3)^2 2 = 2.88*10^-5 m2

J = 20.9/(2.88*10^-5) A/m2 = 725694.444 A/m2

n is density of electrons is no of atoms per cubic meter

given that the a cubic meter of copper of mass is 8.80*10^3 kg, so

the n = 8.80*10^6(6*10^23/63.549) = 8.31*10^28

substituting the values  

Vd = 725694.444 /(8.31*10^28 *1.6*10^-19) m/s

Vd = 5.4579907039711*10^-5 m/s

Vd = 54.58*10^-6 m/s