Common household wiring is 12gauge copper wire This gauge wi

Common household wiring is 12-gauge copper wire. This gauge wire has a cross-sectional area of 5.31 Times 10^-6 m^2. If the wire carries a 10.0 A current, what is the drift speed of the electrons? Assume copper items contribute 1 conduction electron/atom. The density of copper is 8.95g/cm^3 and copper\'s molar mass is 63.5 g/mol.

Solution

Given current I=10.0 A

Area A=3.31x10^-6 m^2

Current Density j=I/A= 3021148 A/m^2

Molar mass of copper=63.5 g/mol

6.023x10^23 atoms of copper has a mass of 63.5 g

Since 1 atom contributes 1 conduction electron, 63.5 g of copper has 6.023x10^23 electrons

Density of copper rho=8.95 g/cm^3

1 cm^3 of copper has a mass of 8.95 g.

Hence, 1 cm^3 of copper has (8.95/63.5)x6.023x10^23= 8.49x10^22 electrons

1 m^3 of copper has 8.49x10^28 electrons

Drift velocity=j/ne= 3021148/(8.49x10^28x1.6x10^-19= 0.00022240489 m/s = 0.222 mm/s