Question

A 10 gauge copper wire carries a current of 12 A. Assuming one free electron per copper atom, calculate the drift velocity of the electrons. (The cross-sectional area of a 10-gauge wire is 5.261 mm².)
...........................mm/s

Answer 1

Drift velocity is given by

where I is the current in Ampere

A is the cross sectional area of the wire in meter²

q is the charge in Coulomb

n is the charge density (m^-3)

Density of copper =8.940 g/cm³

molar mass of copper= 63.546 g/mol

so there are 8.94/63.546=140685 mol/m³ copper atoms

one mole of copper contains 6.023x10²³ copper atoms, so in 1 m³ there are (6.023x10²³x140685) copper atoms.

so n=6.023x10²³x140685=8.47x10²⁸ /m³

crose sectional area= =5.261 mm²= 5.261 x 10^-6 m² , I=12A, q=1.6x10^-19

drift velocity =12/(8.47x10²⁸x5.261 x 10^-6x1.6x10^-19) = 1.683 x 10^-4 m/s

v_d=0.1683 mm/s