Question

The diameter of a 12-gauge copper wire is about 0.790 mm. If the drift velocity of the electrons is 3.25 mm/s what is the electron current in the wire? The number of electron carriers in 1.0 cm3 of copper is 8.5 × 1022.

Answer 1

21.6 A

Step-by-step explanation:

n = number density of free electrons in copper = 8.5 x 10²² cm⁻³ = 8.5 x 10²⁸ m⁻³

e = magnitude of charge on electron = 1.6 x 10⁻¹⁹ C

d = diameter of copper wire = 0.790 mm = 0.790 x 10⁻³ m

Area of cross-section of copper wire is given as

A = (0.25) πd²

A = (0.25) (3.14) (0.790 x 10⁻³)²

A = 4.89 x 10⁻⁷ m²

v = drift speed = 3.25 mm/s = 3.25 x 10⁻³ m /s

the electric current is given as

i = n e A v

i = (8.5 x 10²⁸) (1.6 x 10⁻¹⁹) (4.89 x 10⁻⁷ ) (3.25 x 10⁻³)

i = 21.6 A