Question

A copper wire that has a diameter of 2.00 mm carries a current of 10.0 A. Assuming that each copper atom contributes one free electron to the metal, calculate the drift speed of the electrons in the wire. The molar mass of copper is 63.5 g/mol and the density of copper is 8.95 g/cm3.

Answer 1

Given : d = 2 mm , I = 10 A , M= 63.5 g/mol , = 8.95 g/cm³

Solution:

Step:1

Number density of atom for copper is given by:

n =[ (6×10²³)(8950 kg/m³)]/[63.5×10^-3kg/mol]

n = 8.46 × 10²⁸ m^-3

Step:2

Cross sectional area of the wire is given by :

A = (/4)d²

= (3.14/4)(0.002)²

= 3.14×10^-6 m²

Step:3

Using the equation, I = neAv_d

Where v_d is the drift velocity.

10 A = (8.46×10²⁸ m^-3)(1.6×10^-19 C)(3.14×10^-6 m²)(v_d)

v_d = 10/42503.04 = 2.35×10^-4 m/s

Answer: drift velocity (v_d)= 2.35×10^-4 m/s