Question

1- Building codes usually limit the current carried by a No. 14 copper wire to 15 A. Many household circuits are wired with this size wire. What is the drift velocity of the electrons in this case? The diameter of No. 14 wire is 1.6 mm. Assume one conduction electron per atom in copper. The atomic weight of copper is 63.3 and its density is 8900 kg/m³.

	4.89 x 10-5 m/s
	4.56 x 10-4 m/s
	5.52 x 10-4 m/s
	4.44 x 10-2 m/s
	1.65 x 10-3 m/s The answer is 5.52 x 10-4 m/s useing the equation Vd=J/nq=I/Anq i would like to know who we got the values for n, q, and A. Thank you in advance.

Answer 1

Concepts and reason

The concepts used in this problem are drift velocity and the number density of the free electrons.

Initially, use the concept of the number density of free electrons to find its value and then, determine the drift velocity of the electrons using the concept of drift velocity and number density of the electrons.

Fundamentals

Drift velocity:

The drift velocity is defined as the average velocity with which electrons drift under the influence of the electric field. The expression for the drift velocity is given by:

Here, is the drift velocity of the electrons, is the current flowing through the conductor, is the number density of the free electrons, is the charge on the electrons andis the area of cross-section of the conductor.

The number density of the free electrons:

The number density of the free electrons is defined as the number of electrons per unit volume of the conductor. The formula for the number density of free electrons is given by,

Here, is the number density of the free electrons, is the density of the material, is the Avogadro’s number andis the atomic weight of the conductor.

The expression for the number density of the free electrons is given by,

Substitutefor, forandforin the above equation.

The diameter of the wire is,

The area of the wire is,

Here, is the diameter of the wire.

Substitute forin the above equation

The expression for the drift velocity of the electrons is given by,

Substitute for, for, for and for in the above equation.

Ans:

The drift velocity of the electrons is .