   Chapter 17, Problem 2P

Chapter
Section
Textbook Problem

A copper wire has a circular cross section with a radius of 1.25 mm. (a) If the wire carries a current of 3.70 A, find the drift speed of electrons in the wire. (Take the density of mobile charge carriers in copper to be n = 1.10 × 1029 electrons/m3.) (b) For the same wire size and current, find the drift speed of electrons if the wire is made of aluminum with n = 2.11 × 1029 electrons/m3.

(a)

To determine
The drift speed of electrons. in the copper wire

Explanation

Given Info: Radius of  circular cross section of copper wire is 1.25mm and the current in the copper wire is 3.70A and the charge carrier density is 1.10×1029electrons/m3 , Radius of cross section of copper wire is 1.25mm and the current in the copper wire is 3.70A and the charge carrier density is 1.10×1029electrons/m3 .

Explanation:

Formula to calculate area of circular cross section of wire is

A=πr2

• r is the radius of circular cross section

Substitute 3.14 for π , 1.25mm for r in the above equation to find A

A=(3.14)((1.25mm)(10-3m1mm))2=4.91×106m2

The area of cross section of copper wire is 4.91×106m2

Formula to calculate the drift speed through the metal wire is

vd=IneA

• I is the current flows through the metal wire,
• n is the number of electrons passed,
• e is the charge of an electron,
• A is the area of cross section of copper wire,

Substitute 3

(b)

To determine
The drift speed of electrons. in the aluminum wire

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