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Chapter 27: Q. 62 (page 764)

The two wires in FIGURE P27.62 are made of the same material. What are the current and the electron drift speed in the 2.0-mm-diameter segment of the wire?

Short Answer

Expert verified

The current and the electron drift speed in the 2.0-mmdiameter segment of the wire is vd2=0.5μms.

Step by step solution

01

Given information

Wire 1 diameter =2.0mm

Wire 2 diameter=1.0mm

Drift speed Vd=2.0×10-4m/s

CurrentI=2.0A

02

Explanation

The current will be the same,I=2A

In this case, the electron current (the number of electrons flowing per unit time) would also be the same because of the same current.

That is, ne1A1vd,1=ne2A2vd,2

Due to the same material on both sides, the densities can be simplified, and we can increase the area thanks to the circular pattern.

Simplify byπwe get,

D12vd,1=D22vd,2

Find the drift speed at the second part as,

vd,2=D12D22vd,1

Substitute the values,

vd,2=1mm2mm×0.2m/s

=0.05mm/s.

03

Final Answer

Hence, the current and the electron drift speed in the2.0mmdiameter segment of the wire is0.05mm/s.

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The total amount of charge that has entered a wire at time tis given by the expressionQ=(20C)1-e-4(20s), where tis in seconds andt≥0.
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