EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
16th Edition
ISBN: 8220100546716
Author: Katz
Publisher: CENGAGE L
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Chapter 28, Problem 81PQ
To determine

The time taken for one electron to travel from the generating station to the switching station in the wire.

Expert Solution & Answer
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Answer to Problem 81PQ

The time taken for one electron to travel from the generating station to the switching station in the wire is 1.19×109s_.

Explanation of Solution

Given that the distance between the generating station and the switching station is 140.0km, the transmitted current is 850.0A, the cross-sectional area of the wire is 750.0mm2, and the density of free electrons in the wire is 6.022×1028m3.

Write the expression for the drift velocity of electron in terms of the current density.

  vd=Jne                                                                                                                 (I)

Here, vd is the drift velocity, J is the current density, n is the number density of electrons, and e is the charge of electron.

Write the expression for the current density in the wire.

  J=IA                                                                                                                   (II)

Here, I is the current, and A is the cross-sectional area of the wire.

Use equation (II) in (I).

  vd=IneA                                                                                                             (III)

Write the expression for the time taken for the electron to travel a particular distance through the wire.

  Δt=dvd                                                                                                                (IV)

Here, d is the distance, and Δt is the time taken to cover the distance.

Use equation (III) in (IV).

  Δt=neAdI                                                                                                            (V)

Conclusion:

Substitute 6.022×1028m3 for n, 1.60×1019C for e, 750.0mm2 for A, 140.0km for d, and 850.0A for I in equation (V) to find Δt.

  Δt=(6.022×1028m3)(1.60×1019C)(750.0mm2)(140.0km)850.0A=(6.022×1028m3)(1.60×1019C)(750.0mm2×1m21×106mm2)(140.0km×1000m1km)850.0A=1.19×109s

Therefore, the time taken for one electron to travel from the generating station to the switching station in the wire is 1.19×109s_.

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Chapter 28 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

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