Physics for Scientists and Engineers
Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 26, Problem 1P
To determine

The number of years does one electron takes to travel the full length of the cable.

Expert Solution & Answer
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Answer to Problem 1P

The number of years that takes one electron to travel the full length of the cable is 27.0yr .

Explanation of Solution

Given information: Length of the high voltage transmission line is 200km , diameter of the transmission line is 2.00cm , steady current is 1000A , the number of electrons per unit volume is 8.50×1028electrons/m3 .

Explanation:

Write the expression for the area of cross section of a conductor.

A=π4d2

Here,

A is the area of cross section of a conductor.

d is the diameter of the transmission line.

Substitute 2.00cm for d in equation (1) to find A ,

A=π4(2.00cm×1m100cm)2=3.14×104m2

Thus, the area of cross section of a conductor is 3.14×104m2 .

Formula to calculate the drift velocity of a conductor.

I=neAVdVd=IneA (2)

Here,

Vd is the drift velocity of a conductor.

n is the number of electrons per unit volume.

I is the steady current.

e is the charge of one electron.

The value of charge of one electron is 1.6×1019C .

Substitute 1000A for I , 8.50×1028electrons/m3 for n , 1.6×1019C for e , 3.14×104m2 for A in equation (2) to find Vd ,

Vd=1000A(8.50×1028electrons/m3)×(1.6×1019C)×(3.14×104m2)=2.34×104m/s

Thus, the drift velocity of a conductor is 2.34×104m/s .

Formula to calculate the number of years that takes one electron to travel the full length of the cable.

T=DVd (3)

Here,

T is the number of years that takes one electron to travel the full length of the cable.

D is the length of the high voltage transmission line.

Substitute 200km for D , 2.34×104m/s for Vd in equation (3) to find T ,

T=200km×1000m1km2.34×104m/s=8.54×108s×1yr(365×24×60×60)s=27.0yr

Thus, the number of years that takes one electron to travel the full length of the cable is 27.0yr .

Conclusion:

Therefore, the number of years that takes one electron to travel the full length of the cable is 27.0yr .

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A 200-km-long high-voltage transmission line 2.0 cm in diameter carries a steady current of 1 000 A. If the conductor is copper with a free charge density of 8.5 × 10−8 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable?
A 200-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1 000 A. If the conductor is copper with a free charge density of 8.50 x 1028 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable?
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Chapter 26 Solutions

Physics for Scientists and Engineers

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