Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
bartleby

Concept explainers

Question
Book Icon
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
Check Mark

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 .

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 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
04:53
Students have asked these similar questions
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?
A 190-km-long high-voltage transmission line 2.0 cm in diameter carries a steady current of 1,210 A. If the conductor is copper with a free charge density of 8.5 x1028 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable? (Use 3.156 x107 for the number of seconds in a year.)

Chapter 26 Solutions

Physics for Scientists and Engineers with Modern Physics

Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning