Physics for Scientists and Engineers, Vol. 1
Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
bartleby

Videos

Question
Book Icon
Chapter 28, Problem 63P

(a)

To determine

The initial rate of increase of current.

(a)

Expert Solution
Check Mark

Answer to Problem 63P

The initial rate of increase of current is 3kA/s .

Explanation of Solution

Given:

The inductance of a coil is L=4mH

The resistance of a resistor is R=150Ω

The voltage of ideal battery is εo=12V

Formula used:

The expression for the current in the circuitis given by,

  I=εo(1e t τ )R

Calculation:

The initial rate of increase of current is calculated by differentiating the current with time.

  dIdt=εoRddt(1e t τ )=εoR(e t τ )( 1τ)=εoRτe tτ

Solve further as,

  dIdt t=0=εoRτe 0τ=12V4mH=3kA/s

Conclusion:

Therefore, the initial rate of increase of current is 3kA/s .

(b)

To determine

The rate of increase of current when the current is half of its steady-state value

(b)

Expert Solution
Check Mark

Answer to Problem 63P

The rate of increase of current when the current is half of its steady-state value is 1.5kA/s .

Explanation of Solution

Formula used:

The expression for the current in the circuit is given by,

  I=εo(1e t τ )R

Calculation:

According to the given condition,

  I=0.5IfIIf=1e tτ0.51=e tτe tτ=0.5

The rate of increase of current at I=0.5If is calculated by differentiating the current with time.

  dIdt=εoRddt(1e t τ )=εoR(e t τ )( 1τ)=εoRτe tτ

Solve further as,

  dIdt=0.5×εoL=0.5×12V4mH=1.5kA/s

Conclusion:

Therefore, the rate of increase of current when the current is half of its steady-state value is 1.5kA/s .

(c)

To determine

The steady state value of current.

(c)

Expert Solution
Check Mark

Answer to Problem 63P

The steady state value of current is 0.08A .

Explanation of Solution

Formula used:

The expression for the steady state value of current is given by,

  If=εoR

Calculation:

The steady state value of current is calculated as,

  If=εoR=12V150Ω=0.08A

Conclusion:

Therefore, the steady state value of current is 0.08A .

(d)

To determine

The time taken of the current to reach 99% of its steady-state value

(d)

Expert Solution
Check Mark

Answer to Problem 63P

The time taken of the current to reach 99% of its steady-state value is 0.123ms .

Explanation of Solution

Formula used:

The expression for the current in the circuit is given by,

  I=εo(1e t τ )R

Calculation:

According to the given condition,

  I=0.99IfIIf=1e tτ0.991=e tτe tτ=0.01

Solve further as,

  t=τln(0.01)=LRln(0.01)=4mH150Ωln(0.01)=0.123ms

Conclusion:

Therefore, the time taken of the current to reach 99% of its steady-state value is 0.123ms .

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!
Students have asked these similar questions
Defination of voltage
At point A, 3.20 m from a small source of sound that is emitting uniformly in all directions, the intensity level is 58.0 dB. What is the intensity of the sound at A? How far from the source must you go so that the intensity is one-fourth of what it was at A? How far must you go so that the sound level is one-fourth of what it was at A?
Make a plot of the acceleration of a ball that is thrown upward at 20 m/s subject to gravitation alone (no drag). Assume upward is the +y direction (and downward negative y).

Chapter 28 Solutions

Physics for Scientists and Engineers, Vol. 1

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
University Physics Volume 2
Physics
ISBN:9781938168161
Author:OpenStax
Publisher:OpenStax
Text book image
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
Text book image
Inquiry into Physics
Physics
ISBN:9781337515863
Author:Ostdiek
Publisher:Cengage
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
What is Electromagnetic Induction? | Faraday's Laws and Lenz Law | iKen | iKen Edu | iKen App; Author: Iken Edu;https://www.youtube.com/watch?v=3HyORmBip-w;License: Standard YouTube License, CC-BY