Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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
Sketch a sine wave depicting 3 seconds of wave activity for a 5 Hz tone. Sketch the resulting complex wave form that results from the combination of the following two waves. Is this wave periodic or aperiodic? USE GRAPH PAPER!
Required information A bungee jumper leaps from a bridge and undergoes a series of oscillations. Assume g = 9.78 m/s². If a 60.0-kg jumper uses a bungee cord that has an unstretched length of 30.1 m and she jumps from a height of 45.2 m above a river, coming to rest just a few centimeters above the water surface on the first downward descent, what is the period of the oscillations? Assume the bungee cord follows Hooke's law.
Required information The leg bone (femur) breaks under a compressive force of about 6.50 × 104 N for a human and 12.3 × 104 N for a horse. The human femur has a compressive strength of 160 MPa, whereas the horse femur has a compressive strength of 140 MPa. What is the effective cross-sectional area of the femur in a horse? (Note: Since the center of the femur contains bone marrow, which has essentially no compressive strength, the effective cross-sectional area is about 80% of the total cross-sectional area.) cm2

Chapter 28 Solutions

Physics for Scientists and Engineers

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