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 31, Problem 52CP

(a)

To determine

The emf across L immediately after t=0 .

(a)

Expert Solution
Check Mark

Answer to Problem 52CP

The emf across L immediately after t=0 is 96V .

Explanation of Solution

Given info: The battery emf is 18.0V , inductance is 0.500H , first resistance is 2.00 and second resistance is 6.00 .

Initially switch s is closed so the total current distribute in two current one is flow in the right loop and another current flow in the left loop.

Write the expression for the total current by Kirchhoff junction rule.

i=i1+i2 (1)

Here,

i is the total current.

i1 is the current in the right loop.

i2 is the current in the left loop.

Write the expression for the current in the right loop.

i1=εR1(1eR2t/L)

Here,

ε is the emf of the battery.

R1 is the resistance of the first resistor.

R2 is the resistance of the second resistor.

l is the inductance of the inductor.

Since for the steady state condition t=0 so,

Substitute 0 for t in equation (2).

i1=εR1(1eR2(0)/L)=εR1

Substitute 18.0V for ε and 2.00 for R1 to find i1 .

i1=18.0V2.00×103Ω1kΩ=9×103A×103mA1A=9mA

Write the expression for the current in the left loop.

i2=εR2

Substitute 18.0V for ε , 6.00 for R2 to find i2 .

i2=18.0V6.00×103Ω1kΩ=3×103A×103mA1A=3mA

Substitute 9mA for i1 and 3mA for i2 in equation (1).

i=9mA+3mA=12mA

Write the expression for the voltage across the inductor by Kirchhoff loop rule after t=0 .

i(R1+R2)+ΔVL=0

Rearrange the term for ΔVL .

ΔVL=i(R1+R2)

Substitute 18.0V for ε and, 2.00 for R1 , 6.00 for R2 , 12mA for i to find ΔVL

ΔVL=12mA(2.00+6.00)ΔVL=96V

Conclusion:

Therefore, the emf across L immediately after t=0 is 96V .

(b)

To determine

The point of the coil that have higher potential.

(b)

Expert Solution
Check Mark

Answer to Problem 52CP

The point a is at high potential than point b .

Explanation of Solution

Given info: The battery emf is 18.0V , inductance is 0.500H , first resistance is 2.00 and second resistance is 6.00 .

Since the current flow upwards to downward direction in the inductor coil due to some reactance of the coil the voltage drop across the inductor coil hence the point b  at lower potential in compare to the point a of the coil.

Write the expression for the voltage drop across the inductor coil.

ΔVL=Ldidt

Here,

L is the inductance of the coil.

Conclusion:

Therefore, the point a is at high potential than point b .

(c)

To determine

To draw: The graph of currents in R1 and R2 as a function of time and show values before and after t=0 .

(c)

Expert Solution
Check Mark

Answer to Problem 52CP

The graph of currents in R1 and R2 as a function of time and show values before and after t=0 is shown below.

Physics for Scientists and Engineers with Modern Physics, Chapter 31, Problem 52CP , additional homework tip  1Physics for Scientists and Engineers with Modern Physics, Chapter 31, Problem 52CP , additional homework tip  2

Explanation of Solution

Given info: The battery emf is 18.0V , inductance is 0.500H , first resistance is 2.00 and second resistance is 6.00 .

The currents in R1 and R2 are shown below. After t=0 , the current in R1 decreases from an initial values of 9mA according to i=I1eRt/L . Take the original current direction as positive in each resistor the current decreases from 9mA to zero.

In R2 the currents jumps from 3.00mA to 9.00mA upwards and then decrease in magnitude to zero. The time constant of each decay is 1/e=36.8% of the original value.

Physics for Scientists and Engineers with Modern Physics, Chapter 31, Problem 52CP , additional homework tip  3Physics for Scientists and Engineers with Modern Physics, Chapter 31, Problem 52CP , additional homework tip  4

Figure (I)

(d)

To determine

The time at which the value of current in R2 become 2.00mA .

(d)

Expert Solution
Check Mark

Answer to Problem 52CP

The time at which the value of current in R2 become 2.00mA is 75.2μs .

Explanation of Solution

Given info: The battery emf is 18.0V , inductance is 0.500H , first resistance is 2.00 and second resistance is 6.00 .

Formula to calculate the current in the circuit after t=0 is,

i=i1e((R1+R2)t/L)

Substitute 2.00 for R1 , 6.00 for R2 , 9mA for i1 , 2.00mA for i ,  and 0.500H for L to find i

2.00mA=(9mA)e((2.00+6.00)t/0.500H)e((8.00)t/0.500H)=2.00mA9mA

Take log and solve the equation further,

t=7.52×105s×106μs1s=75.2μs

Conclusion:

Therefore, the time at which the value of current in R2 become 2.00mA is 75.2μs .

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
Consider the RL circuit in the figure with R=10.00 Ω, L1=1.80 H, L2=3.90 H, and V=5.0 V. At time t=0, the switch is closed to connect the circuit to a constant emf. How long (in seconds) does it take for the current to reach a value of Imax/2.71828 of its maximum value, where Imax is the maximum current through the circuit?
For the circuit in the figure, at t = 0 the switch S is closed with the capacitor uncharged. If C = 56 µF, ɛ = 80V, and R = 4 kQ, what is the charge (in mC) on the capacitor when the current in the circuit is | = 8.6 mA? %3D S C Select one: O A. 2.55 В. 3.09 Ос. 6.41 O D. 4.63 O E. 1.38
The capacitor in the circuit shown below is initially uncharged. The switch is closed at t = 0 s. ΔVbattery = 60 V, C = 2.0 F, and R = 3.0 Ω. What is the current in the circuit immediately after the switch is closed, in Ampere?

Chapter 31 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
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Text book image
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
Text book image
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON