EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 9781305804463
Author: Jewett
Publisher: CENGAGE LEARNING - CONSIGNMENT
bartleby

Concept explainers

Question
100%
Book Icon
Chapter 32, Problem 32.31P

(a)

To determine

The time interval the current reach the value 220mA .

(a)

Expert Solution
Check Mark

Answer to Problem 32.31P

The time interval the current reach the value 220mA is 5.66ms .

Explanation of Solution

Given Info: The inductance in the circuit is 140mH , the resistance in the circuit is 4.90Ω and the emf of the battery is 6.00V .

The equation for the current rise in a LR circuit is,

I=εR(1exp(RtL))

Here,

ε is the emf of the battery.

R is the resistance in the circuit.

L is the inductance.

t is the time interval.

Substitute 140mH for L , 4.90Ω for R , 6.00V for ε and 220mA for I in the above equation.

220mA=6.00V4.90Ω(1exp((4.90Ω)t140mH))220mA×(1.00A103mA)=1.22(1exp((4.90Ω)t140mH(1.00H103mH)))0.220A=1.22(1exp((4.90Ω)t0.140H))0.220A1.22=(1exp(35t))

Further solve the above equation.

.220A1.22=(1exp(35t))1.220A1.22=exp(35t)0.82=exp(35t)

Take the logarithms of both sides.

log(0.82)=35t0.1984=35tt=0.198435=5.67×103s

Further solve the above equation.

t=5.67×103s=5.67ms5.66ms

Conclusion:

Therefore, the time interval the current reach the value 220mA is 5.66ms .

(b)

To determine

The current in the inductor after 10.0s .

(b)

Expert Solution
Check Mark

Answer to Problem 32.31P

The current in the inductor after 10.0s is 1.22A .

Explanation of Solution

Given Info: The inductance in the circuit is 140mH , the resistance in the circuit is 4.90Ω and the emf of the battery is 6.00V .

The equation for the current rise in a LR circuit is,

I=εR(1exp(RtL))

Substitute 140mH for L , 4.90Ω for R , 6.00V for ε and 10.0s for t in the above equation.

I=6.00V4.90Ω(1exp(4.90Ω(10.0s)140mH))140mH(1.00H103mH)=1.22(1exp(4.90Ω(10.0s)140mH(1.00H103mH)))=1.22(1exp(350))=1.22A

Conclusion:

Therefore, the current in the inductor after 10.0s is 1.22A .

(c)

To determine

The time interval the current falls to 160mA .

(c)

Expert Solution
Check Mark

Answer to Problem 32.31P

The time interval the current falls to 160mA is 58.1ms .

Explanation of Solution

Given Info: The inductance in the circuit is 140mH , the resistance in the circuit is 4.90Ω and the emf of the battery is 6.00V .

The equation for the current drop in a LR circuit as the battery is detached is,

I=εR(exp(RtL))

Substitute 140mH for L , 4.90Ω for R , 6.00V for ε and 160mA for I in the above equation.

160mA=6.00V4.90Ω(exp((4.90Ω)t140mH))160mA×(1.00A103mA)=1.22(exp((4.90Ω)t140mH(1.00H103mH))).160A=1.22(exp((4.90Ω)t0.140H)).160A1.22=(exp(35t))

Further solve the above equation.

.160A1.22=(exp(35t)).160A1.22=exp(35t)0.131=exp(35t)

Take the logarithms of both sides.

log(0.131)=35t2.032=35tt=2.03235=58.07×103s

Further solve the above equation.

t=58.07×103s=58.07ms58.1ms

Conclusion:

Therefore, the time interval the current falls to 160mA is 58.1ms .

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
No chatgpt pls
Please solve
Please solve

Chapter 32 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

Ch. 32 - Prob. 32.6OQCh. 32 - Prob. 32.7OQCh. 32 - Prob. 32.1CQCh. 32 - Prob. 32.2CQCh. 32 - A switch controls the current in a circuit that...Ch. 32 - Prob. 32.4CQCh. 32 - Prob. 32.5CQCh. 32 - Prob. 32.6CQCh. 32 - The open switch in Figure CQ32.7 is thrown closed...Ch. 32 - After the switch is dosed in the LC circuit shown...Ch. 32 - Prob. 32.9CQCh. 32 - Discuss the similarities between the energy stored...Ch. 32 - Prob. 32.1PCh. 32 - Prob. 32.2PCh. 32 - Prob. 32.3PCh. 32 - Prob. 32.4PCh. 32 - An emf of 24.0 mV Ls induced in a 500-turn coil...Ch. 32 - Prob. 32.6PCh. 32 - Prob. 32.7PCh. 32 - Prob. 32.8PCh. 32 - Prob. 32.9PCh. 32 - Prob. 32.10PCh. 32 - Prob. 32.11PCh. 32 - A toroid has a major radius R and a minor radius r...Ch. 32 - Prob. 32.13PCh. 32 - Prob. 32.14PCh. 32 - Prob. 32.15PCh. 32 - Prob. 32.16PCh. 32 - Prob. 32.17PCh. 32 - Prob. 32.18PCh. 32 - Prob. 32.19PCh. 32 - When the switch in Figure P32.18 is closed, the...Ch. 32 - Prob. 32.21PCh. 32 - Show that i = Iiet/ is a solution of the...Ch. 32 - Prob. 32.23PCh. 32 - Consider the circuit in Figure P32.18, taking =...Ch. 32 - Prob. 32.25PCh. 32 - The switch in Figure P31.15 is open for t 0 and...Ch. 32 - Prob. 32.27PCh. 32 - Prob. 32.28PCh. 32 - Prob. 32.29PCh. 32 - Two ideal inductors, L1 and L2, have zero internal...Ch. 32 - Prob. 32.31PCh. 32 - Prob. 32.32PCh. 32 - Prob. 32.33PCh. 32 - Prob. 32.34PCh. 32 - Prob. 32.35PCh. 32 - Complete the calculation in Example 31.3 by...Ch. 32 - Prob. 32.37PCh. 32 - A flat coil of wire has an inductance of 40.0 mH...Ch. 32 - Prob. 32.39PCh. 32 - Prob. 32.40PCh. 32 - Prob. 32.41PCh. 32 - Prob. 32.42PCh. 32 - Prob. 32.43PCh. 32 - Prob. 32.44PCh. 32 - Prob. 32.45PCh. 32 - Prob. 32.46PCh. 32 - In the circuit of Figure P31.29, the battery emf...Ch. 32 - A 1.05-H inductor is connected in series with a...Ch. 32 - A 1.00-F capacitor is charged by a 40.0-V power...Ch. 32 - Calculate the inductance of an LC circuit that...Ch. 32 - An LC circuit consists of a 20.0-mH inductor and a...Ch. 32 - Prob. 32.52PCh. 32 - Prob. 32.53PCh. 32 - Prob. 32.54PCh. 32 - An LC circuit like the one in Figure CQ32.8...Ch. 32 - Show that Equation 32.28 in the text Ls Kirchhoffs...Ch. 32 - In Figure 31.15, let R = 7.60 , L = 2.20 mH, and C...Ch. 32 - Consider an LC circuit in which L = 500 mH and C=...Ch. 32 - Electrical oscillations are initiated in a series...Ch. 32 - Review. Consider a capacitor with vacuum between...Ch. 32 - Prob. 32.61APCh. 32 - An inductor having inductance I. and a capacitor...Ch. 32 - A capacitor in a series LC circuit has an initial...Ch. 32 - Prob. 32.64APCh. 32 - When the current in the portion of the circuit...Ch. 32 - At the moment t = 0, a 24.0-V battery is connected...Ch. 32 - Prob. 32.67APCh. 32 - Prob. 32.68APCh. 32 - Prob. 32.69APCh. 32 - At t = 0, the open switch in Figure P31.46 is...Ch. 32 - Prob. 32.71APCh. 32 - Prob. 32.72APCh. 32 - Review. A novel method of storing energy has been...Ch. 32 - Prob. 32.74APCh. 32 - Review. The use of superconductors has been...Ch. 32 - Review. A fundamental property of a type 1...Ch. 32 - Prob. 32.77APCh. 32 - In earlier times when many households received...Ch. 32 - Assume the magnitude of the magnetic field outside...Ch. 32 - Prob. 32.80CPCh. 32 - To prevent damage from arcing in an electric...Ch. 32 - One application of an RL circuit is the generation...Ch. 32 - Prob. 32.83CP
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
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
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning