Problem 2: The switch in Fig.2 closes at t = 0s and, after a very long time, the capacitor is fully charged. Find expressions for the total energy supplied by the battery as the capacitor is being charged, total energy dissipated by the resistor as the capacitor is being charged, and the en- ergy stored in the capacitor when it is fully charged. E R FIG. 2: The scheme for Problem 2 a) In an ideal battery, a charge dq gains potential energy Edq as it moves up the 'charge escalator' inside the battery. Therefore, the power supplied by the battery at each moment of time is Phat=&=I& (this expression was derived in paragraph 28.3 of the textbook). The current in an RC circuit with a charging capacitor changes with time as I = Ioe-t/t, where Io = &/R and T = RC (this expression was provided at the end of paragraph 28.9 of the textbook). To compute the total energy supplied by the battery as the capacitor is charging, take the integral Ebat = Pbatdt. Express the final answer for Ebat in terms of & and C only. b) The power dissipated by the resistor is equal to Pres = I2R (note that it is a function of time in this problem). Compute the total energy dissipated in the resistor by taking the integral Eres = Predt. Express your answer in terms of & and C only. c) When the capacitor is fully charged, the potential difference between its plates is equal to &, and there is no current flowing in the circuit. Express the potential energy stored in the capacitor in terms of E and C. d) Do your results for parts a) to c) show that the energy is conserved? Explain.
Problem 2: The switch in Fig.2 closes at t = 0s and, after a very long time, the capacitor is fully charged. Find expressions for the total energy supplied by the battery as the capacitor is being charged, total energy dissipated by the resistor as the capacitor is being charged, and the en- ergy stored in the capacitor when it is fully charged. E R FIG. 2: The scheme for Problem 2 a) In an ideal battery, a charge dq gains potential energy Edq as it moves up the 'charge escalator' inside the battery. Therefore, the power supplied by the battery at each moment of time is Phat=&=I& (this expression was derived in paragraph 28.3 of the textbook). The current in an RC circuit with a charging capacitor changes with time as I = Ioe-t/t, where Io = &/R and T = RC (this expression was provided at the end of paragraph 28.9 of the textbook). To compute the total energy supplied by the battery as the capacitor is charging, take the integral Ebat = Pbatdt. Express the final answer for Ebat in terms of & and C only. b) The power dissipated by the resistor is equal to Pres = I2R (note that it is a function of time in this problem). Compute the total energy dissipated in the resistor by taking the integral Eres = Predt. Express your answer in terms of & and C only. c) When the capacitor is fully charged, the potential difference between its plates is equal to &, and there is no current flowing in the circuit. Express the potential energy stored in the capacitor in terms of E and C. d) Do your results for parts a) to c) show that the energy is conserved? Explain.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Concept explainers
Ohm's law
Ohm’s law is a prominent concept in physics and electronics. It gives the relation between the current and the voltage. It is used to analyze and construct electrical circuits. Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it.
Path of Least Resistance
In a series of alternate pathways, the direction of least resistance is the actual or metaphorical route that offers the least resistance to forwarding motion by a given individual or body.
Question
Hello, I need help with part a, part b, and part c and is there any chance that you label all three of them thank you.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
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.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON