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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. www 7₁ 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==1&(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 = E/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 = Presdt. Express your answer in terms of & and C only. d) Do your results for parts a) to c) show that the energy is conserved? Explain. c) When the capacitor is fully charged, the potential difference between its plates is equal to E, and there is no current flowing in the circuit. Express the potential energy stored in the capacitor in terms of E and C.

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. www 7₁ 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==1&(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 = E/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 = Presdt. Express your answer in terms of & and C only. d) Do your results for parts a) to c) show that the energy is conserved? Explain. c) When the capacitor is fully charged, the potential difference between its plates is equal to E, and there is no current flowing in the circuit. Express the potential energy stored in the capacitor in terms of E and C.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Hello I need help with part d can you label it as well

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. R ww 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 = = 18 (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 = E/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. FIG. 2: The scheme for Problem 2 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 = Presdt. 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 E, 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.
Transcribed Image Text: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. R ww 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 = = 18 (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 = E/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. FIG. 2: The scheme for Problem 2 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 = Presdt. 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 E, 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.
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