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R Assume first that v, = 12V-u(-t) and X is a capacitor with C = 25mF. + (a) What is the initial energy stored in the capacitor? (b) Write an expression for the voltage v as a function of time, then Us X compute v at t = t, 2t, and 37. (c) Write an expression for the current i through the capacitor as a

R Assume first that v, = 12V-u(-t) and X is a capacitor with C = 25mF. + (a) What is the initial energy stored in the capacitor? (b) Write an expression for the voltage v as a function of time, then Us X compute v at t = t, 2t, and 37. (c) Write an expression for the current i through the capacitor as a

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
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PARTS G-L

Hello, a step by step guide would be greatly appreciated. Please follow the NOTES & SUGGESTIONS at the bottom when solving, answering what is asked as I need to learn doing it specifically that way, and show every step, thanks so much :)

 

 
Consider the following circuit, with R = 20. R Assume first that v, = 12V-u(-t) and X is a capacitor with C = 25mF. + (a) What is the initial energy stored in the capacitor? (b) Write an expression for the voltage v as a function of time, then Us compute v at t = t, 2t, and 3t. (c) Write an expression for the current i through the capacitor as a function of time, then compute i at the same three instants of time. (d) Write an expression for the power delivered by the capacitor as a function of time. At what time is the power delivered maximum? What is the value of the power delivered at that time? (e) Sketch voltage, current, and power delivered vs. time from t = 0 tot= 10t. (f) Integrate your expression for power delivered to show that the total energy delivered by the capacitor is exactly equal to the initial energy stored. Assume now that v, = 12V-u(t) and X is an inductor with L = 50mH. (g) What is the final energy stored in the inductor? (h) Write an expression for the current i as a function of time, then compute i at t = t, 2t, and 3t. (i) Write an expression for the voltage v across the inductor as a function of time, then compute v at the same three instants of time. (j) Write an expression for the power absorbed by the inductor as a function of time. At what time is the power absorbed maximum? What is the value of the power absorbed at that time? (k) Sketch current, voltage, and power absorbed vs. time from t = 0 to t= 107. (1) Integrate your expression for power absorbed to show that the total energy absorbed by the inductor is exactly equal to the final energy stored. Show your work and verify. NOTES and SUGGESTIONS Use mJ for the energy stored. You may use MATLAB or Python to compute values and/or to make the sketches. Each set of sketches should be on one page, but on three pairs of axes, arranged vertically. That is, you should not use one pair of axes for all three graphs, as they are different from each other. However, they share the same time axis, so they should be arranged vertically. Further, the three graphs for the capacitor should be separate from the three graphs for the inductor. You must do parts (d) and (j) on your own, i.e., you should be able to find the derivative, set it equal to 0, and solve for the time yourself. (If you plot the functions using MATLAB or Python, you will be able to confirm your calculations.) For the inductor, power is NOT maximum at t = 0. Likewise, you must do parts (f) and (1) on your own.
Transcribed Image Text:Consider the following circuit, with R = 20. R Assume first that v, = 12V-u(-t) and X is a capacitor with C = 25mF. + (a) What is the initial energy stored in the capacitor? (b) Write an expression for the voltage v as a function of time, then Us compute v at t = t, 2t, and 3t. (c) Write an expression for the current i through the capacitor as a function of time, then compute i at the same three instants of time. (d) Write an expression for the power delivered by the capacitor as a function of time. At what time is the power delivered maximum? What is the value of the power delivered at that time? (e) Sketch voltage, current, and power delivered vs. time from t = 0 tot= 10t. (f) Integrate your expression for power delivered to show that the total energy delivered by the capacitor is exactly equal to the initial energy stored. Assume now that v, = 12V-u(t) and X is an inductor with L = 50mH. (g) What is the final energy stored in the inductor? (h) Write an expression for the current i as a function of time, then compute i at t = t, 2t, and 3t. (i) Write an expression for the voltage v across the inductor as a function of time, then compute v at the same three instants of time. (j) Write an expression for the power absorbed by the inductor as a function of time. At what time is the power absorbed maximum? What is the value of the power absorbed at that time? (k) Sketch current, voltage, and power absorbed vs. time from t = 0 to t= 107. (1) Integrate your expression for power absorbed to show that the total energy absorbed by the inductor is exactly equal to the final energy stored. Show your work and verify. NOTES and SUGGESTIONS Use mJ for the energy stored. You may use MATLAB or Python to compute values and/or to make the sketches. Each set of sketches should be on one page, but on three pairs of axes, arranged vertically. That is, you should not use one pair of axes for all three graphs, as they are different from each other. However, they share the same time axis, so they should be arranged vertically. Further, the three graphs for the capacitor should be separate from the three graphs for the inductor. You must do parts (d) and (j) on your own, i.e., you should be able to find the derivative, set it equal to 0, and solve for the time yourself. (If you plot the functions using MATLAB or Python, you will be able to confirm your calculations.) For the inductor, power is NOT maximum at t = 0. Likewise, you must do parts (f) and (1) on your own.
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