The switch in the circuit in Fig. P12.30 has been open for a long time. At / = 0, the switch closes. a) Derive the integrodifferential equation that governs the behavior of the voltage v, for t 2 0. b) Show that Vac/RC g2 + (1/RC)s + (1/LC)' V.(s) = c) Show that Vae/ RLC s[s² + (1/RC)s + (1/LC)]' Figure P12.30 R + V de
The switch in the circuit in Fig. P12.30 has been open for a long time. At / = 0, the switch closes. a) Derive the integrodifferential equation that governs the behavior of the voltage v, for t 2 0. b) Show that Vac/RC g2 + (1/RC)s + (1/LC)' V.(s) = c) Show that Vae/ RLC s[s² + (1/RC)s + (1/LC)]' Figure P12.30 R + V de
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...
Related questions
Question
![The switch in the circuit in Fig. P12.30 has been
open for a long time. At i = 0, the switch closes.
a) Derive the integrodifferential equation that
governs the behavior of the voltage v, for t 2 0.
b) Show that
Vac/RC
V.(s)
g2 + (1/RC)s + (1/LC)'
c) Show that
Vác/ RLC
s[s² + (1/RC)s + (1/LC)]'
1,(8)
Figure P12.30
R
1 = 0
V ac](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cafa13c-3723-4a0f-827c-f778a168ea31%2F183b1cd3-39b4-4718-89a6-17dbab06e474%2Fevemw5p_processed.png&w=3840&q=75)
Transcribed Image Text:The switch in the circuit in Fig. P12.30 has been
open for a long time. At i = 0, the switch closes.
a) Derive the integrodifferential equation that
governs the behavior of the voltage v, for t 2 0.
b) Show that
Vac/RC
V.(s)
g2 + (1/RC)s + (1/LC)'
c) Show that
Vác/ RLC
s[s² + (1/RC)s + (1/LC)]'
1,(8)
Figure P12.30
R
1 = 0
V ac
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Apply KCL at node connecting the resistor, inductor and capacitor .
Using Laplace transform find S domain representation capacitor voltage.
Current through inductor = (Voltage across inductor)/SL.
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Introductory Circuit Analysis (13th Edition)](https://www.bartleby.com/isbn_cover_images/9780133923605/9780133923605_smallCoverImage.gif)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
![Delmar's Standard Textbook Of Electricity](https://www.bartleby.com/isbn_cover_images/9781337900348/9781337900348_smallCoverImage.jpg)
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
![Introductory Circuit Analysis (13th Edition)](https://www.bartleby.com/isbn_cover_images/9780133923605/9780133923605_smallCoverImage.gif)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
![Delmar's Standard Textbook Of Electricity](https://www.bartleby.com/isbn_cover_images/9781337900348/9781337900348_smallCoverImage.jpg)
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
![Fundamentals of Electric Circuits](https://www.bartleby.com/isbn_cover_images/9780078028229/9780078028229_smallCoverImage.gif)
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
![Electric Circuits. (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780134746968/9780134746968_smallCoverImage.gif)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
![Engineering Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780078028151/9780078028151_smallCoverImage.gif)
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,