Consider the first order RC circuit shown in Figure 1. With v.(1) being a symmetrical square-wave voltage having period T and amplitude V, as shown in Figure 2(a), derive an expression for the capacitor voltage vo(1) in the first half-cycle, as shown in Figure 2(a), by following the procedure below: (a) Derive the differential equation (DE) for the capacitor voltage v₁ (t) valid in the interval 0
Consider the first order RC circuit shown in Figure 1. With v.(1) being a symmetrical square-wave voltage having period T and amplitude V, as shown in Figure 2(a), derive an expression for the capacitor voltage vo(1) in the first half-cycle, as shown in Figure 2(a), by following the procedure below: (a) Derive the differential equation (DE) for the capacitor voltage v₁ (t) valid in the interval 0
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
can you solve from a to e
![Consider the first order RC circuit shown in Figure 1. With v.(1) being a symmetrical square-wave
voltage having period T and amplitude V, as shown in Figure 2(a), derive an expression for the
capacitor voltage vo(t) in the first half-cycle, as shown in Figure 2(a), by following the procedure
below:
(a) Derive the differential equation (DE) for the capacitor voltage v, (t) valid in the interval
0<t<T/2, where v, (t) = V. Note that the initial condition for this DE is v. (0) = V, which is
still unknown.
(b) Assume that the solution has the form vo(t) = A + Bea. Then substitute this into the DE and
determine the unknown parameters A, B and a.
(c) Find the unknown initial condition V (in terms of the parameters R, C, T and V) by imposing
the symmetry condition on the solution: v(T/2) = -v(0) = V.
(d) Find the time instant t₁ (in terms of R, C, T and V) at which the capacitor voltage becomes zero
in the first half-cycle.
(e) Calculate the numerical values of V, and t₁ for T=10 ms, Vs = 10 V, R = 10 k2 and C = 0.1 μµF.
Figure 1
vs(t)
risques bris 20
R = 10 kΩ
ww
C=0.1 µF
+
vo(t)
-1.0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b5d4c98-afbd-424f-9855-c5eac84955f5%2F2f799c72-cb0e-48f5-bdd4-f286dbd7dbf9%2Ffene99i.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the first order RC circuit shown in Figure 1. With v.(1) being a symmetrical square-wave
voltage having period T and amplitude V, as shown in Figure 2(a), derive an expression for the
capacitor voltage vo(t) in the first half-cycle, as shown in Figure 2(a), by following the procedure
below:
(a) Derive the differential equation (DE) for the capacitor voltage v, (t) valid in the interval
0<t<T/2, where v, (t) = V. Note that the initial condition for this DE is v. (0) = V, which is
still unknown.
(b) Assume that the solution has the form vo(t) = A + Bea. Then substitute this into the DE and
determine the unknown parameters A, B and a.
(c) Find the unknown initial condition V (in terms of the parameters R, C, T and V) by imposing
the symmetry condition on the solution: v(T/2) = -v(0) = V.
(d) Find the time instant t₁ (in terms of R, C, T and V) at which the capacitor voltage becomes zero
in the first half-cycle.
(e) Calculate the numerical values of V, and t₁ for T=10 ms, Vs = 10 V, R = 10 k2 and C = 0.1 μµF.
Figure 1
vs(t)
risques bris 20
R = 10 kΩ
ww
C=0.1 µF
+
vo(t)
-1.0
![V.
S
V
>V,
-V.
S
Figure 2
t₁ T/2
Vi
Vo
T
t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b5d4c98-afbd-424f-9855-c5eac84955f5%2F2f799c72-cb0e-48f5-bdd4-f286dbd7dbf9%2Fmq628cv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:V.
S
V
>V,
-V.
S
Figure 2
t₁ T/2
Vi
Vo
T
t
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 7 steps with 3 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,