Applying the Kirchhoff's second law, show that the system of differential equa- tions is (a) dl dl. +L +R¡I½ =E (1), dt dle dl +R2- di 1 +-l =0. C R1 dt dt

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...
icon
Related questions
Question
For a
Figure 1 shows an electric circuit that can be represented by a system of differential
equations.
R2
4 la
R1
47
FIGURE 1. Electric circuit
If I, and I. describe the currents of the circuit, by Kirchhoff's first law, we can write
la (1) = I, (1) +1. (1).
Transcribed Image Text:Figure 1 shows an electric circuit that can be represented by a system of differential equations. R2 4 la R1 47 FIGURE 1. Electric circuit If I, and I. describe the currents of the circuit, by Kirchhoff's first law, we can write la (1) = I, (1) +1. (1).
(a)
Applying the Kirchhoff's second law, show that the system of differential equa-
tions is
dl
dle
+L
+RIb = E (t),
dt
dt
dl,
dle
+R2
dt
1
= 0.
-R
dt
Use the Laplace transform to solve the system in (a) if R = 102, R2 = 52,
L= 1H, C =0.2F, I,(0) =0, I(0) = 0 and
(b)
120, 0<1<2,
0,
E(t) =
122.
(c)
Calculate the current I.(t).
Transcribed Image Text:(a) Applying the Kirchhoff's second law, show that the system of differential equa- tions is dl dle +L +RIb = E (t), dt dt dl, dle +R2 dt 1 = 0. -R dt Use the Laplace transform to solve the system in (a) if R = 102, R2 = 52, L= 1H, C =0.2F, I,(0) =0, I(0) = 0 and (b) 120, 0<1<2, 0, E(t) = 122. (c) Calculate the current I.(t).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
State Variable Analysis
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.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,