Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Consider a linear static circuit consisting of three resistors and two independent voltage sources, as shown in Figure 1. Let 11, 12, 13 represent the currents that flow through the re- sistors, R₁, R2, R3 represent their resistances, and Us1, Us2 represent the voltages at the voltage sources. (a) Using Ohm's and Kirchhoff's laws, express 11, 12, 13 as functions of R₁, R2, R3, Usl, Us2. Write your result in the form of y = Ax, where y = [i iz i3] and x = [vs1 s2]. (b) Let R₁ = R₂ = R3 = 1. Is it possible for two distinct pairs of voltages, Us1, Us2 and v1, 2, to produce the same currents i1, 12, 13? Why? Vsl + W R₁ M R₂ R3 Figure 1 V$2

Consider a linear static circuit consisting of three resistors and two independent voltage sources, as shown in Figure 1. Let 11, 12, 13 represent the currents that flow through the re- sistors, R₁, R2, R3 represent their resistances, and Us1, Us2 represent the voltages at the voltage sources. (a) Using Ohm's and Kirchhoff's laws, express 11, 12, 13 as functions of R₁, R2, R3, Usl, Us2. Write your result in the form of y = Ax, where y = [i iz i3] and x = [vs1 s2]. (b) Let R₁ = R₂ = R3 = 1. Is it possible for two distinct pairs of voltages, Us1, Us2 and v1, 2, to produce the same currents i1, 12, 13? Why? Vsl + W R₁ M R₂ R3 Figure 1 V$2

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...
See similar textbooks
icon
Related questions
Question

Parts A and B please

Consider a linear static circuit consisting of three resistors and two independent voltage sources, as shown in Figure 1. Let 11, 12, 13 represent the currents that flow through the re- sistors, R₁, R2, R3 represent their resistances, and Us1, Us2 represent the voltages at the voltage sources. (a) Using Ohm's and Kirchhoff's laws, express 11, 12, 13 as functions of R₁, R2, R3, Usl, Us2. Write your result in the form of y = Ax, where y = [1 12 13] and x = [vs1 US2] T. (b) Let R₁ = R₂ R3 = 1. Is it possible for two distinct pairs of voltages, Us1, Us2 and v1, 2, to produce the same currents i1, 12, 13? Why? = Vsl + W R₁ M R₂ R3 Figure 1 Vs2 (c) Let R₁ = R₂ = R3 = 1. Find Us1, Us2 that yield i₁ = 1, 12 = -4, 13 = 5. Is this possible? Why? (d) Repeat (c) with i₁ = 2, 12 = 0, i3 = -3. What is different this time? (e) Suppose, for safety reasons, the currents must satisfy 1 ≤ i ≤ 2, 1 ≤ i ≤ 2, and 0 ≤ i3 ≤ 1. On a two-dimensional plane, sketch the set of all voltages Us1, Us2 that ensure these conditions.
Transcribed Image Text:Consider a linear static circuit consisting of three resistors and two independent voltage sources, as shown in Figure 1. Let 11, 12, 13 represent the currents that flow through the re- sistors, R₁, R2, R3 represent their resistances, and Us1, Us2 represent the voltages at the voltage sources. (a) Using Ohm's and Kirchhoff's laws, express 11, 12, 13 as functions of R₁, R2, R3, Usl, Us2. Write your result in the form of y = Ax, where y = [1 12 13] and x = [vs1 US2] T. (b) Let R₁ = R₂ R3 = 1. Is it possible for two distinct pairs of voltages, Us1, Us2 and v1, 2, to produce the same currents i1, 12, 13? Why? = Vsl + W R₁ M R₂ R3 Figure 1 Vs2 (c) Let R₁ = R₂ = R3 = 1. Find Us1, Us2 that yield i₁ = 1, 12 = -4, 13 = 5. Is this possible? Why? (d) Repeat (c) with i₁ = 2, 12 = 0, i3 = -3. What is different this time? (e) Suppose, for safety reasons, the currents must satisfy 1 ≤ i ≤ 2, 1 ≤ i ≤ 2, and 0 ≤ i3 ≤ 1. On a two-dimensional plane, sketch the set of all voltages Us1, Us2 that ensure these conditions.
Expert Solution
steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Maximum power transfer theorem
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
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,
SEE MORE TEXTBOOKS