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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, Us1, Us2. Write your result in the form of y= Ax, where [i iz i3] and x = [Usi Us2]. y = (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 ≤i2 ≤ 2, and 0 ≤ i3 ≤ 1. On a two-dimensional plane, sketch the set of all voltages Us1, Us2 that ensure these conditions.

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, Us1, Us2. Write your result in the form of y= Ax, where [i iz i3] and x = [Usi Us2]. y = (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 ≤i2 ≤ 2, and 0 ≤ i3 ≤ 1. On a two-dimensional plane, sketch the set of all voltages Us1, Us2 that ensure these conditions.

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 D and E. Thanks

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
Step 1

(d). given that a linear circuit with two independent voltage sources and three resistors.

R1=R2=R3= 1 ohm  and  i1= 2 i2=0 i3= -3 A

To find Vs1 and Vs2 :

 

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