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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, 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...
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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, 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.
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