Parts D and E. Thanks Consider a linear static circuit consisting of three resistorsand 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, Us2represent the voltages at the voltage sources.(a) Using Ohm's and Kirchhoff's laws, express11, 12, 13 as functions of R₁, R2, R3, Usl, Us2.Write your result in the form of y = Ax, wherey = [1 12 13] and x = [vs1US2] T.(b) Let R₁=R₂ R3 = 1. Is it possible for twodistinct pairs of voltages, Us1, Us2 and v1, 2, toproduce the same currents i1, 12, 13? Why?=Vsl+WR₁MR₂R3Figure 1Vs2(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. Ona 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.

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.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.61P

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