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
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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Parts A and B please
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