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

A resistive load will consume maximum power from a network when the load resistance is equal to the resistance of the network as viewed from the open-circuit terminals, with all energy sources removed leaving only the internal resistances. Physicist Mori…