+- L on Solve for Ki and Ka given these initial conditions and for the case a1 6= 02. Be sure to show Ki and Kz in terms

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L On Solve For Ki And Ka Given These Initial Conditions And For The Case A1 6 02 Be Sure To Show Ki And Kz In Terms 1 (77.56 KiB) Viewed 23 times

+- L on Solve for Ki and Ka given these initial conditions and for the case a1 6= 02. Be sure to show Ki and Kz in terms of ai, a2, R, L, C, Ya Problem 4: Appearing to the right is not our familiar RLC C series circuit. Two nodes are labeled with voltages, vi and HH V2. (a) Write KCL node equations for those nodes and put C2 R2 them in normal d (t) form. Use the p operator p"(t) notation .for - (Remember for n>0 and go(t) = 5 «(t)dt.) Each voltage should be multiplied by a polynomial in p such as cop #3 + $)01. a.)KCL node equations in normal form using p operator notation R. dt b.)Let G denote a matrix of the coefficients of the equations above when written in normal form. (See Homework 4, https://www.ece.Isu.edu/ee2120/2022/hw04.pdf.) The determinant of G provides the characteristic equation used to find the complementary (transient) solution for each voltage. (For those that are curious: Given GV = S, and using the fact that G-1 = adig/det, we get a set of non- simultaneous equations using det(G)V = adj(G)S, where adj(G) is the adiugate of G. Note that det multiplies each element of V whereas adj (G)S is a matrix/vector product.) For this problem with R. +R2 + Rand C + C2+ C, the determinant is: 4C с 21 det G =C?p? + RP+ L + RLP RLC2 = 0 Multiplying by p/Cand equating with zero yields the characteristic equation: 2 pod + ROP+ TOP+ p3 LCP For R = 100k2, L = 20mH, and C = 30uF the factored characteristic equation is (p +0.6667) (p +0.3333 - j1291)( +.3333 +j1291) = 0 Based on this characteristic equation show the complementary solution for vi and provide a sketch of vi over time. (The answer is exactly the same for v2.) (Do not attempt to solve for the constants K_K,K3.) Could an RLC circuit have such a complementary (transient) response? Complementary solution for vi Sketch appearance and indicate if appearance is possible for an RLC circuit in which their is one inductor and one capacitor.