Question

Problem 2. (50 points) a) Using nodal analysis (format approach) find the matrix Y and l of the equation Y× V-I b) Find the unknown node voltages Vi, V2, Vs, and VRI, VR4 of the network in Volt using nodal analysis. Note: The format of the matrix elements is a three digits after decimal point (for example, 0.221); the answers format is three digits after decimal point (for example, 32.223) RI R4 Vi R4 R2 E1-20; I1-12 E3-4.4 R1-40 R2-5 R3-15; E in Volt R4 13; VRI R5 R in kQ R6-2

Answer 1

Node 1 v_1 - v_2/ 2 + v_1/5 + v_1 - v_3/13 + 12 = 0 v_1 [1/ 2 + 1/5 + 1/13] - v_2/ 2 - v_3/ 13 = -12 v_1 [0.7769] - 0.5 (v_2) - 0.076 v_3 = -12 0.776 v_1 - 0.5 v_2 - 0.076 v_3 = -12 rightarrow (1) Node 2 v_2 - 20/40 + v_2 - v_1/ 2 + v_2 - v_3/ 2 = 0 v_2 [1/ 40 + 1/2 + 1/2] -v_1/2 - v_3/2 -1/2 = 0 v_2 (1.025) - 0.5 v_1 - 0.5 v_3 = 0.5 - 0.5 v_1 + 1.025 v_2 - 0.5v_3 = 0.5 rightarrow (2) node3 v_3- v_2/ 2 + v_3 - v_1/ 13 + v_3/ 15 = 0 v_3 [1/ 2 + 1/ 13 + 1/15] -v_2/ 2 - v_1/ 13 = 0 \r\n v_3 [0.643] -v_2/ 2 - v_1/13 = 0 - 0.076 v_1 - 0.5v_2 + 0.643 v_3 = 0 rightarrow (3) from the equations (1), (2) and (3) can be written as [0.776 - 0.5 -0.076 -0.5 1.025 -0.5 -0.076 -0.5 0.643] [v_1 v_2 v_3] = [