Question

Problem 1 [23 points] RIB Os şi C) R = 1012 R2 = 1012 R3 = 202 Ri= 2002 R = 1092 R = 1012 Ist 1A VS2 = 20V . Reference Node (D) 1. Use the General Node Voltage Analysis algorithm to set up the matrix system symbolically. Show your work. It is not sufficient to show only the final matrix system. Use the given Node labeling. 2. Insert the values given above and solve for the unknown voltages

Answer 1

Summary- This problem is solved by using the basics of Nodal Analysis. Below are the details of solution uploaded in sequence.

A 10 I 20v 220 uw un tou VS2 = 20v ; R = 1002 R2 = lore; R₂ = 2002; RuEzowe; Isı = IA R5=10_2; ko alone solution - Using Nodal Analysis, we need to find Node Vollages at A & B VA § VB. from, circuit it is clear that, CEGUGGOUUNITATVVVVVVUJO VR=20v { smce parallel to zov source Apply KCL at Node VA ; Gilet us Assume all the outgoing currents) VA + VA-20 20 10 -1 + VA _ 0 20 A + VA-20 20 10 + VA-Vc 20 =1

VA 20 +2(VA-20) 20 + VA-Vc al 20 VA + 2VA -40 ot VA -Ve=20 YVA -Vc = 60 ☺ 4 VA = Vc = 60 Apply kel at Node ca Ve-VA & Vc t1=0 20 20 V -VA + VE 1 ZVc -VA = -1 20 2 VC-VA =-20 ② UVA - Ve = 60 -VA + ZVC = -20 VB = 2ov EBÉ 1 4 -1 Lo 0 01 -1 2 o ] [ VA VB Luc This is the matrix Representation With VA VB & Ve nodes)

& Solving can ① & ② (4VA - Vc = 60 )*2 -VA + 2 Vc =-20 8 VA-27c = 120 - VA teve =-20 7 A = 100 IVA = 100 v. I put mequ ® - loo + 2V= -20 2Vc = 100 - 20. 2V = 100 – 140 - -40 Ve=-20v Hence, Node voltages are VA= 100 v VB= 200 Ve= -20 V