Question

Problem 03.025-Nodal analysis: Independent current source In the circuit given below, R-15 Ω. Determine the nodal voltages using nodal analysis and MATLAB. 20Ω 10Ω PI 4 A 8Ω 20Ω The value of nodal voltage vi is The value of nodal voltage v2 is The value of nodal voltage vs is The value of nodal voltage vs is V. References eBook&Resources Hints

Answer 1

at node v_1: v_1 - v_2/ 1 + v_1 - v_4/ 20 = 4 v_1 [1/1 + 1/20] - v_2/ 1 - v_4/20 = 4 rightarrow (1) at node v_2: v_2- v_1/ 1 + v_2/ 8 + v_2 - v_3/ 10 = 0 - v_1/ 1 + v_2 [1 + 1/B + 1/10] - v_3/10 = 0 rightarrow (2) at node v_3: v_3 - v_2/ 10 + v_3/20 + v_3- v_4/ 10 = 0 - v_2/10 + v_3 [1/10 + 1/10 + 1/20] - v_4/10 = 0 rightarrow (3) at node v_4 v_4- v_1/20 + v_4- v_3/10 + v_4/15 = 0 - v_1/20 - v_3/10 + v_4 [1/10 + 1/15 + 1/20] = 0 rightarrow (4) [1.05 -1 0 -0.05 -1 1.225 -0.1 0 0 - 0.1 0.25 -0.1 -0.05 0 -0.1 0.21667] [v_1 v_2 v_3 v_4] = [4 0 0 0] Matlab Code: clc clear all R = [1.05 -1 0 -0.05: -1 1.225 -0.1 0: 0 -0.1 0.25 -0.1: -0.05 0 -0.1 0.2166667] = [4;0;0;0] V = inv(R) times I V1 = V(1,1) V2 = V(2,1) V3 = V(3,1) V4 = V(4,1) matlab Output: R =

Matlab Code:

clc
clear all
R=[ 1.05 -1 0 -0.05;
    -1 1.225 -0.1 0;
    0 -0.1 0.25 -0.1;
    -0.05 0 -0.1 0.2166667]
I=[ 4;0;0;0]
V= inv(R)*I
V1= V(1,1)
V2=V(2,1)
V3=V(3,1)
V4=V(4,1)

Matlab Output:

R =

    1.0500   -1.0000         0   -0.0500
   -1.0000    1.2250   -0.1000         0
         0   -0.1000    0.2500   -0.1000
   -0.0500         0   -0.1000    0.2167

I =

     4
     0
     0
     0

V =

   24.0811
   20.7100
   12.8858
   11.5045

V1 =

   24.0811

V2 =

   20.7100

V3 =

   12.8858

V4 =

   11.5045

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