Question

The KCL equations of a circuit are given as follows

5V₁ − 1V₂ − 2V₃ =10
−V₁ + 8V₂ − 4V₃ =0
−2V₁ − 4V₂ + 10V₃ =20
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Write is in form of A.X = b and solve it with Gauss-elimination method, Write the process using MATLAB

Answer 1

The KCL equations can be represented as a matrix equation A.X = b and solved using MATLAB, where MATLAB internally performs Gauss elimination and back substitution to find the voltages.

Step-by-step explanation:

To apply Kirchhoff's Current Law (KCL) and represent it in the matrix form A.X = b, let's first write down the system of equations you've given:

• 5V₁ - V₂ - 2V₃ = 10
• -V₁ + 8V₂ - 4V₃ = 0
• -2V₁ - 4V₂ + 10V₃ = 20

Now, in the matrix form A.X = b, the matrices would look like this:

A = [5 -1 -2; -1 8 -4; -2 -4 10], X = [V₁; V₂; V₃], and b = [10; 0; 20].

To solve for V₁, V₂, and V₃ using Gauss elimination in MATLAB, you can follow this MATLAB code:

A = [5 -1 -2; -1 8 -4; -2 -4 10];
b = [10; 0; 20];
X = A\b;

This MATLAB command performs Gauss elimination and back substitution, providing the solution for the voltages. In a classroom setting, the Gauss elimination steps would include making the matrix A into an upper triangular form and then solving by back substitution, but MATLAB takes care of these steps internally with the backslash operator (\).