By applying Kirchhoff's current law in an DC circuit with three nodes. The three nodes' voltages (V₁, V₂ and V3) can be characterized by the following equations: 5V₂ + 2(V₁-V₂) + V₂ -24 = 0 2(V₂-V₁) + 4V₂ + (V₂-V₂)-12 = 0 (V3-V₂) +2(V₂-V₁) = 0 (2-A) Rearrange the above three equations into a standard matrix form. (2-B) Find V₁, V2, and V3 using the inverse matrix method. (2-C) Find V₁, V2, and V3 using the Gaussian elimination method. (2-D) Verify your answer using MATLAB.
By applying Kirchhoff's current law in an DC circuit with three nodes. The three nodes' voltages (V₁, V₂ and V3) can be characterized by the following equations: 5V₂ + 2(V₁-V₂) + V₂ -24 = 0 2(V₂-V₁) + 4V₂ + (V₂-V₂)-12 = 0 (V3-V₂) +2(V₂-V₁) = 0 (2-A) Rearrange the above three equations into a standard matrix form. (2-B) Find V₁, V2, and V3 using the inverse matrix method. (2-C) Find V₁, V2, and V3 using the Gaussian elimination method. (2-D) Verify your answer using MATLAB.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Activity 2:
By applying Kirchhoff's current law in an DC circuit with three nodes. The three nodes' voltages
(V₁, V₂ and V₂) can be characterized by the following equations:
5V₂ + 2(V₁ - V₂) + V3-24 = 0
2(V₂-V₁) + 4V₂ + (V₂-V₂) - 12 = 0
(V3-V₁) +2(V₂-V₁) = 0
(2-A) Rearrange the above three equations into a standard matrix form.
(2-B) Find V₁, V2, and V3 using the inverse matrix method.
(2-C) Find V₁, V2, and V3 using the Gaussian elimination method.
(2-D) Verify your answer using MATLAB.
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