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  • Anonymous
    5 months ago

    Unknowns:

    V₁,V₂,Vᵣ₁,Vᵣ₂,Vᵣ₃,Vᵣ₄,Vᵣ₅,i₁,i₂,i₃,i₄,i₅

    Ohm's Law: V = iR → iR + V = 0

    i₁(1Ω) + Vᵣ₁ = 0

    i₂(2Ω) + Vᵣ₂ = 0

    i₃(3Ω) + Vᵣ₃ = 0

    i₄(4Ω) + Vᵣ₄ = 0

    i₅(5Ω) + Vᵣ₅ = 0

    Kirchoff's Voltage Loop Law:

    V₁ + Vᵣ₁ - Vᵣ₃ = 0

    V₂ + Vᵣ₅ = 0

    Vᵣ₃ + Vᵣ₄ + Vᵣ₅ = 0

    Vᵣ₁ + Vᵣ₂ + Vᵣ₄ = 0

    Kirchoff's Current Node Law:

    i₁ + i₂ = 3A

    i₁ + i₃ + i₄ = 0

    i₂ + i₄ + i₅ = 7A

    Matrix Equation: [A][x] = [B]

    {{0,0,0,0,0,1,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0},{1,0,0,0,0,1,0,1,0,0,0,0},{0,1,0,0,0,0,0,1,0,0,0,0},{0,0,1,0,0,1,0,1,0,0,0,0},{0,0,0,1,0,0,0,1,1,0,0,0},{0,0,0,0,1,0,1,1,0,0,0,0},{1,0,0,0,0,0,0,0,0,1,1,0},{0,2,0,0,0,0,0,0,0,1,0,1},{0,0,3,0,0,0,0,0,0,0,1,0},{0,0,0,4,0,0,0,0,0,0,1,1},{0,0,0,0,5,0,0,0,0,0,0,1}}{V₁,V₂,Vᵣ₁,Vᵣ₂,Vᵣ₃,Vᵣ₄,Vᵣ₅,i₁,i₂,i₃,i₄,i₅} = {0,0,0,0,0,0,0,0,0,3,0,7}

    Solve: https://www.mathstools.com/section/main/system_equ...

    {V₁,V₂,Vᵣ₁,Vᵣ₂,Vᵣ₃,Vᵣ₄,Vᵣ₅,i₁,i₂,i₃,i₄,i₅} = {52,-110,26,-58,-78,0,110,-26,29,26,0,-22}

    V₁ = 52V

    V₂ = 110V

  • 5 months ago

    Try the Physics category . This is not math. Math is use here as a tool to solve it. Good luck. Physics category is the perfect one for you.

     

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