### 2 Answers

- Anonymous5 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

- jacob sLv 75 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.