The solution of this system is (i₁, i₂, i₃) = (- 10.852 A, 8.479 A, - 2.374 A). The negative signs indicate that real direction of the current is opposite than supposed.
How to find the missing current in a circuit
In this question we must make use of Kirchhoff's laws to find the values of the missing currents in the circuit presented in the picture. There are two rules according to Kirchhoff's laws:
- The sum of currents found at nodes of circuits is always equal to zero.
- The net sum of voltages in a closed loop of a circuit is always equal to zero.
Based on the information given by the picture, we have the following system of linear equations that describes the entire circuit:
i₃ = i₁ + i₂
- i₁ · R₁ + ε₁ - i₁ · r₁ - i₁ · R₅ + ε₂ - i₂ · (r₂ + R₂) = 0
ε₂ - i₂ · (r₂ + R₂) - i₃ · r₄ - ε₄ - i₃ · r₃ + ε₃ - i₃ · R₃ = 0
- i₁ - i₂ + i₃ = 0 (1)
(R₁ + r₁ + R₅) · i₁ + (r₂ + R₂) · i₂ = ε₁ + ε₂ (2)
(r₂ + R₂) · i₂ + (r₄ + r₃ + R₃) · i₃ = ε₂ + ε₃ - ε₄ (3)
If we know that R₁ = 5 Ω, r₁ = 0.10 Ω, R₅ = 20 Ω, r₂ = 0.50 Ω, R₂ = 40 Ω, r₄ = 0.20 Ω, r₃ = 0.05 Ω, R₃ = 78 Ω, ε₁ = 22 V, ε₂ = 49 V, ε₃ = 10.5 V and ε₄ = 33 V, then the currents flowing in the circuit are:
- i₁ - i₂ + i₃ = 0
25.1 · i₁ + 40.5 · i₂ = 71
25.1 · i₂ + 78.25 · i₃ = 26.5
The solution of this system is (i₁, i₂, i₃) = (- 10.852 A, 8.479 A, - 2.374 A). The negative signs indicate that real direction of the current is opposite than supposed.
To learn more on Kirchhoff's laws: https://brainly.com/question/6417513
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