The solution of this system is (i₁, i₂, i₃) = (- 10.852 A, 8.479 A, - 2.374 A). The <em>negative</em> signs indicate that <em>real</em> direction of the current is opposite than supposed.
<h3>How to find the missing current in a circuit</h3>
In this question we must make use of Kirchhoff's laws to find the values of the <em>missing</em> 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 <em>closed</em> loop of a circuit is always equal to zero.
Based on the information given by the picture, we have the following system of <em>linear</em> equations that describes the <em>entire</em> 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 <em>negative</em> signs indicate that <em>real</em> direction of the current is opposite than supposed.
To learn more on Kirchhoff's laws: brainly.com/question/6417513
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