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HACTEHA [7]
2 years ago
14

Have my equation written out but struggling to solve. Can someone help me solve!

Physics
1 answer:
Nina [5.8K]2 years ago
6 0

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:

  1. The sum of currents found at nodes of circuits is always equal to zero.
  2. 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

#SPJ1

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6 0
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To which group/family does each of these belong? A. Sulfur _________ B. Sodium _________ C. Argon _________ D. Silicon _________
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Answer:

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An entertainer pulls a table cloth off a table leaving behind the plates and sliverware undisturbed is an example of
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Answer:

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Newton's first law of inertia says that an object will remain how it is, unless affected by an outside force. In this case, the plates want to remain stationary(not moving). Therefore, if you pull the table cloth fast enough, the force of friction produced will be small enough so that the Inertia of the plates will overcome the force of friction.

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Two motorcyclists are riding side-by-side at night and the distance between their center-mounted headlights is 1.40 m. (a) If th
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Answer:

θ = 1.591 10⁻² rad

Explanation:

For this exercise we must suppose a criterion when two light sources are considered separated, we use the most common criterion the Rayleigh criterion that establishes that two light sources are separated census the central maximum of one of them coincides with the first minimum of the other source

         

Let's write the diffraction equation for a slit

       a sin θ = m λ

The first minimum occurs for m = 1, also field in these we experience the angles are very small, we can approximate the sin θ = θ

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In our case, the pupil is circular, so the system must be solved in polar coordinates, so a numerical constant is introduced.

           θ = 1.22 λ / D

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 Let's apply this equation to our case

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        θ = 1.591 10⁻² rad

This is the angle separation to solve the two light sources

6 0
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