What is the relationship between I_eq and i_1, i_2, i_3 in Kirchhoff's Laws?

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Homework Help Overview

The discussion revolves around a circuit analysis problem involving Kirchhoff's Laws, specifically exploring the relationship between the equivalent current \(I_{eq}\) and the individual currents \(i_1\), \(i_2\), and \(i_3\).

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship \(i_1 = i_2 + i_3\) and question the relative sizes of \(i_2\) and \(i_3\). There is also inquiry into how \(I_{eq}\) relates to these currents.

Discussion Status

Participants have identified a relationship between the currents and are exploring the implications of this relationship. Some guidance has been offered regarding the equivalence of currents, but the discussion remains open-ended without a definitive conclusion.

Contextual Notes

The original poster has provided an image of the circuit, which may contain additional information relevant to the discussion. There is an implicit assumption regarding the equality of currents \(i_2\) and \(i_3\), but this has not been explicitly resolved.

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Homework Statement


I have the following circuit
10fq6hk.jpg

What is the relation between $$I_{eq}~~and~~ i_1, i_2, i_3$$?

Homework Equations


Kirchhoff Laws

The Attempt at a Solution


See the image above
 
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You have correctly found that i1=i2+i3. What can you say about the relative size of i2 and i3?
 
kuruman said:
You have correctly found that i1=i2+i3. What can you say about the relative size of i2 and i3?
I think they are equal
 
They are, but do you know the reason why?
 
kuruman said:
They are, but do you know the reason why?
Yes:
rvdh5w.png
 
OK great. You have found the relations between i1, i2 and i3. All that remains is how Ieq. fits in the picture. Any ideas?
 
kuruman said:
OK great. You have found the relations between i1, i2 and i3. All that remains is how Ieq. fits in the picture. Any ideas?
I would say it's the same as i1 because it's the same current that flows through the resistors.
 
Correct. It looks like you are done.
 

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