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

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SUMMARY

The relationship between the equivalent current \(I_{eq}\) and the individual currents \(i_1\), \(i_2\), and \(i_3\) in a circuit governed by Kirchhoff's Laws is established through the equation \(i_1 = i_2 + i_3\). This indicates that the total current entering a junction equals the total current leaving it. Furthermore, it is confirmed that \(i_2\) and \(i_3\) are equal, leading to the conclusion that \(I_{eq} = i_1\) since it represents the same current flowing through the resistors.

PREREQUISITES
  • Understanding of Kirchhoff's Current Law (KCL)
  • Basic knowledge of electrical circuits
  • Familiarity with current flow and circuit analysis
  • Ability to interpret circuit diagrams
NEXT STEPS
  • Study Kirchhoff's Voltage Law (KVL) for a comprehensive understanding of circuit analysis.
  • Learn about series and parallel circuits to understand current distribution.
  • Explore Ohm's Law to relate voltage, current, and resistance in circuits.
  • Investigate the concept of node voltage analysis for complex circuits.
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Students studying electrical engineering, educators teaching circuit theory, and anyone interested in mastering Kirchhoff's Laws and circuit analysis.

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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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