Mesh Analysis: Solving Loop Equations with KVL/KCL for Homework

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SUMMARY

The discussion focuses on solving loop equations using Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) for a homework problem involving three loops. The equations presented are: Loop 1: 20 = 6i1 - 4i2 - 2i3, Loop 2: -4i1 + 18i2 - 8i3 = 0, and Loop 3: 2i1 + 8i2 + 6i3 + 10i0 = 0. The user struggles to find the correct value for i0, which should equal -5A, and receives feedback indicating a potential error in the Loop 3 equation regarding the coefficients and sign changes. The discussion emphasizes the importance of accurately applying KVL and KCL in mesh analysis.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Understanding of Kirchhoff's Current Law (KCL)
  • Familiarity with mesh analysis techniques
  • Basic knowledge of electrical circuit components and their relationships
NEXT STEPS
  • Review the principles of Kirchhoff's Laws in circuit analysis
  • Practice solving mesh analysis problems with multiple loops
  • Study superposition theorem applications in circuit analysis
  • Learn about Thevenin's and Norton's theorems for circuit simplification
USEFUL FOR

Students studying electrical engineering, particularly those preparing for exams on circuit analysis, as well as educators looking for examples of KVL and KCL applications in mesh analysis.

hoahoa
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Homework Statement


Wqddo.png


Homework Equations


KVL/KCL

The Attempt at a Solution


Meshes for;

Loop 1
20 = 6i1 - 4i2 - 2i3

Loop 2
-4i1 + 18i2 - 8i3 = 0

Loop 3
2i1 + 8i2 + 6i3 +10i0 = 0
For the life of me I cannot get -5A as the answer. I have tried the following for i0;

i0 = i1 - i2
i0 = i2

And neither give the correct answer (-5A). Help please! trying to get this down and subsequently superposition/thevenins and nortons theorem down for an exam next week
 
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Your Loop 3 equation looks suspicious. I don't see the sum of the loop resistances as a coefficient for i3, and there should be sign changes for some terms.

io = i2 is fine.
 

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