Finding independent loops in basic circuits.

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SUMMARY

The discussion centers on identifying independent loops in a basic electrical circuit as presented in a homework assignment. The definition of an independent loop is clarified: it must contain at least one branch not included in any other independent loop. The circuit in question has five branches and three nodes, leading to confusion regarding the correct identification of independent loops. The participant realizes that overlapping branches, such as resistors in parallel, disqualify certain loops from being independent.

PREREQUISITES
  • Understanding of basic circuit theory
  • Familiarity with electrical components like resistors and current sources
  • Knowledge of loop analysis in circuit design
  • Ability to interpret circuit diagrams
NEXT STEPS
  • Study the concept of mesh analysis in circuit theory
  • Learn about Kirchhoff's Voltage Law (KVL) and its application in loop identification
  • Explore techniques for simplifying complex circuits to identify independent loops
  • Practice with circuit simulation tools like LTspice to visualize loop behavior
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing and designing electrical circuits will benefit from this discussion.

NewtonianAlch
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Homework Statement


This was a question on my lecture slides which I didn't quite understand during the lecture.

Here is the circuit:

http://img843.imageshack.us/img843/3548/nodesbranchesloops.jpg

The question was to find independent loops in the circuit.

On the left-hand side I drew in the loops that my lecturer indicated.

This was the given definition for an independent loop:

A loop is said to be independent if it contains at least one branch which is not part of any other independent loop.

So there are 5 branches in the circuit and 3 nodes.

My initial thought of the independent loops is on the right-hand side, which was supposedly incorrect, but I don't see how it's wrong. The third loop on the right I drew has at least one branch (current source) which is not part of any other independent loop.

Also, wouldn't this entirely depend on how you draw the loops? For e.g. would this be correct?

http://img198.imageshack.us/img198/3092/nodesbranchesloops2.jpg

Thanks
 
Last edited by a moderator:
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Nvm! I see why it can't be now. Making the right-hand side an independent loop would mean the middle one is no longer independent because the two resistors in parallel (branches) are shared.
 

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