For a connected network, the number of independent meshes is L = b - n + 1. If 4 mesh-current equations are required, 4 = b - n + 1, giving b = n + 3.
Formula / Key Relation
L = b - n + 1
4 = b - n + 1
b = n + 3
Detailed Explanation
Concept & ReasoningMesh-current analysis uses one equation for each independent loop of a planar connected network. Graph theory gives the cyclomatic number L = b - n + 1, where b is the number of branches and n the number of nodes. With L = 4, rearranging yields b = n + 3. This relation is a frequent exam shortcut and avoids drawing or counting a particular circuit.How to Solve It in the ExamIndependent loops = branches - nodes + 1.Important Exam PointUse this relation only for a connected network; additional connected components change the graph formula.Related Revision PathThis question…
Concept & Reasoning
Mesh-current analysis uses one equation for each independent loop of a planar connected network. Graph theory gives the cyclomatic number L = b - n + 1, where b is the number of branches and n the number of nodes. With L = 4, rearranging yields b = n + 3. This relation is a frequent exam shortcut and avoids drawing or counting a particular circuit.
How to Solve It in the Exam
Independent loops = branches - nodes + 1.
Important Exam Point
Use this relation only for a connected network; additional connected components change the graph formula.
Related Revision Path
This question sits in the revision path Network Theory → Graph Theory → Mesh Analysis .
Quick Trick
Independent loops = branches - nodes + 1.
Common Mistake
Do not use b-n or b-n-1; the +1 term is essential for a connected graph.
Exam Tip
Use this relation only for a connected network; additional connected components change the graph formula.
SEO + Knowledge GraphRelated PYQs & Exam ContextExam path, knowledge path and deeper practice links.
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 117
