Discussion
If a network contains B branches and N nodes, then the number of mesh current equations would be :
Answer: A
The number of mesh equations is B − (N − 1).
For a connected planar network, the number of independent loops (meshes) equals the number of links, the branches not in a tree. A tree joining N nodes has N − 1 branches, so:
\[ \begin{aligned} \text{meshes} &= B - (N - 1) \\ &= B - N + 1 \end{aligned} \]
For example, a network with 5 branches and 4 nodes needs 2 mesh equations. N − 1 itself is the number of independent node equations. B − N − 1 has the wrong sign on the 1, and the other two forms have no basis in network topology.
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