Independent Meshes Planar Count — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Independent Meshes (Planar Count) This formula applies specifically to connected, planar graphs representing electrical circuits, where L is the number of independent loops (meshes). Start with Euler's formula for planar graphs: N - B + F = 2, where F is the number of faces. For a circuit, the number of independent meshes (L) is related to the number of faces (F). The number of independent meshes L is given by L = F - 1 (since one face is the exterior). Substitute F = L + 1 into Euler's formula: N - B + (L + 1) = 2. Rearrange to solve for L: L = B - N + 1. The graph must be connected. The graph must be planar (can be drawn on a plane without edges crossing). Confusing the number of meshes (L) with the number of faces (F). Applying the formula to non-planar graphs (e.g., K5 or K3,3). Forgetting the '+1' term, which accounts for the relationship between faces and meshes.