Applicability of the mesh (loop-current) method Statement: “The mesh method can be applied to circuits with any number of loops.”

Introduction / Context:
The mesh (loop-current) method is powerful but not universally applicable. Recognizing its domain of validity prevents wasted effort and mistakes when analyzing nonplanar networks or circuits with certain source placements.

Given Data / Assumptions:

• Mesh analysis uses independent meshes (windows) of a planar circuit.
• Nonplanar circuits cannot be drawn without crossing branches; meshes are not well-defined.
• Current sources between two meshes can complicate writing KVL directly.

Concept / Approach:

Mesh analysis requires planarity. While the number of loops can be large, the method does not extend to nonplanar networks directly. Also, floating current sources between meshes necessitate supermesh handling or alternative formulations. Therefore, the unconditional statement “any number of loops” is false because topology, not just loop count, governs applicability.

Step-by-Step Solution:

Verification / Alternative check:

Compare with nodal analysis, which is applicable to a broader set of circuits (including nonplanar), reinforcing that mesh is conditional.

Why Other Options Are Wrong:

“True” ignores topology limits. “True only if there are no current sources” is too restrictive because supermeshes handle many such cases. The best precise qualifier is “planar circuits,” captured by option C (but the statement under test, as written, is false).

Common Pitfalls:

Attempting mesh on bridge networks that are nonplanar in their electrical graph; forgetting to add current-source constraint equations.

Final Answer:

False.