Equation count: In general practice, the mesh-current (loop) method produces fewer simultaneous equations than the node-voltage method. True or false?

Introduction / Context:
Two cornerstone analysis techniques in circuit theory are the node-voltage (KCL-based) method and the mesh-current (KVL-based) method. Which one yields fewer equations depends on circuit topology; there is no universal rule favoring meshes over nodes.

Given Data / Assumptions:

• Planar circuits are assumed for mesh analysis applicability.
• Node-voltage method requires N−1 equations for N nodes (with a chosen reference ground).
• Mesh-current method requires M equations for M meshes (independent loops).

Concept / Approach:

The relative sizes of N−1 and M determine which method is more compact. Many practical circuits have fewer essential nodes than meshes, making node-voltage equations fewer. Conversely, in some sparse planar layouts, M can be small. Hence, the blanket statement that mesh “generally” yields fewer equations is not reliable and is often false in modern network topologies.

Step-by-Step Solution:

Verification / Alternative check:

Example: a ladder with many series elements per rung often has relatively few nodes compared to the number of small loops, favoring node analysis. Simulation tools also often use nodal formulations internally, reflecting this efficiency.

Why Other Options Are Wrong:

• Selecting “True” overlooks counterexamples where meshes greatly outnumber nodes.

Common Pitfalls:

Applying mesh analysis to non-planar circuits or circuits with many current sources, which complicates loop equations. Selecting the method should be dictated by topology, source types, and convenience.

Final Answer:

False