Foundations of mesh analysis: The mesh-current method is fundamentally based on Kirchhoff’s Current Law (KCL). True or false?

Introduction / Context:
Understanding which Kirchhoff law underpins each classical method helps you set up the right equations and avoid sign mistakes. Mesh analysis and node analysis complement each other but rest on different laws of circuit theory.

Given Data / Assumptions:

• Mesh-current method writes loop equations around independent meshes.
• Kirchhoff’s Voltage Law (KVL) states the algebraic sum of voltages around a closed loop is zero.
• Kirchhoff’s Current Law (KCL) states the algebraic sum of currents at a node is zero.

Concept / Approach:

Mesh analysis assigns loop currents and applies KVL to each mesh. While KCL is still valid globally, it is not the primary law used to derive the mesh equations. Conversely, node-voltage analysis is directly based on KCL at each non-reference node.

Step-by-Step Solution:

Verification / Alternative check:

Compare with node-voltage analysis: there, you would write ΣI_out = 0 at each node (KCL), not loop sums. This contrast confirms which law each method fundamentally uses.

Why Other Options Are Wrong:

• Choosing “True” confuses the basis of the methods: mesh → KVL; node → KCL.

Common Pitfalls:

Attempting mesh analysis on non-planar circuits or with many current sources, which complicates forming loop equations. In such cases, node analysis (KCL-based) may be more straightforward.

Final Answer:

False