Mesh analysis

Mesh analysis is a systematic method for determining the currents flowing in each independent loop (mesh) of a planar electrical circuit. It applies Kirchhoff's voltage law around each mesh to generate a set of linear equations, with mesh currents as the unknown variables. The method is dual to nodal analysis: where nodal analysis solves for node voltages using current conservation, mesh analysis solves for loop currents using voltage conservation. For circuits with many series elements and voltage sources, mesh analysis often produces fewer equations than nodal analysis. The choice between the two methods is not merely computational convenience; it is a choice of which conservation law to treat as primary, and that choice reflects the circuit's topology.