Mesh Currents and Essential Meshes
Mesh analysis works by arbitrarily assigning mesh currents in the essential meshes (also referred to as independent meshes). An essential mesh is a loop in the circuit that does not contain any other loop. Figure 1 labels the essential meshes with one, two, and three.
A mesh current is a current that loops around the essential mesh and the equations are set solved in terms of them. A mesh current may not correspond to any physically flowing current, but the physical currents are easily found from them. It is usual practice to have all the mesh currents loop in the same direction. This helps prevent errors when writing out the equations. The convention is to have all the mesh currents looping in a clockwise direction. Figure 2 shows the same circuit from Figure 1 with the mesh currents labeled.
Solving for mesh currents instead of directly applying Kirchhoff's current law and Kirchhoff's voltage law can greatly reduce the amount of calculation required. This is because there are fewer mesh currents than there are physical branch currents. In figure 2 for example, there are six branch currents but only three mesh currents.
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