meshcurrent

Mesh current is a method used in circuit analysis to solve linear circuits by assigning a distinct loop current to each independent mesh in a planar circuit. A mesh is a loop that does not contain any other loops inside it, and the assigned mesh currents are typically assumed to flow in a consistent direction, usually clockwise.

In the mesh current method, Kirchhoff's voltage law is applied to each mesh. For a resistor that lies in a single mesh, the voltage drop is R times the mesh current. For a resistor shared by two meshes, the voltage drop for one mesh is R times the difference between the two mesh currents (R(I_i − I_j)). This yields a system of linear equations in the mesh currents. After solving for the mesh currents, branch currents and node voltages can be computed by combining the relevant mesh currents according to how each element is shared between meshes.

When a circuit includes current sources, a common technique is to form a supermesh: remove the current source and apply KVL around the outer loop, while using the current source value to relate the adjacent mesh currents. If a current source lies between two meshes, it establishes a relation between the corresponding mesh currents (for example, I_i − I_j equals the known source value).

The mesh current method is particularly efficient for planar circuits with many resistors and few current sources. It is one of several approaches to circuit analysis, complementary to nodal analysis. Its primary use is to reduce the number of equations in circuits where loop currents provide a natural description of the currents through elements.