Mesh analysis is a method used in electrical circuit analysis to determine the current flowing through each branch of a circuit. It is particularly useful for solving complex circuits with multiple loops. By applying Kirchhoff's voltage law (KVL), which states that the sum of the voltages around any closed loop in a circuit is equal to zero, mesh analysis allows us to determine the current flowing through each loop or mesh in the circuit.

The main purpose of mesh analysis is to determine the unknown currents in a circuit. By assigning a clockwise or counterclockwise direction to each mesh current, we can write equations based on KVL for each loop. These equations can then be solved simultaneously to find the values of the mesh currents.

To apply mesh analysis, the circuit must be divided into meshes or loops. A mesh is a loop that does not contain any other loops within it. Each mesh is assigned a unique mesh current, typically denoted by I1, I2, etc. The number of mesh currents required is equal to the number of meshes in the circuit.

Once the mesh currents are defined, KVL is applied to each mesh. The voltage drop across each component in the loop is expressed in terms of the corresponding mesh current. This allows us to write equations for each mesh using Ohm's law (V = I * R) and KVL. The equations are then solved simultaneously to determine the values of the mesh currents.

Since the mesh currents represent the currents flowing through each loop of the circuit, they provide valuable information about the current distribution in the circuit. By knowing the mesh currents, we can calculate the current flowing through any component in the circuit using the relationship between the mesh currents and the branch currents.

In conclusion, mesh analysis is a powerful technique used in electrical circuit analysis to determine the current flowing through each branch of a circuit. It is based on the application of KVL to each mesh in the circuit and allows us to solve complex circuits with multiple loops.