Mesh Current Analysis Method

The Mesh Current Analysis Method is utilized to analyze and solve electrical networks with multiple sources or circuits comprising numerous meshes (loops) containing voltage or current sources. Also known as the Loop Current Method, this approach involves assuming a distinct current for each loop and determining the polarities of voltage drops across loop elements based on the assumed direction of the loop current.

In mesh current analysis, the unknowns are the currents in different meshes, and the governing principle is Kirchhoff’s Voltage Law (KVL), which states:
"In any closed circuit, the net applied voltage equals the sum of the products of current and resistance. Alternatively, in the direction of current flow, the sum of voltage rises within the loop is equal to the sum of voltage drops."

Let us understand the Mesh Current method with the help of the circuit shown below：

In the Above Network

• R₁, R₂, R₃, R₄, and R5 represent various resistances.

• V₁ and V₂ are voltage sources.

• I₁ is the current flowing in mesh ABFEA.

• I₂ is the current flowing in mesh BCGFB.

• I₃ is the current flowing in mesh CDHGC.

• For simplicity in network analysis, the current direction is assumed to be clockwise in all meshes.

Steps for Solving Networks via Mesh Current Method

Using the circuit diagram above, the following steps outline the mesh current analysis process:

Step 1 – Identify Independent Meshes/Loops

First, identify the independent circuit meshes. The diagram above contains three meshes, which are considered for analysis.

Step 2 – Assign Circulating Currents to Each Mesh

Assign a circulating current to each mesh, as shown in the circuit diagram (I₁, I₂, I₃ flowing in each mesh). To simplify calculations, it is preferable to assign all currents in the same clockwise direction.

Step 3 – Formulate KVL Equations for Each Mesh

Since there are three meshes, three KVL equations will be derived:

Applying KVL to Mesh ABFEA:

Step 4 – Solve Equations (1), (2), and (3) simultaneously to obtain the values of currents I₁, I₂, and I₃.

With the mesh currents known, various voltages and currents in the circuit can be determined.

Matrix Form

The above circuit can also be solved using the matrix method. The matrix form of Equations (1), (2), and (3) is expressed as:

Where,

• [R] is the mesh resistance

• [I] is the column vector of mesh currents and

• [V] is the column vector of the algebraic sum of all the source voltages around the mesh.

This is all about the mesh current analysis method.