Mesh Analysis

Mesh Analysis

In Mesh analysis, we will consider the currents flowing through each mesh. Hence, Mesh analysis is also called as Mesh-current method.

A branch is a path that joins two nodes and it contains a circuit element. If a branch belongs to only one mesh, then the branch current will be equal to mesh current.

If a branch is common to two meshes, then the branch current will be equal to the sum (or difference) of two mesh currents, when they are in same (or opposite) direction.

Procedure of Mesh Analysis

Follow these steps while solving any electrical network or circuit using Mesh analysis.

Step 1 − Identify the meshes and label the mesh currents in either clockwise or anti-clockwise direction.

Step 2 − Observe the amount of current that flows through each element in terms of mesh currents.

Step 3 − Write mesh equations to all meshes. Mesh equation is obtained by applying KVL first and then Ohm’s law.

Step 4 − Solve the mesh equations obtained in Step 3 in order to get the mesh currents. Now, we can find the current flowing through any element and the voltage across any element that is present in the given network by using mesh currents.

Example:-

Mesh1:-

10 = 10I₁ + 40(I₁-I₂)                     ----------------- (i)

Mesh2:-

-20 = -20I₂ + 40(I₂-I₁)                   ---------------- (ii)

Or reducing equation, the above equation becomes

-20 = 20I₂ - 40I₁

10 = -40I₂ + 50I₁

Hence by calculating I₁ = 1A and I₂ = 1A