Mesh current analysis is one of the most universal methods of solving electrical circuits or networks. We use this analysis to determine currents flowing in the individual mesh by forming a system of linear equations with help of Kirchhoff’s Voltage Law. Mesh current analysis is also known as Maxwell’s circulating current theorem.

Such as for the circuit shown below and also for most of the cases the circuit or the electrical network can be assumed to have mesh. Where mesh is the most elementary form of a loop.

Mesh Current Analysis

Figure:1

Such as in the circuit above, AEFDA and EBCFE are mesh and ABCDA is a loop.

Mesh= AEFDA and EBCFE.

Loop= ABCDA

Application of Mesh Current Analysis

For the application of this theorem for circuit or network analysis, we assume a current to be flowing around a mesh by a curved arrow in a particular direction. We can take the direction of the current either clockwise or counterclockwise. But for the systematic and easy solution of the network, we assume all the currents for the mesh to be flowing in a clockwise direction i.e. assuming all currents in a particular direction.

After this, we apply KVL or Kirchhoff’s second law to the individual mesh to form a system of a linear algebraic equation. This system of linear algebraic equations can be solved to determine the unknown mesh currents which were previously assumed for the mesh current analysis.

Steps for Mesh Current Analysis

Let’s consider the network given below.

Mesh Current Analysis

Figure: 2

  1. First, consider the mesh currents. Here for two mesh, currents I1 and I2 are assumed to be flowing clockwise direction as shown above.
  2. Now write the KVL equation for each mesh. Such as in the above network: for mesh 1 i.e. AEFDA, the KVL equation is given by

Similarly for mesh 2 i.e. EBCFE, the KVL equation is given by

Finally, these two systems of linear equations can be solved and the unknowns I1 and I2 can be determined.

NOTE: For the ‘N’ number of mesh in a circuit, there will be an ‘N’ number of currents to be assumed and consequently there will be an ‘N’ number of linear algebraic equations formed to determine the respective currents.

Examples

For more clear perspective on mesh current analysis, we will be looking at two example problems.

Example-1:

In the circuit below we will determine the currents flowing in the three mesh by mesh current analysis.

Mesh Current Analysis

Figure: 3

At first, the mesh currents i1, i2, and i3 are assumed as shown above.

Now we apply KVL for mesh 1, 2, and 3 respectively as below.

Then, solving equation (i), (ii), and (iii) we have

Example-2:

In the circuit below we will determine the currents flowing in the three mesh. Where, R1 = R2 = R3 = 5 Ω.

Mesh Current Analysis

Figure: 4

At first, we assume the mesh currents I1, I2, and I3.

Now we apply KVL for mesh 1, 2, and 3 respectively as below.

Then, solving equation (i), (ii) and (iii) we have

I1 = I2 = I3 = 2 Amps.


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