Mesh Analysis

A Mesh is a loop that does not contain any other loop within it.

~ a loop can be a mesh, but a mesh can't be a loop.

Same as the nodal analysis, a mesh analysis have also a steps in getting the equation but they differ for some aspects which is the Nodal analysis talks about the nodal voltages while the Mesh analysis talks about mesh currents. 

~ a mesh current is quite similar to the Branch Current method in that it uses simultaneous equations, Kirchhoff's Voltage Law, and Ohm's Law to determine unknown currents in a network.

Why is it QUITE SIMILAR TO THE BRANCH CURRENT?
-  it is quite similar, then of course it is also quite different but it depends on how the mesh is being ISOLATED.


There are steps in determining mesh currents same as nodal analysis, there are steps to determine nodal voltage in order to form an equation.

STEPS TO DETERMINE MESH CURRENTS:
1. Assign mesh currents I1, I2,... In to the n meshes.
2. Apply KVL to each  of the n meshes. Use ohm's law to express the voltages in terms of the mesh currents.
3. Solve the resulting n simultaneous equations to get the mesh currents.

Example:

As you observe the figure, the current flow counter clockwise but wherever the mesh currents will flow, it's direction is arbitrary and does not affect the validity of the solution.

~ as a class, we are more prefer to have the mesh currents direction clockwise because for us it is more convenient and easier to analyze.

Mesh analysis with current sources

Case 1:

When a current source exists only in one mesh

Case 2:

When a current source exists between two meshes and that is SUPERMESH.

What is supermesh?

A SUPERMESH results when two meshes have current source in common.

For more information about mesh, just watch this: