Week 7: Mesh Analysis

Mesh Analysis

What is Mesh Analysis?

-Mesh analysis or the Mesh Current Method, also known as the Loop Current Method, 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. It differs from the Branch Current method in that it does not use Kirchhoff's Current Law, and it is usually able to solve a circuit with less unknown variables and less simultaneous equations, which is especially nice if you're forced to solve without a calculator.

What is a "Mesh"?

-Basically, A mesh is a loop that does not have any loops in it.

In the figure above, the following meshes are: B1-R1-R2-B1, and B2-R3-R2-B2 but B1-R1-R3-B2-B1 is not a mesh because it contains other loops in it.

Mesh Analysis without Current Sources

Steps:

1. Identify loops within the circuit encompassing all components.

2. Assign mesh currents to the number of meshes found in the circuit.

3. Apply current directions to each of the mesh currents in the circuit. The choice of each current's direction is entirely arbitrary. If the assumed direction is wrong, the answer for that current will be a negative answer.

4. Apply Kirchoff's Voltage Law (KVL) to each of the meshes.

5. Use Ohm's Law to express the voltages in terms of mesh currents.

6. Solve the resulting n simultaneous equations to get the mesh currents.

Mesh Analysis with Current Sources

Two cases to consider:

Case 1: A current source exists only in one mesh.

Case 2: A current source exists between two meshes.

What is a Supermesh?

 - A supermesh occurs when a current source is contained between two essential meshes. The circuit is first treated as if the current source is not there. This leads to one equation that incorporates two mesh currents. Once this equation is formed, an equation is needed that relates the two mesh currents with the current source. This will be an equation where the current source is equal to one of the mesh currents minus the other. The following is an example of a supermesh.

Reflection:

This week, I learned that meshes in a circuit are loops that does not have any loops in them and that they require Mesh Analysis to be solved. Mesh Analysis or Mesh Current Method are almost similar in Branch Current method because the way to solve them are both exactly the same except that mesh analysis requires KVL while nodal analysis requires KCL. Both methods of circuit analysis are very useful in solving all types of circuit problems. Overall, I learned that mesh analysis is much easier than the Branch current method because unlike in the Branch current method, We don't need any reference components or parts like the reference nodes in the Branch current method.

Videos:

Mesh Analysis Introduction:

Mesh Analysis with Independent current sources:

Mesh and Supermesh:

Thanks for visiting my Blog!!! The eight post will be arriving next week. See ya!!!

“The best teachers are those that can influence even the poorest of all learners.”

― Kim Panti