Mesh Analysis

| Mesh Current Analysis Circuit |

• Nodal analysis was developed by applying KCL at each non-reference

node.

• Mesh-Current method is developed by applying KVL around

meshes in the circuit.

• A mesh is a loop which doesn't contain any other loops within it.

• Loop (mesh) analysis results in a system of linear equations which

must be solved for unknown currents.

• Reduces the number of required equations to the number of meshes

• Can be done systematically with little thinking

• As usual, be careful writing mesh equations – follow sign convention.

•Powerful analysis method which applies KVL to find unknown currents.

•It is applicable to a circuit with no branches crossing each other.

| What is a Mesh ? |

 A mesh is a loop which does not contain any other loops within it.

| Steps of Mesh Analysis |

.

 Step1:    Identify the number of basic meshes. 

Step 2:  Assign a current to each mesh.

Step 3:  Apply KVL around each loop to get an equation in terms of the loop currents.

Step 4:  Solve the resulting system of linear equations.

                   As an example

                                          V1 + I1 R1 + (I1 - I2) R3 = 0

                                            I2 R2 + V2 + (I2-I1) R3 = 0

| Cases to be considered for Mesh Analysis |

Case I

A current source exists only in one mesh

set i2 = −5A and write a mesh equation for the other mesh

Case II   

A current source exists between two meshes

exclude the circle part

a supermesh was created by

excluding the current source and any

elements connected in series with it,

| What is a Supermesh ? |

A supermesh results when two meshes have a (dependent or independent) current source in common.

| My Learning Experience XD |

I learned that in  Mesh analysis it is a method that is used to solve planar circuits for the currents at any place in the circuit. Planar circuits are circuits that can be drawn on a plane 

surface with no wires crossing each other. Hence, the difference between mesh and loop is that the mesh is a loop which does not contain any other loops within it while loop is any continuous path  available for current flow from a given point in a circuit and back to that same point in the circuit from the opposite direction that it left from without crossing or retracing it`s own path. I learned also the steps and cases of mesh analysis which most important to know on how to  determine and solve the mesh analysis.