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.

Wye - Delta Transformation

| WYE - DELTA TRANSFORMATION |

Most of the time we can solve the circuit using our idea of series and parallel connection and ohm’s law or KCL or KVL. But sometimes we encounter some circuitwhere the formations of elements are neither in series nor in parallel. For example look at the figure of bridge network below:

Now look at the following two formations which look like Wye and Delta. Theseformations usually found in three phase connections, filters, or in matching networks.

(a) Y netwrk (b) Delta Network

(a) Delta Network

(b) Pie Network

When we analyze a circuit we may find a certain formation to be helpful. And we might want to change one formation into other. Suppose it might helpful for us to work with Wye formation in three phase rather in Delta formation. So we have to know how to transform a Delta network into Wye network.

| Delta to Wye conversion: |

Look at the figure below:

Now for Delta to Wye conversion:

R1 = (Rb . Rc) / (Ra + Rb + Rc)

R2 = (Rc . Ra) / (Ra + Rb + Rc)

R3 = (Ra . Rb) / (Ra + Rb + Rc)

We don’t have to memorize these formulas rather we can easily remember these.Each resistor of the Wye network is the product of the two adjacent resistors of Delta network, divided by the sum of all three resistors of the Delta network.

| Wye to Delta Conversion: |

Look at the figure below:

Now for Wye to Delta conversion:

Ra = (R1.R2 + R2.R3 + R3.R1) / R1

Rb = (R1.R2 + R2.R3 + R3.R1) / R2

Rc = (R1.R2 + R2.R3 + R3.R1) / R3

We don’t have to memorize this also. The easy way to remember is, each resistorin the Delta Network is the sum of all possible product formation of Wye network’s resistors taken two at a time, divided by the opposite Wye resistor.

| My Learning Experience XD |

I learned that in making the transformation or conversion the circuit with wye to delta (vice versa), we do not take out anything or put anything new of the circuit, I realized that when we take our quiz about this topic. hahaha XD. We are merely substituting different but mathematically equivalent three-terminal network patterns to create a circuit, which are either in series or in parallel, allowing us to calculate Req.