MESH ANALYSIS

What is mesh analysis?

Branch
-This is a circuit elements that connected two nodes

Loop
-This a closed path in a circuit. A set of these loops are used to create constraint equations.


Mesh
-A loop passing though at least on branch
Basic rule: The sum of voltage around any loop must be Zero.(from KVL) 

Manual Mesh/Loop Analysis algorithm:

* Choose a conventional current flow

* Identify and Number Loops or meshes

* Apply KVL to identified mesh and formulate circuit equation

* Create Matrix system from KVL equation obtained

* Solve matrix for unknown Mesh Currents by using Cramer's rule

* Uses solved Mesh Currents to solve for the desired circuit entity

Example:

Consider this figure with the following Parameter:

V1 = 15 V

V2 = 7 V

R1 = 2

R2 = 20

R3 = 10

R4 = 5

R5 = 2

R6 = 2

Find current through R3 using mesh analysis method
solution:

-We can see that there are three closed paths (loop) where we can apply KVL in, Mesh 1,2 and 3 as shown in the figure
- We can now apply KVL around the Mesh remembering Passive Convention When defining Currents and Voltages