Mesh Analysis Notes

Mesh analysis provides another general procedure for analyzing circuits, using mesh currents as the circuit variables. Using mesh currents instead of element
currents as circuit variables is convenient and reduces the number of equations thatmust be solved simultaneously. Recall that a loop is a closed path with no node
passed more than once. A mesh is a loop that does not contain any other loop within it. Nodal analysis applies KCL to find unknown voltages in a given circuit,
while mesh analysis applies KVL to find unknown currents.
The procedure for writing the equations is as follows:
1. Assume the smallest number of mesh currents so that at least one mesh current links every element. As a matter of convenience, all mesh currents arc assumed to
have a clockwise direction. The number of mesh currents is equal to the number of meshes in the circuit.

2. For each mesh write down the Kirchhoffs voltage law equation. Where more than one mesh current flows through an element, the algebraic sum of currents
should be used. The algebraic sum of mesh currents may be sum or the difference of the currents flowing through the element depending on the direction of mesh
currents.

3. Solve the above equations and from the mesh currents find the branch currents.