## PHYS345 Electricity and Electronics

Mesh Analysis

Sample Circuit: 2 Meshes
Consider three lossy voltage sources in parallel as a context for outlining the procedure of mesh analysis.

Step 1: Assignment of Mesh Currents
Assign a current to each mesh, circulating clockwise. A mesh is the same as an inner loop from our previous application of KVL to multiloop circuits. There may not be any elements cutting across the mesh; if so, an additional mesh must be considered. [See final figure below.]

Step 2: Apply KVL to Each Mesh
The usual formulation of mesh analysis provides a quick and convenient way of writing loop equations in standard form as shown below.

The so-called self-resistance is the effective resistance of the resistors in series within a mesh. The mutual resistance is the resistance that the mesh has in common with the neighboring mesh.

To write the mesh equation in standard form, evaluate the self-resistance, then multiply by the mesh current. This will have units of voltage.

From that, subtract the product of the mutual resistance and the current from the neighboring mesh for each such neighbor.

Equate the result above to the driving voltage, taken to be positive if its polarity tends to push current in the same direction as the assigned mesh current.

For the circuit above:

Mesh 1:

Mesh 2:

Step 3: Solve for the Mesh Currents
At this point, use your preferred method to solve the mesh equations simultaneously for the currents.

Sample Circuit: 3 Meshes

For the circuit above:

Mesh 1:

Mesh 2:

Mesh 3: