**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.

For the circuit above:

**Mesh 1:**

**Mesh 2:**

**Mesh 3:**

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Comments, suggestions, or requests to ghw@udel.edu.

"http://www.physics.udel.edu/~watson/phys345/class/4-mesh.html"

Last updated Sept. 10, 1998.

Copyright George Watson, Univ. of Delaware, 1998.