3.6 The Mesh-Current Method Figure 3.21 Illustrations of the concept of a mesh. A mesh is a circuit loop that does not enclose any elements The mesh currents are fictitious currents that are defined to flow only around the mesh

The general rules for writing mesh-current equations 1.Define the mesh currents 2.Write the total current through each element in terms of the mesh currents flowing through them 3. Write KVL around each mesh 4. Put these equations in standard form, and solve them for the mesh currents A three-mesh circuit and the mesh currents

For example KVL around each mesh give: Grouping and placing in a standard form In matrix form Once these equations are solved, the current through each element Can be written in terms of the Mesh currents

Ex 3.14 Write the mesh-current equations and determine I Ex 3.14: Write the mesh-current equations and determine current I Direction of mesh current does not affect solution KVL around each mesh In matrix form Solving for mesh currents Therefore:

3.6.1 Circuit Containing Current Sources Mesh-current equations when a circuit contains a current source 1.Define the mesh currents in the usual fashion 2.Write the constraints that are imposed on the mesh currents by any current sources. 3. Draw loops around all pairs of meshes that share a current source 4. Write KVL for all these loops and all other meshes except those meshes that have a current source in an outside branch 5. Substitute the constraints imposed on the mesh currents by the current sources into these equations and place them in standard form Hence only one mesh current is unknown Voltage across current source is unknown, so we apply KVL around mesh 2 and mesh 3 Substitute constraints:

Ex 3.16 Determine V by writing mesh equations Constraints: KVL around mesh 2 and 3 Substituting current constraints Hence the voltage is