3.3: Analysis with Mesh or Loop Equations

3.3 Analysis with Mesh or Loop Equations

In writing mesh or loop equations, we follow these steps:

1. For a circuit containing M = L = B ? N + 1 meshes (or loops), we assign a mesh or loop current i ₁, i ₂, , i _{n ? 1} for each mesh or loop.

2. If the circuit does not contain any current sources, we apply KVL around each mesh or loop.

3. If the circuit contains a current source between two meshes or loops, say meshes or loops j and k denoted as mesh variables i _j and i _k, we replace the current source with an open circuit thus forming a common mesh or loop, and we write a mesh or loop equation for this common mesh or loop in terms of both i _j and i _k. Then, we relate the current source to the mesh or loop variables i _j and i _k.

Example 3.3

For the circuit of Figure 3.9, write mesh equations in matrix form and solve for the unknowns using matrix theory, Cramer's rule, or Gauss's elimination method. Verify your answers with Excel or MATLAB. Please refer to Appendix A for procedures and examples. Then construct a table showing the voltages across, the currents through, and the power absorbed or delivered by each device.

Figure 3.9: Circuit for Example 3.3

Solution:

For this circuit we need M = L = B ?