EXAMPLE $4\mathrm{.}12$

Evaluate the three unknown currents in the circuit of Fig. $4\mathrm{.}26.$

The current sources appear in meshes $1$ and $3.$ Since the $15$ A source is located on the perimeter of the circuit, we may eliminate mesh $1$ from consideration$-$it is clear that $i_1=15A.$

We find that because we now know one of the two mesh currents relevant to the dependent current source, there is no need to write a supermesh equation about meshes $1$ and $3.$ Instead, we simply relate $i_1$ and $i_3$ to the current from the dependent source using KCL:

$\frac{v_x}{9}=i_3-i_1=\frac{3(i_3-i_2)}{9}$

$($Continued on next page$)$

riuUKE $4\mathrm{.}20$ a tnree$-$mesn circuit with one dependent and one independent current source.