Mesh Analysis with Dependent Sources

Mesh Analysis requires no modifications when there are dependent sources. Just include dependent current source currents in the mesh current relationships, or dependent voltage source voltages in the KVL equations.

Let’s say the source $V_x$ is governed by:

$$V_x=6I_B\left[\frac{V}{mA}\right]$$

The resulting mesh equations would be:

$$\begin{array}{rl}\text{Mesh A:}& 2I_A+4(I_A-I_C)+10=0\\ \text{Mesh B:}& 2(I_B-I_C)+3I_B-10=0\\ \text{Mesh C:}& 2(I_C-I_B)+4(I_C-I_A)-6I_B=0\end{array}$$

Resulting in:

$$\text{Solution:}{I}_A=45\text{mA},I_B=30\text{mA },I_C=70\text{mA}$$