Nodal Analysis with Dependent Sources

Nodal analysis also works when there are dependent sources.

• Dependent current source: Include in KCL equations
• Dependent voltage source: Include in node voltage relationships

$$\begin{array}{rl}\text{Node A:}& 2+I_1+(-2I_1)=\frac{V_A-V_B}{1}\\ \text{Node B:}& 0=\frac{V_B-0}{3}+\frac{V_B-V_A}{1}+(-2I_1)\end{array}$$

Since there are three unknowns, a third equation is required. This must come from a device equation since there are no more circuit equations:

$$I_1=\frac{10-V_A}{2}$$

Solution:

$$V_A=9\text{V},V_B=7.5\text{V},I_1=0.5\text{A}$$