Nodal Analysis

KCL can be applied systematically to find all node voltages in a circuit.

Steps:

1. Label nodes and ground. Nodes that are connected to voltage sources are not labelled because they have known voltages.
2. Write KCL equations at each node, referencing the current leaving the node unless otherwise indicated.
3. Replace currents with device equations using node voltages.
4. Solve systems of equations.

$$\begin{array}{rl}\text{Node A: }0& =\frac{V_A-5}{0.5}+\frac{V_A-0}{4}+\frac{V_A-V_B}{2}\\ \text{Node B: }0& =\frac{V_B-V_A}{2}+\frac{V_B-0}{2}\\ \text{Solve: }{V}_A& =2,V_B=2\end{array}$$