Nodal Analysis

1. Choose a reference node (ground).
2. Label the remaining node voltages $V_1, V_2, \dots$
3. Apply KCL at each non-reference node, writing each branch current as $(V_a - V_b)/R$.
4. Solve the simultaneous equations.

Example — a node $V_1$ fed from 10 V through 2 Ω, with 4 Ω to ground and 4 Ω to another node at 0 V:

$\frac{V_1 - 10}{2} + \frac{V_1}{4} + \frac{V_1}{4} = 0 \;\Rightarrow\; V_1 = 5\ \text{V}$

A voltage source between two non-reference nodes forms a supernode. Nodal analysis is what circuit simulators such as SPICE use internally.