If you have been following this series, you know voltage, current, Ohm’s law, KCL, and KVL. Now it is time to put them all together into a systematic method for solving any circuit.

Node Voltage Analysis (also called Nodal Analysis) is that method. Once you learn it, you never go back to guessing.

The Big Idea

Node Voltage Analysis = Apply KCL at every node, solve the equations.

Pick a reference node (ground), write KCL equations at every other node, solve for voltages, find everything else from Ohm’s law.

Step-by-Step

Step 1: Pick a Reference Node (Ground)

Choose one node as 0V. Usually the bottom of the circuit or the node with the most connections.

Step 2: Label All Other Nodes

Give each remaining node a variable name: V₁, V₂, V₃, etc.

Step 3: Write KCL at Each Node

For each node, sum the currents leaving the node = 0. Express each current using Ohm’s law in terms of the node voltages.

Step 4: Solve the Equations

N equations with N unknowns. Solve with substitution, elimination, or a calculator.

Why This Works So Well

Earlier methods work for simple circuits. But when circuits have 3+ loops or dependent sources, those methods become a mess. Nodal analysis is systematic. You always follow the same steps.

Simple Example

Circuit with: 10V source from ground to V₁, 1kΩ from V₁ to ground, 2kΩ from V₁ to V₂, 3kΩ from V₂ to ground.

At node V₁: V₁ = 10V (voltage source forces it).

At node V₂: (V₂ − V₁)/2k + V₂/3k = 0

Solving: V₂ = 6V. Simple.

The Supernode

When a voltage source connects between two non-reference nodes, treat the two nodes as a single supernode. Write one KCL equation for the combined region, then add the voltage constraint.

Example: a 5V source connects V₁ to V₂. You know V₁ − V₂ = 5V.

Common Mistakes

  • Forgetting to count all nodes (every junction counts)
  • Wrong sign convention for currents
  • Not handling voltage sources correctly

Next up: Mesh Current Analysis — the dual of nodal analysis, using KVL instead of KCL.