node analysis

In general, the method is:

1. Identify each node.
2. Let one node be common or ground, to establish a reference voltage.
3. For each node attached to the (+) terminal of a voltage source, write the voltage at that node as the voltage at the (-) terminal plus the voltage boost given by the source.
4. Establish a voltage variable for each remaining node, where the exact voltage is unknown.
5. For each of the unknown voltage nodes, write Kirchoff's Current Law (KCL).
6. Use the characteristics of devices attached between each node to determine the current in terms of the voltages at each node. For example: if a resistor is attached between nodes having voltages of V₁ and V₂, you would use Ohm's Law to write:

   I_1->2=(V₁-V₂)/R

7. Substitute each of these device currents into the KCL equations. There should be no unknown currents left: they must all be in terms of the node voltages.
8. Simultaneously solve the substituted KCL equations: there should have been one unknown voltage created for each node, and one KCL for each node, so you are guaranteed enough equations.
9. At this point you have values for all voltages, substitute back into the device current formulae you derived to find all the branch currents.
10. You know now all of the voltages and currents in the circuit.

Also called Node Voltage Analysis or perhaps just Node Voltage.

Contrast with Mesh Current Analysis.