Which sequence correctly outlines the node-voltage method for circuits with multiple non-reference nodes?

• A. Apply Kirchhoff's Current Law for each loop and solve for loop currents.
• B. Choose a reference node, assign node voltages to non-reference nodes, apply KCL at each node, and solve the resulting equations.
• C. Assume mesh currents and apply KVL for each mesh.
• D. Transform the circuit to a Thevenin equivalent and then solve.

Answer: (B)

The essential idea is to solve circuits by tracking node voltages rather than loop currents. In this method you start by picking a reference (ground) node and assigning a voltage variable to every other node relative to that reference. Then you apply Kirchhoff’s Current Law at each non-reference node: the sum of currents leaving (or entering) the node must be zero. The currents through each element are written in terms of the node voltages (for a resistor between two nodes, the current is (Vi − Vj)/R). This gives you a set of simultaneous linear equations in the unknown node voltages, which you solve to find all node voltages. Once those voltages are known, you can determine any branch current or node voltage of interest.

This sequence is natural for circuits with multiple non-reference nodes because it directly yields the unknown voltages at all those nodes, and from there all currents follow. If a voltage source directly connects two non-reference nodes, you form a supernode and write an extra equation for the known voltage difference between those nodes; if a current source is present, its value is included in the KCL sum at the connected node(s).

Other approaches—for example, assuming mesh currents and applying Kirchhoff’s Voltage Law around each mesh, or converting the circuit to a Thevenin equivalent first—address different formulations and aren’t the standard step-by-step description of the node-voltage method.