Circuit analysis – Foundational concept check for the node-voltage (nodal) method Statement: “The node-voltage method is based on Kirchhoff’s voltage law (KVL).” Decide whether the statement is correct and choose the best option.

Introduction / Context:
The node-voltage (nodal) method is one of the two cornerstone systematic techniques for linear circuit analysis, the other being the mesh-current method. Many learners mix up which Kirchhoff law underpins which technique. This question checks that foundational association.

Given Data / Assumptions:

• We are analyzing linear lumped circuits using Kirchhoff’s laws.
• “Node-voltage method” refers to writing node equations in terms of node potentials relative to a common reference (ground).
• No special source or element types (e.g., dependent sources) are required for the basic statement under test.

Concept / Approach:

Kirchhoff’s current law (KCL) states that the algebraic sum of currents leaving/entering a node is zero. The node-voltage method writes one equation per essential node by summing currents (expressed via conductances/admittances and node voltages) to satisfy KCL. KVL is involved implicitly when expressing element currents by Ohm’s law using node-to-node voltage differences, but the governing equations are KCL equations at nodes.

Step-by-Step Solution:

Verification / Alternative check:

Compare with the mesh-current method, which explicitly writes KVL around meshes. The clear division—nodal ↔ KCL; mesh ↔ KVL—confirms the statement is false.

Why Other Options Are Wrong:

“True” misattributes the primary law. “True only for single-loop circuits” and “Cannot be determined” add conditions that are irrelevant; the method’s foundation does not change with loop count or source type.

Common Pitfalls:

Assuming that because voltages are unknowns, the method must be “about KVL.” In reality, voltages are unknowns but the conservation law applied is KCL at each node.

Final Answer:

False.