Question

The nodal method of circuit analysis is based on

• A. KVL and Ohm’s law
• B. KCL and Ohm’s law
• C. KCL and KVL
• D. KCL, KVL and Ohm’s law

Hint:

Nodal analysis always starts with KCL at nodes and uses Ohm’s law to relate currents and voltages.

Answer 1

The Correct Option is B

Step 1: Understanding nodal analysis.
Nodal analysis is a systematic method used to determine the voltages at different nodes of an electrical circuit with respect to a reference node (usually ground). The method focuses on node voltages rather than loop currents.
Step 2: Identifying the governing law.
At each node (except the reference node), Kirchhoff’s Current Law (KCL) is applied. According to KCL, the algebraic sum of currents entering and leaving a node is zero.
Step 3: Use of Ohm’s law.
To express currents in terms of node voltages, Ohm’s law is used. Currents through resistive elements are written as the voltage difference divided by resistance.
Step 4: Eliminating incorrect options.
(A) KVL is not directly used in nodal analysis.
(C) KVL applies mainly to mesh analysis.
(D) Although Ohm’s law is used, KVL is not a fundamental requirement of nodal analysis.
Step 5: Final conclusion.
Hence, nodal analysis is fundamentally based on KCL and Ohm’s law.

Answer 2

Nodal analysis can be understood by walking through exactly what is written down at each step of the method, and then checking which laws each step actually uses.

1. KVL and Ohm's law: Nodal analysis is built around writing one current-balance equation per node, not a voltage-loop equation, so KVL is not the law being applied at each node; this option wrongly credits KVL for a step it does not perform.
2. KCL and Ohm's law: At every non-reference node, the sum of currents leaving the node is set to zero, which is precisely KCL, and each of those branch currents is written as a node-voltage difference divided by the branch resistance, which is precisely Ohm's law. These two laws alone are sufficient to build and solve the full set of nodal equations.
3. KCL and KVL: While KCL is indeed used, KVL is not separately invoked once the node voltages (each referenced to a common ground) are used as the unknowns, since a node-voltage formulation already encodes voltage consistency around every loop automatically.
4. KCL, KVL and Ohm's law: This over-includes KVL, which, as explained, is not an extra law that needs to be separately applied once voltages are expressed relative to a single reference node.

Since the method centers on a current balance at each node with branch currents expressed via Ohm's law, and does not require writing loop voltage equations, the two laws that define nodal analysis are KCL and Ohm's law.

Therefore, the correct answer is KCL and Ohm's law.