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

Nodal analysis writes one KCL equation at each non-reference node and expresses every branch current using Ohm's law in terms of the node voltages.

1. KVL and Ohm's law: Incorrect, since loop voltage equations are not what is written at each node.
2. KCL and Ohm's law: Correct, this is exactly the two ingredients used to build the node equations.
3. KCL and KVL: Incorrect, since Ohm's law (not KVL) is what converts voltages into the currents that KCL balances.
4. KCL, KVL and Ohm's law: Incorrect, since KVL is not a separate requirement once all node voltages share one reference.

Answer 2

A useful way to pin down which laws underlie nodal analysis is to contrast it with mesh (loop) analysis, which is nodal analysis's natural counterpart. Mesh analysis assigns a loop current to each independent loop and writes one KVL equation per loop, with Ohm's law converting those loop currents into voltage drops. Nodal analysis instead assigns a voltage to each node and writes one KCL equation per node, with Ohm's law converting those node voltages into branch currents.

1. KVL and Ohm's law: This pairing actually describes mesh analysis, not nodal analysis, since KVL is the loop-based law, while nodal analysis is node-based.
2. KCL and Ohm's law: This is the correct pairing for nodal analysis, mirroring how KVL and Ohm's law pair up for mesh analysis.
3. KCL and KVL: Nodal analysis needs Ohm's law to translate node voltages into currents before KCL can be applied; leaving out Ohm's law and only citing KCL and KVL misses this essential conversion step.
4. KCL, KVL and Ohm's law: Adding KVL on top is unnecessary, since KVL is the defining law of the dual method (mesh analysis), not of nodal analysis itself.

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