Branch current method (circuit analysis): Which pair of laws or theorems is directly applied when solving networks using the branch current method?

Introduction / Context:
The branch current method is a systematic way to analyze circuits by assuming currents in each branch and writing equations based on conservation and element relationships. It is especially effective in multi-node resistive networks, where direct application of laws reduces the problem to solvable linear equations.

Given Data / Assumptions:

• A general resistive network with identifiable branches and nodes.
• We wish to determine which fundamental principles underpin the branch current method.

Concept / Approach:
Two ingredients are used: Kirchhoff's Current Law (KCL), which enforces current conservation at nodes, and Ohm's law, which relates voltage and current for resistive elements. KVL emerges implicitly when KCL and element laws are applied around the network, but the explicit setup centers on KCL at nodes and Ohm's law on branches.

Step-by-Step Solution:

Verification / Alternative check:
After solving, check KVL around loops (sum of voltage rises and drops equals zero) as a consistency test. Correct KCL and Ohm's-law modeling will satisfy KVL automatically in linear resistive networks.

Why Other Options Are Wrong:

• Kirchhoff's voltage and current laws: KVL isn't the direct setup tool here; KCL is primary along with Ohm's law.
• Thevenin's and superposition theorems: Useful alternatives, but not the essence of the branch current method.

Common Pitfalls:

• Mistaking loop-current (mesh) method—which uses KVL—as the branch current method.

Final Answer:
Kirchhoff's current law and Ohm's law