Branch-current (direct) method – Which Kirchhoff laws does it use? Statement: “The branch current method is based on Kirchhoff’s voltage law and Kirchhoff’s current law.”

Introduction / Context:
The branch-current (direct) method writes unknowns as the actual currents in circuit branches and sets up equations using both Kirchhoff laws. Understanding this helps you choose between branch-current, nodal, and mesh methods for a given problem size and topology.

Given Data / Assumptions:

• We have n branches with assigned current variables.
• We can form node equations (KCL) and loop equations (KVL) as needed to close the system.
• Ohm’s law links branch voltages and currents for passive elements.

Concept / Approach:

Branch-current analysis typically uses KCL at nodes to relate the unknown branch currents and KVL around independent loops to introduce element voltages and source effects. Thus both KCL and KVL are employed, unlike nodal (primarily KCL) or mesh (primarily KVL).

Step-by-Step Solution:

Verification / Alternative check:

Counting equations vs. unknowns confirms that both node and loop constraints are needed unless special structures reduce the set.

Why Other Options Are Wrong:

“It uses only KCL” or “only KVL” understate the method; while some problems may be solvable with just one set of equations, the general branch-current framework relies on both laws.

Common Pitfalls:

Creating dependent equations (linear dependence) by choosing redundant KVL loops; forgetting reference polarities leading to sign errors.

Final Answer:

True.