Mesh/loop analysis – Is a loop current an actual branch current? Statement: “A loop current is an actual current in a branch.”

Introduction / Context:
In mesh (loop) analysis, we introduce loop currents as mathematical variables to simplify KVL writing. It is important to distinguish these from the physical branch currents measured in components.

Given Data / Assumptions:

• Loop currents are hypothetical variables assigned to each mesh.
• Branch current equals the algebraic sum of all loop currents passing through that branch, considering direction.
• No special source/element constraints are assumed.

Concept / Approach:

A loop current itself is not necessarily the actual branch current. Only in a branch that is exclusive to one loop does the branch current equal that loop current. In shared branches, the actual branch current equals the difference (or sum) of the relevant loop currents depending on assumed directions. Therefore, the blanket statement is false.

Step-by-Step Solution:

Verification / Alternative check:

Consider two meshes sharing a resistor. If I1 = 2 A and I2 = 0.5 A with opposing directions, the shared resistor’s branch current is 1.5 A in the direction of I1, not equal to either loop current alone.

Why Other Options Are Wrong:

“True” confuses variables with physical quantities. “True only in dc” is incorrect because the relationship holds for ac phasor analysis as well. “True only if the branch belongs to a single loop” is a conditional truth, but the original unconditional statement remains false.

Common Pitfalls:

Reporting mesh currents as branch currents without combining them in common branches; mixing up assumed directions leading to sign errors.

Final Answer:

False.