Assigning branch current directions – Do initial arrow choices matter? Statement: “When assigning branch currents, you need not be concerned with the direction you choose.”

Introduction / Context:
Choosing current directions is the first step in writing KCL and KVL equations. Students often worry about “guessing wrong.” This item clarifies what happens if your initial choice differs from the actual physical current direction.

Given Data / Assumptions:

• Linear lumped circuits analyzed with Kirchhoff’s laws.
• Currents are assigned with arbitrary reference directions for writing equations.
• Solutions can be positive or negative real numbers (or phasors).

Concept / Approach:

The reference direction is arbitrary. If the solved current value is positive, actual current flows in the assumed direction; if negative, the actual current flows opposite to the assumed arrow. The mathematics is consistent regardless of the initial choice. Therefore, you need not worry about “correctness” of the guess—only be consistent in equations.

Step-by-Step Solution:

Verification / Alternative check:

Try a simple series resistor example with a voltage source: assume current right-to-left; you will obtain a negative value, indicating left-to-right flow in reality, but the magnitude is correct.

Why Other Options Are Wrong:

“False” suggests the initial guess must match reality, which is untrue. The statements adding conditions (dc only, planar only) are irrelevant; the property is general across linear circuits.

Common Pitfalls:

Changing assumed directions mid-derivation, which breaks consistency; forgetting to flip voltage polarities when reversing current directions in element equations.

Final Answer:

True.