Repaired stem — total resistance claim: Consider three equal resistors of 1.44 kΩ each connected in parallel across an ideal source. A student claims, “The total resistance is 480 Ω.” Decide whether this claim is correct.

Introduction / Context:
This question was incomplete originally (“The total resistance is 480 Ω.”). Applying the Recovery-First Policy, we minimally repair the stem to a standard parallel-resistor scenario. It now evaluates whether a common rule for identical resistors in parallel has been applied correctly. Such checks are routine in lab pre-calculations and troubleshooting.

Given Data / Assumptions:

• Three identical resistors, each R = 1.44 kΩ (i.e., 1440 Ω).
• Connected in parallel across the same two nodes.
• Ideal conditions; ignore wire resistance and tolerances.

Concept / Approach:
For n identical resistors in parallel, R_eq = R / n. With R = 1440 Ω and n = 3, the equivalent resistance should be 1440 / 3 = 480 Ω. This simple proportional rule arises because the total conductance is n/R, and the inverse gives the equivalent resistance decreasing with added branches.

Step-by-Step Solution:

Verification / Alternative check:
Compute using pairwise first: two 1.44 kΩ in parallel give 720 Ω. Then 720 Ω in parallel with another 1.44 kΩ yields (720 * 1440) / (720 + 1440) = (1,036,800) / 2160 = 480 Ω, confirming the result by a different route.

Why Other Options Are Wrong:

• Incorrect: The calculation shows the claim is correct.
• True only if one branch is open: An open would leave two branches, giving 720 Ω, not 480 Ω.
• True only at DC, not AC: For purely resistive loads, DC vs AC does not change the equivalent resistance.
• Cannot be decided without the source current: Equivalent resistance depends on component values and topology, not the source current.

Common Pitfalls:
Mixing up series (R_eq = nR) with parallel (R_eq = R/n) for identical resistors; forgetting to convert kΩ to Ω before arithmetic; skipping a quick pairwise check that can catch arithmetic slips.

Final Answer:
Correct