Identical resistors in parallel — equivalent resistance rule: For like-value resistors connected in parallel, is the equivalent resistance equal to the individual resistor value multiplied by the number of resistors, or does it follow a different relationship?

Introduction / Context:Memorizing the right shortcut for identical components saves time. In series, resistances add. In parallel, conductances add, giving a very different shortcut for identical resistors that many students initially mix up.

Given Data / Assumptions:

• n identical resistors, each of value R, connected in parallel.
• Ideal components; parasitics neglected.
• We compare with an incorrect series-like rule.

Concept / Approach:For identical parallel resistors: 1/R_eq = n * (1/R) so R_eq = R / n. The false statement claims R_eq = R * n, which is the series rule. Therefore, in parallel, the more identical branches you add, the smaller the equivalent resistance becomes, not larger.

Step-by-Step Solution:

Verification / Alternative check:Example with R = 120 Ω and n = 3: R_eq = 120/3 = 40 Ω, clearly not 360 Ω. Bench tests confirm decreasing R_eq with added parallel branches.

Why Other Options Are Wrong:

• Correct: Not correct; that is the series behavior.
• True only for series connections: This option is closer to the truth about series, but the given statement concerns parallel and remains incorrect.
• True when resistors are wirewound: Construction type does not invert the rule.
• True for temperature-compensated parts: Compensation does not convert parallel math to series math.

Common Pitfalls:Applying series addition to parallel networks; failing to switch to conductance thinking for parallel combinations.

Final Answer:Incorrect