Dependence of total series resistance — does the equivalent resistance of a series circuit “always depend only on the highest-value resistor” present in that circuit?

Introduction / Context:
Designers sometimes use rules of thumb when one element dominates. However, rigorous analysis of series circuits requires summation of all resistances. This item probes whether you know that every series element contributes to the total, not just the largest one, even if approximation may be acceptable in special contexts.

Given Data / Assumptions:

• Series chain of N resistors.
• Ideal lumped model.
• No element is bypassed or shorted.

Concept / Approach:
The series formula is exact: R_total = R1 + R2 + … + Rn. While a large resistor may dominate numerically, the exact total still includes the smaller ones. Approximations (e.g., neglecting 1 Ω alongside 10 kΩ) are engineering conveniences, not the governing law. Therefore, the claim that total resistance “always depends only” on the largest value is false.

Step-by-Step Solution:

Verification / Alternative check:
Example: 9,900 Ω + 100 Ω = 10,000 Ω. The 100 Ω contributes 1% and cannot be ignored for precise work. Bench measurements reflect the full sum within tolerances.

Why Other Options Are Wrong:

• Correct: Misstates the series rule.
• Correct only if >10×: Even then, the smaller parts still add; the claim “only” remains wrong.
• Temperature stability: Unrelated to the additive rule; it affects value drift, not whether each resistor counts.

Common Pitfalls:
Mistaking a convenient approximation for an exact law; overlooking that billing, power, and tolerance stacks rely on the exact sum, not a dominant-single-value simplification.

Final Answer:
Incorrect — the total series resistance is the sum of all resistors, not merely the largest one.