Resistor tolerance application — 100 Ω ± 10%: For a resistor rated at 100 Ω with a tolerance of ±10%, determine the minimum and maximum permissible resistance values.

Introduction / Context:
Component tolerances define acceptable manufacturing variation. Being able to compute the allowable resistance range from a rated value and a percentage tolerance is a basic skill in circuit design, parts selection, and worst-case analysis.

Given Data / Assumptions:

• Nominal resistance R_nom = 100 Ω.
• Tolerance = ±10% of the nominal value.
• We assume standard linear tolerance interpretation (no temperature coefficient or aging effects included).

Concept / Approach:
The allowable range is R_nom * (1 − tol) to R_nom * (1 + tol), where tol is expressed as a decimal. Here tol = 0.10. Compute both bounds to find the minimum and maximum permissible resistances that still meet specification.

Step-by-Step Solution:
Compute the decrease: 10% of 100 Ω is 10 Ω.Minimum value: 100 Ω − 10 Ω = 90 Ω.Maximum value: 100 Ω + 10 Ω = 110 Ω.Therefore, the acceptable range is 90 Ω to 110 Ω.

Verification / Alternative check:
Use ratio form: Lower bound = 0.9 * 100 Ω = 90 Ω; Upper bound = 1.1 * 100 Ω = 110 Ω. The results match the direct arithmetic.

Why Other Options Are Wrong:
(a) Upper bound 101 Ω is inconsistent with ±10%. (c) and (d) are far too tight (more like 1–2% tolerance). (e) Invalid because a correct range is available.

Common Pitfalls:
Confusing absolute ohms with percentage points; forgetting to apply the tolerance to both sides; mixing up ±10 Ω with ±10% (coincidentally equal here because the nominal is 100 Ω).

Final Answer:
90 Ω to 110 Ω.