Tolerance interpretation — resistor value range: A resistor marked 9.9 kΩ, tolerance ±10%, may have an actual value in what range? Evaluate the statement: “between 8.91 kΩ and 10.89 kΩ.”

Introduction / Context:
Resistor tolerances define the permissible deviation from the nominal value at the time of manufacture under specified conditions. Being able to compute tolerance bands quickly is essential when checking component bins, assembling filters, and ensuring bias networks fall within design margins.

Given Data / Assumptions:

• Nominal resistance R_nom = 9.9 kΩ.
• Tolerance = ±10% (i.e., ±0.10 of nominal).
• Room-temperature initial tolerance is implied; long-term drift and temperature coefficient are separate specifications.

Concept / Approach:
For a tolerance of ±T, the minimum and maximum initial values are R_min = R_nom * (1 − T) and R_max = R_nom * (1 + T). With T = 0.10, compute the endpoints and compare to the claim. This is a straightforward percentage calculation based on the nominal value.

Step-by-Step Solution:

Verification / Alternative check:
Express deviation in absolute terms: 10% of 9.9 kΩ is 0.99 kΩ. Bounds are 9.9 − 0.99 = 8.91 kΩ and 9.9 + 0.99 = 10.89 kΩ—same result by a different arithmetic path.

Why Other Options Are Wrong:

• Incorrect: Conflicts with basic percentage math.
• Only for 5% / only at 25 °C / needs power rating: Tolerance is specified independently of power rating; temperature and aging are separate specs.

Common Pitfalls:
Confusing tolerance (initial manufacturing spread) with temperature coefficient (change with temperature) or with derating due to power dissipation. Also, mixing kΩ and Ω in calculations can create decimal errors.

Final Answer:
Correct