A 33 kΩ resistor with ±20% tolerance is measured with an ohmmeter. Which reading is within the acceptable tolerance band?

Introduction / Context:
Tolerance defines the acceptable spread around a resistor’s nominal value. Checking whether a measured resistance falls inside the permissible band prevents unnecessary replacements and ensures circuits perform to design targets.

Given Data / Assumptions:

• Nominal resistance R_nom = 33 kΩ = 33,000 Ω.
• Tolerance = ±20%.
• Measured candidates: 26,400 Ω; 24,183 Ω; 6,600 Ω; 39,970 Ω.

Concept / Approach:
The acceptable range is computed as R_nom * (1 ± tolerance). For ±20%, limits are 0.8 * R_nom and 1.2 * R_nom. Any measurement within [lower, upper] is acceptable.

Step-by-Step Solution:
Compute lower limit: R_low = 0.8 * 33,000 = 26,400 Ω.Compute upper limit: R_high = 1.2 * 33,000 = 39,600 Ω.Compare readings: 26,400 Ω (on the lower limit) → acceptable; 24,183 Ω (below lower limit) → unacceptable; 6,600 Ω (far below) → unacceptable; 39,970 Ω (above upper limit) → unacceptable.

Verification / Alternative check:
Express deviations in percent relative to 33,000 Ω: 26,400 Ω is −20%; 39,970 Ω is +21.1%, exceeding the +20% cap. The band is inclusive of the endpoints, so 26,400 Ω qualifies.

Why Other Options Are Wrong:

• 24,183 Ω: More than −20% deviation; out of tolerance.
• 6,600 Ω: Extremely out of tolerance (−80%).
• 39,970 Ω: Greater than +20% deviation; out of tolerance.

Common Pitfalls:

• Mistaking kΩ and Ω during calculation; always convert to the same unit.
• Rounding the limits incorrectly; compute limits first, then compare.

Final Answer:
26400 ohms