For a 4-band resistor with colors brown, red, yellow, gold, what is the maximum resistance value when tolerance is included?

Introduction / Context:
Component tolerances define allowable variation from nominal values. Reading the color code and then applying tolerance limits helps you evaluate worst-case circuit performance and ensure designs remain within specification.

Given Data / Assumptions:

• Bands: brown (1st), red (2nd), yellow (multiplier), gold (tolerance).
• Gold tolerance = ±5%.

Concept / Approach:
Digits: brown = 1, red = 2 → '12'. Multiplier yellow = 10^4. Nominal value R_nom = 12 * 10^4 = 120,000 Ω. Maximum value R_max = R_nom * (1 + tolerance).

Step-by-Step Solution:

Verification / Alternative check:
Minimum would be 120,000 * 0.95 = 114,000 Ω. This brackets the tolerance band and confirms the calculation of the maximum value as 126,000 Ω.

Why Other Options Are Wrong:

• 126,600 Ω: Incorrect arithmetic for +5% of 120,000 Ω (should be +6,000 Ω, not +6,600 Ω).
• 114,000 Ω: That is the minimum value (−5%), not the maximum.
• 132,000 Ω: Would correspond to +10%, not +5%.

Common Pitfalls:

• Mistaking yellow (10^4) for orange (10^3), which would change the nominal value completely.
• Applying tolerance to the color digits rather than to the computed nominal resistance.

Final Answer:
126,000 Ω