Using the 4-band color code, what is the nominal resistance of a resistor with bands: red, red, orange, gold?

Introduction / Context:The 4-band resistor color code encodes two significant digits, a multiplier, and a tolerance. Mastering this code is essential for quickly identifying components during circuit design, repair, and troubleshooting without relying on printed values.

Given Data / Assumptions:

• Bands: red (1st), red (2nd), orange (multiplier), gold (tolerance).
• Standard 4-band scheme: 1st digit, 2nd digit, multiplier, tolerance.
• Assume E24 series and standard color mapping.

Concept / Approach:Color-to-digit mapping: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9. The multiplier band represents 10^(color value). Tolerance gold = ±5%.

Step-by-Step Solution:

Verification / Alternative check:Compute extremes: 22,000 Ω ± 5% → 22,000 * 0.95 = 20,900 Ω and 22,000 * 1.05 = 23,100 Ω. The nominal center value stays 22,000 Ω, confirming the color interpretation.

Why Other Options Are Wrong:

• 2,200 Ω: Would require a red multiplier (10^2) with digits 22; here the multiplier is orange (10^3).
• 22 Ω or 2.2 Ω: These would need multipliers of 10^0 or 10^-1 respectively, which we do not have.

Common Pitfalls:

• Swapping digit and multiplier bands; always read left-to-right: digit, digit, multiplier.
• Confusing orange (10^3) with red (10^2) or yellow (10^4).

Final Answer:22,000 Ω