For a 4-band resistor with colors blue, gray, red, silver, what is the minimum resistance value when tolerance is applied?

Introduction / Context:
Tolerance bands indicate variability around a nominal resistance. Calculating the minimum and maximum values helps verify whether a measured component is within specification and supports worst-case circuit analysis.

Given Data / Assumptions:

• Bands: blue (6), gray (8), red (multiplier 10^2), silver (tolerance ±10%).
• Standard 4-band reading order is used.

Concept / Approach:
First two colors are significant digits; third is the decade multiplier; fourth is tolerance. After computing nominal resistance, apply the tolerance factor to determine the minimum value: R_min = R_nom * (1 − tolerance).

Step-by-Step Solution:

Verification / Alternative check:
Maximum value check: R_max = 6,800 * 1.10 = 7,480 Ω, which brackets common measurements and confirms the tolerance application.

Why Other Options Are Wrong:

• 612 Ω: Off by a factor of 10; incorrect multiplier/tolerance application.
• 6,800 Ω: This is the nominal, not the minimum.
• 6,460 Ω: Not equal to a 10% decrement of 6,800 Ω.

Common Pitfalls:

• Mistaking silver tolerance for ±5% (that is gold). Silver is ±10% in 4-band codes.
• Arithmetic errors when applying the percentage.

Final Answer:
6,120 Ω