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Difficulty: HardResistors and Potentiometers

A quality assurance technician is inspecting a four-band carbon-composition resistor with the color bands in order: Yellow, Violet, Red, and Silver. To meet quality standards, the resistor must operate within its specified manufacturer tolerance. What is the minimum acceptable resistance value, in ohms (Ω\Omega), for this component?

Answer: 4230 Ω

Answer

The minimum acceptable resistance value is 4230 Ω4230\text{ }\Omega.
The first two bands (Yellow = 4, Violet = 7) establish the significant figures of 47. The third band (Red) indicates a multiplier of 102=10010^2 = 100, giving a nominal rating of 4700 Ω4700\text{ }\Omega. The fourth band (Silver) specifies a ±10%\pm 10\% tolerance. Subtracting 10%10\% of 4700 Ω4700\text{ }\Omega (470 Ω470\text{ }\Omega) from the nominal rating gives the minimum allowable threshold of 4230 Ω4230\text{ }\Omega.

Step-by-Step Solution

1
Decode the first two color bands to obtain the significant numerical digits.
Yellow represents the digit 44, and Violet represents the digit 77, forming the base value of 4747.
Standard EIA four-band resistor color coding assigns the first two bands as significant figures of the resistance value.
2
Multiply the base significant figures by the power of ten indicated by the third band.
Red indicates a multiplier of 10210^2 (100100), so the nominal resistance is 47×100=4700 Ω47 \times 100 = 4700\text{ }\Omega.
The third band functions as the decimal multiplier for four-band fixed resistors.
3
Identify the tolerance rating from the fourth band.
Silver represents a tolerance of ±10%\pm 10\%.
The fourth band specifies the allowable deviation range from the nominal resistance value.
4
Calculate the lower allowable resistance threshold.
Tolerance amount is 4700 Ω×0.10=470 Ω4700\text{ }\Omega \times 0.10 = 470\text{ }\Omega. Minimum acceptable value is 4700 Ω−470 Ω=4230 Ω4700\text{ }\Omega - 470\text{ }\Omega = 4230\text{ }\Omega.
The minimum acceptable value represents the nominal value minus the total tolerance deviation.

Key Concept

Four-Band Resistor Color Code Decoding and Tolerance Range Calculation

Alternative Method

Multiply the nominal resistance directly by the minimum percentage factor: 4700 Ω×(1.00−0.10)=4700 Ω×0.90=4230 Ω4700\text{ }\Omega \times (1.00 - 0.10) = 4700\text{ }\Omega \times 0.90 = 4230\text{ }\Omega.
Estimated Time:45s
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Topics

Resistors and Potentiometers

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