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Difficulty: MediumResistors and Potentiometers

A carbon-film resistor has four distinct color bands in sequence: Red, Violet, Orange, and Gold. What is the minimum acceptable resistance of this resistor in kilohms (kΩ\text{k}\Omega) based on its color code and tolerance rating?

Answer: 25.65 kΩ

Answer

The minimum acceptable resistance is 25.65 kilohms (kΩ).
According to the standard EIA 4-band resistor color code, Red = 2, Violet = 7, Orange = multiplier 10^3 (1,000), and Gold = ±5% tolerance. The nominal resistance is 27 × 1,000 Ω = 27,000 Ω = 27 kΩ. The allowable variation is 5% of 27 kΩ, which is 1.35 kΩ. Subtracting this from the nominal value gives a minimum acceptable resistance of 27 kΩ - 1.35 kΩ = 25.65 kΩ.

Step-by-Step Solution

1
Identify the significant digits from the first two color bands.
Red represents 2 and Violet represents 7, forming the base number 27.
In standard 4-band resistor color codes, the first two bands represent the first two significant figures.
2
Apply the decimal multiplier from the third color band and convert to kilohms.
Orange represents a multiplier of 10^3 (1,000), giving a nominal value of 27 × 1,000 Ω = 27,000 Ω = 27 kΩ.
The third band indicates the power of ten by which the significant digits are multiplied.
3
Calculate the tolerance value based on the fourth band.
Gold indicates a ±5% tolerance. 5% of 27 kΩ is 0.05 × 27 kΩ = 1.35 kΩ.
The fourth band specifies the allowable percentage deviation from the nominal resistance value.
4
Compute the lower limit of the allowable resistance range.
27 kΩ - 1.35 kΩ = 25.65 kΩ.
The minimum acceptable value is obtained by subtracting the allowable tolerance from the nominal resistance.

Key Concept

Four-Band Resistor Color Code and Tolerance Calculation

Alternative Method

Calculate the minimum multiplier directly: 27 kΩ × (1 - 0.05) = 27 kΩ × 0.95 = 25.65 kΩ.
Estimated Time:45s
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Topics

Resistors and Potentiometers

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