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Difficulty: HardResistors and Potentiometers

A technician servicing a radio receiver needs to verify a fixed carbon-film resistor with four color bands: Brown, Black, Yellow, and Silver. Calculate the nominal resistance and the minimum allowable resistance under its tolerance rating, and complete the statement below.

Answer:The nominal resistance of the resistor is 【100】 kΩ\text{k}\Omega, and its minimum allowable resistance within tolerance is 【90】 kΩ\text{k}\Omega.

Answer

The nominal resistance is 100 kΩ100\text{ k}\Omega and the minimum allowable resistance is 90 kΩ90\text{ k}\Omega.
According to the electronic color code system, Brown represents 1 and Black represents 0, forming the base number 10. The third band, Yellow, represents a multiplier of 10410^4 (1000010{}000), giving a nominal resistance of 10×10000=100000 Ω=100 kΩ10 \times 10{}000 = 100{}000\ \Omega = 100\text{ k}\Omega. The fourth band, Silver, designates a ±10%\pm 10\% tolerance. Ten percent of 100 kΩ100\text{ k}\Omega is 10 kΩ10\text{ k}\Omega, meaning the minimum allowable resistance under tolerance is 100 kΩ−10 kΩ=90 kΩ100\text{ k}\Omega - 10\text{ k}\Omega = 90\text{ k}\Omega (and the maximum is 110 kΩ110\text{ k}\Omega).

Step-by-Step Solution

1
Decode the significant digits from the first two color bands.
Band 1 (Brown) = 11, Band 2 (Black) = 00, giving significant digits 1010.
In standard 4-band EIA color coding, the first two bands represent the first two significant figures of the resistance value.
2
Apply the multiplier from the third color band and convert to kilohms.
Band 3 (Yellow) = multiplier 10410^4 (1000010{}000). Nominal resistance =10×10000=100000 Ω=100 kΩ= 10 \times 10{}000 = 100{}000\ \Omega = 100\text{ k}\Omega.
The third band determines the power of ten by which the significant digits are multiplied.
3
Determine the tolerance percentage from the fourth color band.
Band 4 (Silver) = ±10%\pm 10\% tolerance.
Silver indicates a manufacturing variation of plus or minus ten percent from nominal value.
4
Calculate the minimum allowable resistance limit.
Tolerance amount =100 kΩ×0.10=10 kΩ= 100\text{ k}\Omega \times 0.10 = 10\text{ k}\Omega. Minimum resistance =100 kΩ−10 kΩ=90 kΩ= 100\text{ k}\Omega - 10\text{ k}\Omega = 90\text{ k}\Omega.
Subtracting the tolerance deviation from the nominal value establishes the lower acceptable boundary.

Key Concept

Standard 4-band resistor color decoding and tolerance range calculation
Estimated Time:45s
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Topics

Resistors and Potentiometers

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