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Difficulty: MediumResistors and Potentiometers

During a quality control inspection, a technician measures a resistor marked with the color bands Brown, Gray, Red, and Gold. For this resistor to meet its manufactured specification, what is the acceptable range of measured resistance?

  1. A
    171 Ω to 189 Ω171\ \Omega\text{ to } 189\ \Omega
  2. 1,710 Ω to 1,890 Ω1,710\ \Omega\text{ to } 1,890\ \OmegaAnswer
  3. C
    1,620 Ω to 1,980 Ω1,620\ \Omega\text{ to } 1,980\ \Omega
  4. D
    172.9 Ω to 191.1 Ω172.9\ \Omega\text{ to } 191.1\ \Omega

Answer

1,710 Ω to 1,890 Ω1,710\ \Omega\text{ to } 1,890\ \Omega
A four-band resistor with colors Brown (1), Gray (8), Red (102=10010^2 = 100), and Gold (±5%\pm 5\%) has a nominal value of 1,800 Ω1,800\ \Omega. With a ±5%\pm 5\% tolerance, the allowable variance is 1,800×0.05=90 Ω1,800 \times 0.05 = 90\ \Omega. Subtracting and adding 90 Ω90\ \Omega gives the acceptable operational range of 1,710 Ω1,710\ \Omega to 1,890 Ω1,890\ \Omega.

Step-by-Step Solution

1
Determine the nominal resistance from the first three color bands.
Brown = 1, Gray = 8, Red = multiplier of 10210^2 (100100). The nominal value is 18×100=1,800 Ω18 \times 100 = 1,800\ \Omega.
In a standard four-band resistor, the first two bands represent significant digits and the third band represents the power-of-ten multiplier.
2
Identify the tolerance percentage from the fourth band.
Gold band = ±5%\pm 5\%.
The fourth band specifies the manufacturing tolerance rating.
3
Calculate the acceptable tolerance deviation in ohms.
1,800 Ω×0.05=90 Ω1,800\ \Omega \times 0.05 = 90\ \Omega.
The allowable deviation is found by multiplying the nominal resistance by the tolerance percentage.
4
Calculate the minimum and maximum acceptable resistance boundaries.
Minimum: 1,800−90=1,710 Ω1,800 - 90 = 1,710\ \Omega; Maximum: 1,800+90=1,890 Ω1,800 + 90 = 1,890\ \Omega.
The acceptable range spans from nominal minus tolerance to nominal plus tolerance.

Key Concept

Decoding four-band resistor color codes and calculating nominal tolerance boundaries
Estimated Time:45s
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Topics

Resistors and Potentiometers

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