Resistor Color Code Fundamentals

The color code system is used to identify the resistance value, tolerance, and sometimes the temperature coefficient of a resistor. Resistors typically have 4, 5, or 6 color bands. For the given problem, we assume a 4-band resistor as it's common for indicating resistance and tolerance.

Here's how the color bands are interpreted for a 4-band resistor:

• First Band: Represents the first significant digit of the resistance value.
• Second Band: Represents the second significant digit of the resistance value.
• Third Band: Represents the decimal multiplier. This indicates how many zeros follow the significant digits.
• Fourth Band: Represents the tolerance of the resistor, indicating the permissible variation from its stated resistance value.

Understanding the standard color code values is crucial. Here is a table summarizing the common color code values for digits, multipliers, and tolerance:

Decoding 47 Ω Resistor Color

We need to find the color code for a 47 Ω resistor with 1% tolerance. Let's break down the value:

Resistance Value: 47 Ω

• First Digit (4): According to the color code table, the digit '4' corresponds to the color Yellow. This will be our first band.
• Second Digit (7): The digit '7' corresponds to the color Violet. This will be our second band.
• Multiplier: To get 47 Ω from the digits 4 and 7, we need a multiplier of \(10^0\), which is 1. The color corresponding to a multiplier of \(10^0\) is Black. This will be our third band.

Tolerance: 1%

• The color corresponding to a tolerance of \(\pm 1\%\) is Brown. This will be our fourth band.

Therefore, the color code for a 47 Ω resistor with 1% tolerance is Yellow, Violet, Black, Brown.

Option Analysis

Let's evaluate the given options based on our derived color code:

• 1. yellow, blue, black, black:
  • Yellow = 4
  • Blue = 6
  • Black = \(10^0\) (Multiplier)
  • Black (Tolerance) = This is not a standard tolerance color for 4-band resistors, often implies 20% or not specified.
  • Resulting value: \(46 \times 10^0 = 46\) Ω. Tolerance is not 1%. This option is incorrect.
• 2. yellow, green, brown, gold:
  • Yellow = 4
  • Green = 5
  • Brown = \(10^1\) (Multiplier)
  • Gold = \(\pm 5\%\) (Tolerance)
  • Resulting value: \(45 \times 10^1 = 450\) Ω. Tolerance is 5%. This option is incorrect.
• 3. yellow, blue, brown, silver:
  • Yellow = 4
  • Blue = 6
  • Brown = \(10^1\) (Multiplier)
  • Silver = \(\pm 10\%\) (Tolerance)
  • Resulting value: \(46 \times 10^1 = 460\) Ω. Tolerance is 10%. This option is incorrect.
• 4. yellow, violet, black, brown:
  • Yellow = 4
  • Violet = 7
  • Black = \(10^0\) (Multiplier)
  • Brown = \(\pm 1\%\) (Tolerance)
  • Resulting value: \(47 \times 10^0 = 47\) Ω. Tolerance is 1%. This option matches our derived color code perfectly.

Based on the detailed analysis, the color code yellow, violet, black, brown correctly represents a 47 Ω resistor with 1% tolerance.