Question

The four bands of a colour coded resistor are of the colours gray, red, gold and gold. The value of the resistance of the resistor is

• A. 82Ω ± 10%
• B. 8.2Ω ± 5%
• C. 82Ω ± 5%
• D. 5.2Ω ± 5%

Answer 1

The Correct Option is B

Step 1: Identify the color code clearly:

• 1st Band: Gray (Digit: 8)
• 2nd Band: Red (Digit: 2)
• 3rd Band (Multiplier): Gold (\(10^{-1}\))
• 4th Band (Tolerance): Gold (\(\pm 5\%\))

Step 2: Calculate the resistance:

Resistance is calculated as follows:

\[ R = (1^{st}\,digit)(2^{nd}\,digit) \times (\text{Multiplier}) \]

Substitute values from the given color code:

\[ R = 82 \times 10^{-1} = 8.2\,\Omega \]

Step 3: Include tolerance:

The 4th band (gold) indicates tolerance of ±5%.

Therefore, the resistor's value is:

\[ 8.2\,\Omega \pm 5\% \]

Quick Tip: Remember standard multipliers:
Gold: \(10^{-1}\), Silver: \(10^{-2}\), Black: \(10^{0}\), Brown: \(10^{1}\), Red: \(10^{2}\), etc.

Final Answer: Option (B) 8.2Ω ± 5%

Answer 2

1. Identify the Color Bands and their Order:
The colors are given in order: Gray, Red, Gold, Gold.

• Band 1: Gray
• Band 2: Red
• Band 3: Gold (Multiplier)
• Band 4: Gold (Tolerance)

 

2. Recall the Resistor Color Code Standard (4-Band):
 

• Band 1: First significant digit.
• Band 2: Second significant digit.
• Band 3: Multiplier (power of 10).
• Band 4: Tolerance.

 

3. Determine the Value for Each Band using the Standard Code:

• Band 1 (Gray): Digit 8
• Band 2 (Red): Digit 2
• Band 3 (Gold): Multiplier \(10^{-1}\) (or 0.1)
• Band 4 (Gold): Tolerance ±5%

 

4. Calculate the Resistance Value:
Combine the digits and the multiplier: \[ \text{Resistance} = (\text{Digit 1})(\text{Digit 2}) \times \text{Multiplier} \] \[ \text{Resistance} = 82 \times 10^{-1} \, \Omega = 82 \times 0.1 \, \Omega = 8.2 \, \Omega \]

5. Add the Tolerance:
Include the tolerance from the fourth band: \[ \text{Resistance} = 8.2 \, \Omega \pm 5\% \]

Answer: The value of the resistance is \(8.2\Omega \pm 5\%\). This corresponds to option (B).