$ ext{The value of carbon resistance is } 54 imes 10^3 \, \Omega. ext{ The percentage tolerance is 5\%. What is the colour code sequence of carbon resistance ?}$

Q: $\text{The value of carbon resistance is } 54 \times 10^3 \, \Omega. \text{ The percentage tolerance is 5\%. What is the colour code sequence of carbon resistance ?}$

$\text{The value of carbon resistance is } 54 \times 10^3 \, \Omega. \text{ The percentage tolerance is 5\%. What is the colour code sequence of carbon resistance ?}$

Question

$	ext{The value of carbon resistance is } 54 	imes 10^3 \, \Omega. 	ext{ The percentage tolerance is 5\%. What is the colour code sequence of carbon resistance ?}$

Accepted Answer

To determine the color code sequence for a carbon resistor with a resistance value of $54 \times 10^3 \, \Omega$ and a tolerance of 5%, we need to understand how the resistor color code works. The color code for resistors is a system of colored bands that represent the resistance value and tolerance.

### Explanation for Option 2: Green, Yellow, Orange, Golden bands

1. **Resistance Value: $54 \times 10^3 \, \Omega$**
   - The first two bands represent the first two significant digits of the resistance value.
   - The third band represents the multiplier.
   - The fourth band represents the tolerance.

2. **First Band (Green):**
   - The color green represents the digit 5. This is the first significant digit of the resistance value.

3. **Second Band (Yellow):**
   - The color yellow represents the digit 4. This is the second significant digit of the resistance value.

4. **Third Band (Orange):**
   - The color orange represents the multiplier $10^3$. This matches the multiplier in the resistance value $54 \times 10^3 \, \Omega$.

5. **Fourth Band (Golden):**
   - The color gold represents a tolerance of 5%. This matches the given tolerance in the problem.

Thus, the color code sequence Green, Yellow, Orange, Golden correctly represents a resistance value of $54 \times 10^3 \, \Omega$ with a 5% tolerance.

### Explanation for Why Other Options are Incorrect:

1. **Option 1: Yellow, Green, Orange, Golden bands**
   - Yellow as the first band would represent the digit 4, which does not match the first significant digit of 54, which is 5.

3. **Option 3: Blue, Grey, Yellow, Silver bands**
   - Blue represents the digit 6, and Grey represents the digit 8, which do not match the significant digits 5 and 4 of the resistance value.
   - Yellow as the multiplier represents $10^4$, which does not match the required multiplier $10^3$.

4. **Option 4: Blue, Yellow, Orange, Silver bands**
   - Blue as the first band represents the digit 6, which does not match the first significant digit of 54, which is 5.
   - Silver as the tolerance band represents a 10% tolerance, which does not match the given 5% tolerance.

In conclusion, Option 2 (Green, Yellow, Orange, Golden bands) is the correct color code sequence for a carbon resistor with a resistance value of $54 \times 10^3 \, \Omega$ and a tolerance of 5%.