The resistance value of a carbon resistor having red, violet, orange and gold colour band is
27 kΩ ± 5%
This solution explains how to determine the resistance value of a carbon resistor using its color bands.
Understanding Carbon Resistor Color Codes
Carbon resistors use colored bands to indicate their resistance value and tolerance. Each color corresponds to a specific number or multiplier. The standard sequence for a four-band resistor is:
- Band 1: First significant digit
- Band 2: Second significant digit
- Band 3: Multiplier (power of 10)
- Band 4: Tolerance
Resistor Color Code Chart
| Color | Band 1 (Digit) | Band 2 (Digit) | Band 3 (Multiplier) | Band 4 (Tolerance) |
|---|---|---|---|---|
| Black | 0 | 0 | $10^0$ (1) | - |
| Brown | 1 | 1 | $10^1$ (10) | ±1% |
| Red | 2 | 2 | $10^2$ (100) | ±2% |
| Orange | 3 | 3 | $10^3$ (1k) | - |
| Yellow | 4 | 4 | $10^4$ (10k) | - |
| Green | 5 | 5 | $10^5$ (100k) | ±0.5% |
| Blue | 6 | 6 | $10^6$ (1M) | ±0.25% |
| Violet | 7 | 7 | $10^7$ (10M) | ±0.1% |
| Gray | 8 | 8 | $10^8$ (100M) | ±0.05% |
| White | 9 | 9 | $10^9$ (1G) | - |
| Gold | - | - | $10^{-1}$ (0.1) | ±5% |
| Silver | - | - | $10^{-2}$ (0.01) | ±10% |
Calculating the Resistance Value
The given resistor has the following color bands:
- Band 1: Red
- Band 2: Violet
- Band 3: Orange
- Band 4: Gold
Using the color code chart:
- Red (Band 1) corresponds to the digit 2.
- Violet (Band 2) corresponds to the digit 7.
- Orange (Band 3) corresponds to the multiplier $10^3$ (kilo-ohms).
- Gold (Band 4) corresponds to a tolerance of ±5%.
To find the resistance value, combine the first two digits and multiply by the multiplier:
Resistance = (Digit 1)(Digit 2) × Multiplier
Resistance = (2)(7) × $10^3 \Omega$
Resistance = $27 \times 10^3 \Omega$
Resistance = $27 \text{ k}\Omega$
The tolerance is ±5%.
Final Resistance and Tolerance
Therefore, the resistance value of the carbon resistor is $27 \text{ k}\Omega \pm 5\%$. This matches the second option provided.
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