A resistor has the following 4 color bands (in this order): yellow, yellow, brown and gold, Its nominal value is:
440 Ω ± 5%
Resistor Color Code Fundamentals
Understanding the resistor color code is crucial for determining the electrical resistance and tolerance of a resistor. Resistors are fundamental passive components in electronic circuits that control current flow. This question asks us to find the nominal value of a resistor given its four color bands: yellow, yellow, brown, and gold.
Resistor Color Band System Explained
The standard 4-band resistor color code system uses a series of colored bands to represent the resistor's value, multiplier, and tolerance. Each band holds a specific meaning:
- First Band: This band indicates the first significant digit of the resistance value.
- Second Band: This band indicates the second significant digit of the resistance value.
- Third Band (Multiplier): This band represents the power of ten by which the combined value of the first two digits is multiplied.
- Fourth Band (Tolerance): This band specifies the permissible percentage deviation (accuracy) of the actual resistance value from its nominal value.
Here is a common table summarizing the resistor color codes:
| Color | Digit | Multiplier | Tolerance |
|---|---|---|---|
| Black | 0 | \(10^0\) | |
| Brown | 1 | \(10^1\) | \(\pm 1\%\) |
| Red | 2 | \(10^2\) | \(\pm 2\%\) |
| Orange | 3 | \(10^3\) | |
| Yellow | 4 | \(10^4\) | |
| Green | 5 | \(10^5\) | \(\pm 0.5\%\) |
| Blue | 6 | \(10^6\) | \(\pm 0.25\%\) |
| Violet | 7 | \(10^7\) | \(\pm 0.1\%\) |
| Gray | 8 | \(10^8\) | \(\pm 0.05\%\) |
| White | 9 | \(10^9\) | |
| Gold | \(10^{-1}\) | \(\pm 5\%\) | |
| Silver | \(10^{-2}\) | \(\pm 10\%\) | |
| None | \(\pm 20\%\) |
Resistor Color Band Analysis
Let's analyze each color band of the given resistor: yellow, yellow, brown, and gold, using the resistor color code system:
- First Band (Yellow): From the color code table, yellow corresponds to the digit 4.
- Second Band (Yellow): Again, yellow corresponds to the digit 4.
- Third Band (Brown - Multiplier): Brown signifies a multiplier of \(10^1\) (which is 10).
- Fourth Band (Gold - Tolerance): Gold indicates a tolerance of \(\pm 5\%\).
Nominal Value Calculation
To find the nominal value of the resistor, we combine the digits from the first two bands to form a two-digit number, then multiply it by the multiplier value from the third band. Finally, we attach the tolerance percentage from the fourth band.
The resistance value is calculated using the formula:
Resistance \( = (\text{First Digit})(\text{Second Digit}) \times \text{Multiplier} \pm \text{Tolerance}\)
Substituting the values we obtained from the color band analysis:
Resistance \( = 44 \times 10^1 \, \Omega \pm 5\%\)
Resistance \( = 44 \times 10 \, \Omega \pm 5\%\)
Resistance \( = 440 \, \Omega \pm 5\%\)
Final Resistor Value
Thus, based on the color bands yellow, yellow, brown, and gold, the nominal value of the resistor is \(440 \, \Omega \pm 5\%\). This means the actual resistance of the component should be within 5% of 440 ohms, ranging from \(440 - (0.05 \times 440) = 440 - 22 = 418 \, \Omega\) to \(440 + (0.05 \times 440) = 440 + 22 = 462 \, \Omega\).
Important Questions from Resistance and Resistivity
Which of the following metals has the lowest electrical resistivity?
A uniform wire of resistance 9Ω is bent in the form of an equilateral triangle. Find the effective resistance across a side of the triangle.
The value of carbon resistance is 54 × 103 Ω. The percentage tolerance is 5%. What is the colour code sequence of carbon resistance?
Which of the following relations are wrong?
I. The specific conductance is given by the relation \(k = \frac{1}{R}\left( {l/A} \right)\)
II. The equivalent conducting is given by the relation \(\lambda = \frac{{100\;K}}{C}\)
III. The specific resistance is given by the relation \(\rho = \frac{{Rl}}{A}\)
A current is flowing through a metallic wire. If the wire is heated, which quantities change?
