A 10,000-9 resistor has a tolerance of 5%. What are the minimum and maximum values of this resistor?
The correct answer and explanation is :
A 10,000-ohm (or 10kΩ) resistor with a 5% tolerance means its actual resistance can vary by ±5% of its nominal value.
Calculations:
- Nominal Value = 10,000 ohms
- Tolerance = 5% of 10,000 = 0.05 × 10,000 = 500 ohms
So:
- Minimum value = 10,000 – 500 = 9,500 ohms
- Maximum value = 10,000 + 500 = 10,500 ohms
Explanation (Approx. 300 words):
Resistors are fundamental electronic components used to limit current, divide voltage, and manage signal levels in circuits. Each resistor has a nominal value—the intended resistance—and a tolerance, which indicates how much the actual resistance might vary from the nominal.
In this case, we are given a 10,000-ohm resistor with a 5% tolerance. Tolerance represents the allowable deviation due to manufacturing imperfections. The ±5% means the actual resistance could be as much as 5% lower or higher than 10,000 ohms.
To calculate this, we take 5% of 10,000:
10,000 × 0.05 = 500
Then subtract and add this from the nominal value to find the minimum and maximum possible resistance:
- Minimum: 10,000 – 500 = 9,500 ohms
- Maximum: 10,000 + 500 = 10,500 ohms
This range (9,500 to 10,500 ohms) is important in circuit design, especially where precise resistance is required. For example, in timing circuits or voltage dividers, too much deviation can alter performance. Therefore, understanding and accounting for tolerance helps engineers choose the right resistor for the job.
A 5% tolerance is considered moderate and is common in general-purpose resistors. For higher precision, resistors with 1% or even 0.1% tolerances are used, although they tend to be more expensive.
Knowing how to interpret tolerance ensures that you design circuits that function correctly despite real-world manufacturing variations. Always factor in tolerance when calculating expected outcomes in electronic designs.