Many beginners in circuit design might find resistor values puzzling. Why are standard resistor values not round numbers? For example, why are they often 4.7kΩ or 5.1kΩ instead of 5kΩ?

This is because resistors are designed and manufactured using an exponential distribution system, adhering to the standard resistor value system defined by the International Electrotechnical Commission (IEC). This system includes various series of resistor values, such as the E3, E6, E12, E24, E48, E96, and E192 series.

For example:

The E6 series has a ratio of approximately 10^(1/6) ≈ 1.5

The E12 series has a ratio of approximately 10^(1/12) ≈ 1.21

In actual production, resistors cannot be manufactured with perfect accuracy; there is always some tolerance. For instance, a 100Ω resistor with a 1% tolerance is acceptable if its value is between 99Ω and 101Ω. Therefore, the American Electronics Industry Association defined a standard resistor value system in the last century.

To understand this standard resistor value system, let's take resistors with a 10% tolerance as an example. If we have already produced a 100Ω resistor, there's no need to make a 105Ω resistor because the 100Ω resistor's tolerance range is 90Ω to 110Ω.

Similarly, the next resistor we need to produce should be 120Ω, as the 120Ω resistor's tolerance range is 110Ω to 130Ω. Thus, for resistors ranging from 100Ω to 1000Ω, we only need to produce values like 100Ω, 120Ω, 150Ω, 180Ω, 220Ω, 270Ω, 330Ω, etc., instead of making resistors for every possible value. By reducing the variety of resistor values on the production line, the manufacturing cost of resistors is lowered.

In reality, many value designs follow an exponential relationship. For example, the Chinese currency has denominations of 1 RMB, 2 RMB, 5 RMB, and 10 RMB, but not 3 RMB or 4 RMB. This is because using 1, 2, and 5 allows for convenient combinations to make any value between 1 and 10, thus reducing the number of denominations needed while still being easy to use. Similarly, pen tip sizes often come in 0.25, 0.35, 0.5, and 0.7.

Moreover, the exponential distribution of resistor values allows users to find suitable resistor values within the tolerance range. If resistor values follow an exponential distribution with a defined percentage tolerance, then the resulting values in mathematical operations (addition, subtraction, multiplication, division) will also have a defined tolerance.