# A Simple Procedure for Creating Any Resistance Using Standard Resistors

## Have you ever needed an unusual, non-standard resistance value for the project you are building? This article will provide you with a simple series of steps to build the resistance you need from a collection of resistors.

You could have a whole box of E12 series resistors, as shown in Figure 1, but still not be able to get a value close enough to your desired resistance. If you need a 50 kΩ resistor, the closest you will get is 47 kΩ. Sure, that is within 10%, but maybe that isn’t good enough for your application. What are you going to do?

**Figure 1.** The E12 series resistors with their color codes. Image used courtesy of EEPower

**Figure 1.**The E12 series resistors with their color codes. Image used courtesy of EEPower

This article will introduce a simple step-by-step procedure for using multiple resistors in series or parallel to fine-tune your resistance value. We will even provide the equations and some examples to make it easy for you.

### A Quick Tolerance Discussion

One rule to remember is that ANY combination of resistors with a specific tolerance also has the same tolerance. So, if you are using E12 series resistors with a ±10% tolerance, your final combination of resistors will also have a ±10% tolerance.

In all of our calculations below, remember that your final result will always be limited by the tolerance of the resistors you choose. Of course, you can always measure your resistors with an ohmmeter to improve the calculations below and your results.

### Choosing Series or Parallel Resistors?

The first step in the process is choosing whether to use resistors in series or parallel. The selection process is as easy as answering a simple question:

**Question**: Is the nearest standard value resistor greater than the desired resistance?

- No: build a network of series resistors.
- Yes: build a network of parallel resistors.

Figure 2 demonstrates this process as a decision tree.

**Figure 2**. The selection process for series or parallel resistors

**Figure 2**. The selection process for series or parallel resistors

### Solving for the Series Resistor Values

The math on this one is really easy since the total series resistance is simply the sum of the resistances:

$$R_S = R_1 + R_2$$

*Equation 1.*

*Equation 1.*

Let’s assume our desired resistance is 50 kΩ. The closest E12 resistor is 47 kΩ. We can solve for *R _{2}* using simple subtraction:

$$R_2 = R_S - R_1 = 50000 - 47000 = 3000 \text{ } \Omega$$

*Equation 2.*

*Equation 2.*

We have two E12 resistors to choose from here: 2700 Ω or 3300 Ω. They would both provide a result that is only 300 Ω from our target resistance for an error of only -0.6% (with a ±10% tolerance for the E12 resistors, of course).

If we want to get closer, we can select the E12 value lower than desired and repeat the process to calculate a third series resistance:

$$R_3 = R_S - R_1 - R_2 = 50000 - 47000 - 2700 = 300 \text{ } \Omega$$

*Equation 3.*

*Equation 3.*

The closest standard resistor value is 270 Ω. This gives us a final series resistance of:

$$R_S = 47000 + 2700 +270 = 49970 \text{ } \Omega$$

*Equation 4.*

*Equation 4.*

Repeating the process three times probably only makes sense if you measure your resistors with an ohmmeter and can eliminate the ±10% variation.

### Solving for the Parallel Resistor Values

Let’s assume our target is 5200 Ω. Using the E12 resistors, the closest we can get is 5600 Ω. Since this is greater than our target resistance, we will use a parallel set of resistors.

Now, here is a trick you don’t find in most textbooks. They give the total resistance formula for parallel resistors, *R _{1}* and

*R*as:

_{2}$$R_P = \frac{R_1 \times R_2}{R_1 + R_2}$$.

*Equation 5.*

*Equation 5.*

Since we know *R _{P}* and

*R*, we can solve for

_{1}*R*:

_{2}$$R_2 = \frac{R_1 \times R_P}{R_1 - R_P}$$

*Equation 6.*

*Equation 6.*

Note the minus sign in Equation 6.

#### Using Two Parallel Resistors

Applying Equation 6, we can solve for our second resistor:

$$R_2 = \frac{5600 \times 5200}{5600 - 5200} = 72800 \text{ } \Omega = 72.8 \text{ k} \Omega$$

*Equation 7.*

*Equation 7.*

The closest we can get to 72.8 kΩ with E12 resistors is 68.0 kΩ. Plugging this actual resistor value back into Equation 5, we can find our actual parallel resistance value.

$$R_P = \frac{5600 \times 68000}{5600 + 68000} = 5174 \text{ } \Omega$$.

*Equation 8.*

*Equation 8.*

This result is only -0.50% smaller than our target, which is good enough in most cases. But don’t forget that we will still have a ±10% variation around this value due to the tolerances of our resistors.

#### Using Three Parallel Resistors

If we want to get even closer to our target of 5200 Ω, we could have chosen the next larger E12 series resistor for *R _{2}*; in this case, 82.0 kΩ.

$$R_P = \frac{5600 \times 82000}{5600 + 82000} = 5242 \text{ } \Omega$$.

*Equation 9.*

*Equation 9.*

Then, we repeat the parallel resistor calculations using this value for *R _{1}* in Equation 2:

$$R_3 = \frac{5242 \times 5200}{5242 - 5200} = 649010 \text{ } \Omega = 649 \text{ k} \Omega$$

*Equation 10.*

*Equation 10.*

The closest E12 resistor is 680 kΩ, so we will use that. Now, our total parallel resistance is:

$$R_P = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}} = \frac{1}{\frac{1}{5600}+\frac{1}{82000}+\frac{1}{680000}} = 5202 \text{ } \Omega$$

*Equation 11.*

*Equation 11.*

Our error has been reduced to 0.04% (±10%, of course).

### Another Helpful Hint About Resistor Selection

Before we leave, here is one more helpful hint. To make up an exact value from two resistors (within the tolerance of the parts), it’s best to choose very different values, as we have done using this process.

Why? Well, let’s go back to our original example of a target of 50 kΩ. We could have placed a 22 kΩ resistor in series with a 27 kΩ resistor and been pretty close (49 kΩ). Our circuit calculations may have led us to believe that 50 kΩ was ideal. Unfortunately, reality is sometimes a little different.

Imagine we now decide that we need to increase our resistance but only want to replace one resistor. The smallest change we can make is replacing that 22 kΩ resistor with another 27 kΩ resistor. A change of over 10% from 49 kΩ to 54 kΩ.

However, if we had used our 47 kΩ and 2700 Ω resistors as calculated in our first example above, we could now make very subtle resistance changes. We could replace the 2700 Ω resistor with a 3300 Ω resistor. Our total resistance changes only 1.2%, a much more subtle change than 10%!

As you can see, following the process outlined in this article provides an easy solution and a better methodology for additional circuit fine-tuning if needed.

*Editor’s Note: Dale Wilson co-authored this article*

*Featured background image used courtesy of Adobe*

3 CommentsInstead of using several E12 series in combination, just use a single 49.9kΩ from E96 series. It’s smaller, less expensive, and easier to replace a single part if a different resistance is needed later on.