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Voltage Dividers Explained: Harnessing the Potential of Parallel and Series Resistors


Before we can get too deep into voltage dividers, it is essential to have a good understanding of what happens with Parallel and Series Resistors. Once you understand how a voltage drops over a resistor, you’re about halfway done with understanding a voltage divider. If you need a voltage lower in your circuit than the voltage that is provided by your power source, you can use a voltage divider. This uses two (or more!) resistors in series and the nodes between the resistors will have a lower voltage than the input. The voltage depends on the value of the different resistors compared to each other.

What is a voltage divider?

Voltage Divider Diagram
Voltage Divider Diagram

I’ve already stated this but I’ll say it again. A voltage divider is literally just two resistors in series. But the crucial part is that you’re measuring the voltage between those resistors (VOUT) and it’s going to be less than the voltage input (VIN). To figure out exactly what that output is, given the resistor values, you use the following equation.

Voltage Divider Equation
Voltage Divider Equation

Stepping through this slowly, the math makes a lot of sense.

  • First, in the denominator, you’re figuring out the total resistance of the two resistors, R1 + R2.
  • Second, in the numerator, you have the value of the resistor over which you want to measure the voltage, R2. In essence, you’re establishing the percentage of resistance that R2 is of the total R1 + R2.
  • Third, you’re multiplying that percentage with VIN.

Two things to note from this:

  1. If you understand the concept of doing it with two, and understand how/why the math represents it, it is very easy to expand the number of resistors that are being used together. It’s all about percentages.
  2. If R1 = R2, then VOUT is simply VIN/2. Keep things nice and simple.

If you want to double-check your work or take a shortcut, we've made a tool to help with voltage dividers.

Is there anything else I should take into consideration?

Reality is complicated. Or at least nuanced. So, yes.

The Biggest Issue

Let’s imagine we have a 5V supply and we have two resistors in series, 10KΩ each, which makes the voltage between the two resistors 2.5V.

Voltage Divider Tool Screen Shot
Voltage Divider Tool Screen Shot

Now, we have a device that needs 2.5V and ideally consumes 2.5mA, or has an equivalent resistance of 1KΩ. We throw it on the voltage divider and it doesn’t work. Why?

Voltage Divider Schematic Diagram with 0.42V
Voltage Divider Schematic Diagram with 0.42V

It’s because we’ve changed the circuit completely with our load! Instead of being two 10KΩ resistors in series, it’s a 10KΩ resistor in series with an equivalent 909Ω resistor. With a 5V source, this means that the voltage is actually ~0.42V, 2V less than anticipated.

Parallel Equivalence Tool
Parallel Equivalence Tool
Voltage Divider Tool with 10ohms
Voltage Divider Tool with 10ohms

You can circumvent this problem by using smaller valued resistors. Instead of 10KΩ, you could use 10Ω resistors, which, with a 1KΩ load, would give you about 2.487V, only 0.013V away from the ideal 2.5V. But, now we have another issue.

Voltage Divider Schematic Diagram with 0.5% efficiency
Voltage Divider Schematic Diagram with 0.5% efficiency

With two 10Ω resistors, one of which is in parallel with 1KΩ load, we have the equivalent of 19.9Ω between our voltage source and ground. This is 0.2513 amps, or a total power dissipation of 1.257 watts! When, in reality, our device needs only 2.5V and 2.5mA, or 6.25 milliwatts. That means that our fictional circuit is wasting ~1.25 watts, or is only about 0.5% efficient. So, that’s the trade-off between using large resistors and small resistors for your voltage divider. Efficiency versus rigidity.

Some other voltage divider issues

Depending on your application, if you need a precise voltage then you also need a very precise, accurate, and stable voltage input as well as a very precise resistor. So, your costs may be higher than originally anticipated.

Also, you can get a more consistent voltage by using a Zener diode. We’re not going to go into it, but Zener diodes are another relatively inexpensive way to get a lower voltage. It has its own issues, but is another alternative for easy and inexpensive voltage regulation.

Finally - in real life, a potentiometer is a voltage divider that changes the resistance values depending on where the knob ends up. You can connect a microcontroller to a potentiometer and the microcontroller periodically measures the output voltage, giving you a way to manually give an input to that controller. This is extremely common. But it also suffers from that balance between rigidity and power wastage.

Well, darn. Is there any benefit of using a voltage divider?

Despite these drawbacks, there are applications where a voltage divider is exactly what you need. Voltage dividers are extremely simple and, if you know what you incoming voltage is, you can easily and inexpensively get the exact voltage you want. As long as it’s lower than the incoming voltage. By using two resistors, which, in bulk, could cost you a grand total of well less than a penny, you can avoid using a pesky and expensive power supply.

One of the most common uses is setting a reference voltage for an ADC. If you want to take samples and would like to narrow the sampling range to increase your resolution, you can set a reference voltage that is lower than the supply voltage.

Voltage Divider Summary

Voltage dividers can be very useful but they’re more limited in their use than one would expect when first thinking about it. But that doesn’t reduce the importance of learning about them and understanding how they work, as they come up frequently in designs, whether intentionally or as a side effect of some other design feature.

Voltage Dividers Pros:

  • Inexpensive
  • Easy

Voltage Dividers Cons:

  • Not very stable
  • Not very rigid
  • Unnecessary or excessive power dissipation
  • Plenty of other option
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