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The Voltage Divider

  • 4 min
  • Beginner

A voltage divider is a circuit that obtains a fraction of the input voltage by means of two impedances connected in series.

For example, you might have a 9V or 12V signal that a 5V or 3.3V input cannot directly accept. For a low-power signal, two resistors provide a simple way to reduce it.

What it is and how it works

A voltage divider is a simple linear circuit that uses Ohm’s Law and Kirchhoff’s Law to distribute the input voltage between two components.

Physically, it is nothing more than two resistors connected in SERIES between the voltage () and Ground (GND).

We take the output signal () right at the midpoint, between the two resistors.

The voltage divider formula

You don’t need to memorize it if you understand the logic, but you’ll use it so often it will become second nature.

The formula is:

Where:

  • : Input Voltage (Total).
  • : Output Voltage (At the midpoint).
  • : Upper resistor (connected to ).
  • : Lower resistor (connected to GND).

Where this formula comes from

It’s pure Ohm’s Law + Kirchhoff:

  1. Calculate the total circuit current:

  1. Calculate the voltage drop across the lower resistor (), which is our output:

  1. Substitute the current into this equation and we obtain the voltage divider formula.

Common practical cases

The exact midpoint ()

If you place two EQUAL resistors (), the voltage divides exactly in half.

  • Example: and .
  • Input: 10V → Output: 5V.

The car sensor (12V to 5V)

You want to read the state of a car light (12V) with an Arduino (max 5V). We need to be approximately 5V (or slightly less to maintain margin).

Using the formula:

If we choose (a standard value), we can solve for : Doing the math (), we find that should be about . Since isn’t very common, we use .

Perfect! It’s a safe logic “1” and we don’t burn the Arduino.

In a vehicle, the nominal 12V can include transients and overvoltages. A divider calculates the normal level, but a real input may need additional filtering and protection.

Potentiometers

Have you noticed that a potentiometer has 3 pins?

  • Pin 1: .
  • Pin 3: GND.
  • Pin 2 (Wiper): Output.

A potentiometer is literally a mechanical voltage divider. When you turn the knob, you change the ratio between and , causing the output voltage to vary smoothly from 0% to 100%. This is how the volume control on your radio works.

The load trap

Here comes the most important part of the article. If the voltage divider is so great… Why don’t we use it to power things?

You have a 12V source. You have a motor that runs on 6V. You think: “Easy! I put two equal resistors, get 6V, and connect the motor.”

Result: The motor doesn’t move and the voltage drops to almost 0V.

Why does it fail? Because the ideal formula assumes nothing is connected to the output (or that whatever is connected has infinite resistance).

The moment you connect a “Load” (the motor, ) in parallel with , the bottom resistance changes. Now the bottom resistance is not , but the parallel combination of and the Motor ().

Since the motor has low resistance, drops drastically → The output voltage collapses.

Voltage dividers are used for signals and low-power references, not for powering motors, power LEDs, or chargers.

To step down voltage with power, you need DC-DC converters or linear regulators.

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