Covered in This Tutorial: Ohm's Law

Introduction
A voltage divider is a simple circuit which turns a large voltage into a smaller one. Using just two
series resistors and an input voltage, we can create an output voltage that is a fraction of the input.
Voltage dividers are one of the most fundamental circuits in electronics. If learning Ohm’s law was
like being introduced to the ABC’s, learning about voltage dividers would be like learning how to
spell cat.
Covered in this Tutorial

 What a voltage divider circuit looks like.
 How the output voltage depends on the input voltage and divider resistors.
 How voltage dividers behave in the real-world.
 Real-life voltage divider applications.
Ideal Voltage Divider

There are two important parts to the voltage divider: the circuit and the equation.
The Circuit
A voltage divider involves applying a voltage source across a series of two resistors. You may see it
drawn a few different ways, but they should always essentially be the same circuit.
Examples of voltage divider schematics. Shorthand, longhand, resistors at same/different angles,

etc.
We’ll call the resistor closest to the input voltage (Vin) R1, and the resistor closest to ground R2. The
voltage drop across R2 is called Vout, that’s the divided voltage our circuit exists to make.
That’s all there is to the circuit! Vout is our divided voltage. That’s what’ll end up being a fraction of the
input voltage.
The Equation
The voltage divider equation assumes that you know three values of the above circuit: the input
voltage (Vin), and both resistor values (R1 and R2). Given those values, we can use this equation to
find the output voltage (Vout):
Memorize that equation!

This equation states that the output voltage is directly proportional to the input voltage and
theratio of R1 and R2. If you’d like to find out where this comes from, check out this section where
the equaion is derived. But for now, just write it down and remember it!
Calculator
Have some fun experimenting with inputs and outputs to the voltage divider equation! Below, you
can plug in numbers for Vin and both resistors and see what kind of output voltage they produce.
5
Vin = V
1700
R1 = Ω
3300
R2 = Ω
3.30
Vout = V
Or, if you adjust Vout, you’ll see what resistance value at R2 is required (given a Vin and R1).
Simplifications
There are a few generalizations that are good to keep in mind when using voltage dividers. These
are simplifications that make evaluating a voltage dividing circuit just a little easier.
First, if R2 and R1 are equal then the output voltage is half that of the input. This is true regardless
of the resistors' values.
If R2 is much larger (at least an order of magnitude) than R1, then the output voltage will be very
close to the input. There will be very little voltage across R1.
Conversely, if R2 is much smaller than R1, the output voltage will be tiny compared to the input. Most
of the input voltage will be across R1
Applications
Voltage dividers have tons of applications, they are among the most common of circuits electrical
engineers use. Here are just a few of the many places you’ll find voltage dividers.
Potentiometers
A potentiometer is a variable resistor which can be used to create an adjustable voltage divider.
A smattering of potentiometers. From top-left, clockwise: a standard 10k trimpot, 2-axis

joystick,softpot, slide pot, classic right-angle, and a breadboard friendly 10k trimpot.
Internal to the pot is a single resistor and a wiper, which cuts the resistor in two and moves to adjust
the ratio between both halves. Externally there are usually three pins: two pins connect to each end
of the resistor, while the third connects to the pot’s wiper.
A potentiometer schematic symbol. Pins 1 and 3 are the resistor ends. Pin 2 connects to the wiper.
If the outside pins connect to a voltage source (one to ground, the other to V in), the output (Vout at the
middle pin will mimic a voltage divider. Turn the pot all the way in one direction, and the voltage may
be zero; turned to the other side the output voltage approaches the input; a wiper in the middle
position means the output voltage will be half of the input.
Potentiometers come in a variety of packages, and have many applications of their own. They may
be used to create a reference voltage, adjust radio stations, measure position on a joystick, or in
tons of other applications which require a variable input voltage.
Reading Resistive Sensors

Many sensors in the real world are simple resistive devices. A photocell is a variable resistor, which
produces a resistance proportional to the amount of light it senses. Other devices like flex
sensors,force-sensitive resistors, and thermistors, are also variable resistors.
It turns out voltage is really easy for microcontrollers (those with analog-to-digital converters - ADC’s
- at least) to measure. Resistance? Not so much. But, by adding another resistor to the resistive
sensors, we can create a voltage divider. Once the output of the voltage divider is known, we can go
back and calculate the resistance of the sensor.
For example, the photocell’s resistance varies between 1kΩ in the light and about 10kΩ in the dark.
If we combine that with a static resistance somewhere in the middle - say 5.6kΩ, we can get a wide
range out of the voltage divider they create.
Photocell makes up half of this voltage divider. The voltage is measured to find the resistance of the
light sensor.
Light Level R (Sensor)

2 R (Fixed)
1 Ratio R /(R +R )
2 1 2 V out
Light 1kΩ 5.6kΩ 0.15 0.76 V

Dim 7kΩ 5.6kΩ 0.56 2.78 V
Dark 10kΩ 5.6kΩ 0.67 3.21 V
A swing of about 2.45V from light to dark. Plenty of resolution for most ADCs!
Level Shifting
More complicated sensors may transmit their readings using heavier serial interfaces, like
a UART,SPI, or I2C. Many of those sensors operate at a relatively low voltage, in order to conserve
power. Unfortunately, it’s not uncommon that those low-voltage sensors are ultimately interfacing
with a microcontroller operating at a higher system voltage. This leads to a problem of level shifting,
which has a number of solutions including voltage dividing.
For example, an ADXL345 accelerometer allows for a maximum input voltage of 3.3V, so if you try to
interface it with an Arduino (assume operating at 5V), something will need to be done to step down
that 5V signal to 3.3V. Voltage divider! All that’s needed is a couple resistors whose ratio will divide a
5V signal to about 3.3V. Resistors in the 1kΩ-10kΩ range are usually best for such an application;
let’s
3.3kΩ resistors (orange, orange, red) are the R2’s, 1.8kΩ resistors are the R1’s. An example of
voltage dividers in a breadboard, level shifting 5V signals to 3.24V. (Click to see a larger view).
Keep in mind, this solution only works in one direction. A voltage divider alone will never be able to
step a lower voltage up to a higher one.
Application Dont’s
As tempting as it may be to use a voltage divider to step down, say, a 12V power supply to
5V,voltage dividers should not be used to supply power to a load.
Any current that the load requires is also going to have to run through R 1. The current and voltage
across R1 produce power, which is dissipated in the form of heat. If that power exceeds the rating of
the resistor (usually between ⅛W and 1W), the heat begins to become a major problem, potentially
melting the poor resistor.
That doesn’t even mention how inefficient a voltage-divider-power-supply would be. Basically, don’t
use a voltage divider as a voltage supply for anything that requires even a modest amount of power.
If you need to drop down a voltage to use it as a power supply, look into voltage regulators or
switching supplies.
Extra Credit: Proof

If you haven’t yet gotten your fill of voltage dividers, in this section we’ll evaluate how Ohm’s law is
applied to produce the voltage divider equation. This is a fun exercise, but not super-important to
understanding what voltage dividers do. If you’re interested, prepare for some fun times with Ohm’s
law and algebra.
Evaluating the circuit

So, what if you wanted to measure the voltage at Vout? How could Ohm’s law be applied to create a
formula to calculate the voltage there? Let’s assume that we know the values of V in, R1, and R2, so
let’s get our Vout equation in terms of those values.
Let’s start by drawing out the currents in the circuit–I 1 and I2–which we’ll call the currents across the
respective resistors.
Our goal is to calculate Vout, what if we applied Ohm’s law to that voltage? Easy enough, there’s just
one resistor and one current involved:
Sweet! We know R2’s value, but what about I2? That’s an unknown value, but we do know a little
something about it. We can assume (and this turns out to be a big assumption) that I1 is equivalent
to I2. Alright, but does that help us? Hold that thought. Our circuit now looks like this, where I equals
both I1 and I2.
What do we know about Vin? Well, Vin is the voltage across both resistors R1 and R2. Those resistors
are in series. Series resistors add up to one value, so we could say:
And, for a moment, we can simplify the circuit to:
Ohm’s law at its most basic! Vin = I * R. Which, if we turn that R back into R1 + R2, can also be written
as:
And since I is equivalent to I2, plug that into our Vout equation to get:
And that, my friends, is the voltage divider equation! The output voltage is a fraction of the input
voltage, and that fraction is R2 divided by the sum of R1 and R2.

Covered in This Tutorial: Ohm's Law

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Introduction

Covered in this Tutorial

Ideal Voltage Divider

Examples of voltage divider schematics. Shorthand, longhand, resistors at same/different angles,

Memorize that equation!

A smattering of potentiometers. From top-left, clockwise: a standard 10k trimpot, 2-axis

Reading Resistive Sensors

Light Level R (Sensor)

Light 1kΩ 5.6kΩ 0.15 0.76 V

Extra Credit: Proof

Evaluating the circuit

And, for a moment, we can simplify the circuit to:

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