# Voltage Dividers

## 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 (V_{in}) R_{1}, and the resistor closest to ground R_{2}. The voltage drop across R_{2} is called V_{out}, that’s the divided voltage our circuit exists to make.

That’s all there is to the circuit! V_{out} 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 (V_{in}), and both resistor values (R_{1} and R_{2}). Given those values, we can use this equation to find the output voltage (V_{out}):

*Memorize that equation!*

This equation states that the output voltage is **directly proportional** to the **input voltage** and the **ratio of R _{1} and R_{2}**. If you’d like to find out where this comes from, check out this section where the equation 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 V_{in} and both resistors and see what kind of output voltage they produce.

Or, if you adjust V_{out}, you’ll see what resistance value at R_{2} is required (given a V_{in} and R_{1}).

### 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 R_{2} is *much* larger (at least an order of magnitude) than R_{1}, then the output voltage will be very close to the input. There will be very little voltage across R_{1}.

Conversely, if R_{2} is much smaller than R_{1}, the output voltage will be tiny compared to the input. Most of the input voltage will be across R_{1}