# Voltage Divider

The voltage divider is shown below. It is two resistors in series used to reduce the input voltage (in this case VDC) to a smaller voltage (Vout). Voltage divider are useful in many applications. One of the most popular application for voltage divider is voltage monitoring with microcontroller. Microcontroller analog to digital converter (ADC) generally tolerate low voltage because of the reference used by the ADC. Let’s say you wanna monitor high voltage rail with a microcontroller, you would need to lower the voltage to accommodate the microcontroller. This is where the voltage divider is handy. Note : Designing a voltage divider for a microcontroller is not that simple since you need to consider the input impedance of the voltage divider, leakage current, etc. This is not cover here.

The equation for the voltage divider is :

$Vout=Vin*\cfrac{R2}{R1+R2}$

where Vin = VDC in the image above.

If you wonder how we found this equation, it is by combining two equations :

$1) Vout=R2*I$

$2) I=\cfrac{Vin}{R1+R2}$

where Vin = VDC in the image above.

We replace I in the first equation and we get the equation for the voltage divider.

Example :

In the image below, we have 12V from the D.C voltage source. R1 = 100 ohms and R2 = 50 ohms. We want to calculate Vout. (Vout = V2 in the image below)

$Vout=Vin*\cfrac{R2}{R1+R2}$

$Vout=12V*\cfrac{50\Omega}{50\Omega+100\Omega}$

$Vout=4V$

We can also calculate V1 with the equation above. We only need to modify the equation for V1. We replace Vout with V1 and instead of R2, we have R1 :

$V1=Vin*\cfrac{R1}{R1+R2}$

$V1=12V*\cfrac{100\Omega}{50\Omega+100\Omega}$

$V1=8V$

This equation could be modify for more than two resistors too if needed as long as the resistors are in series :

$Vx=Vin*\cfrac{Rx}{Rx+Rn1+Rn2+\dots}$

where Vx is the voltage across the resistor Rx and Vin is the voltage across all resistors in series.