Voltage Divider Formula Derivation

If you have not gotten your fill of voltage dividers yet, in this
section we’ll evaluate how Ohm’s law is applied to produce the voltage divider equation. This is a fun exercise.
If you are interested, prepare for some tours with Ohm’s law and algebra.

Voltage Divider formula Derivation

Evaluating the circuit
So, what if you wanted to measure the voltage at Vout ?

Let’s assume that we know the
values of V , R1, and R2 , so let’s get our Vout equation in terms of those values.
Let’s start by referring to the currents in the circuit, I1 and
I2 –which we shall call the currents through 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:

Vout = I2 * R2

Sweet! Right?! We know R2 ’s value, but what about I2 ? That’s an unknown value, but we do know a little thing 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: R =R1+R2

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

Common Current

Ohm’s law at its most basic!

V = I * R.

Which, if we turn that R back into R1 + R2 , can also be written as:

I = Vin / (R1+R2)

And since I1 is equivalent to I2 , plug that into our Vout equation to get:

Vout = R2 * (Vin/R1+R2)

This is so by just replacing I with Vin/(R1+R2) . 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.

Expect tutorials on sensors based on this voltage divider principle soon.

See you then and please do not forget to leave us a comment