The voltage divider is a circuit that produces an Vout that is a fraction of an Vin.
The two resistors in series can be seen as a single potentiometer.
This circuit will be heavily used in our website so we have decided to do a standalone article for this circuit.
From the Ohms law we know that V=I*R
From the Kirchhoff's current law (first rule) we know ΣI=0 So we have I1=I2+I3
From the Kirchhoff's voltage law (second rule) we know that ΣV=0 So we have Vin=V1+V2
Observe that V2=Vout
Let's now do some considerations about this circuit.
We will assume that at Vout we will connect a really big resistor. This means that I3 will tend to zero.
So we have I1=I2=I at our circuit.
After all these considerations the second law becomes Vin=V1+V2 = I*R1 + Vout (1)
But we know that V2=Vout so we have :
Vout = V2 = I2*R2 = I*R2 => I = Vout/R2 (2)
The function (1) becomes with the use of (2)
So finally we get :
Notice that if R1 << R2 then Vout=Vin
and if R1=R2=R then Vout=Vin/2
Some more considerations and a simple demonstration can be found in the next page