Voltage dividers explained

Voltage Divider

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)

Vin=\left({\frac{{Vout}}{{R2}}}\right)R1+Vout \Rightarrow Vin=Vout\left({\frac{{R1+R2}}{{R2}}}\right)

 

So finally we get :

Vout=Vin\left({\frac{{R2}}{{R1 + R2}}}\right)

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