The voltage divider

Principle of the voltage divider

In a circuit where two resistors R1 and R2 are in series, powered by a total voltage U, this voltage is distributed between the two resistors in proportion to their value. The voltage across R1 is:

U1 = ( R1 / (R1 + R2) ) * U

And likewise for R2:

U2 = ( R2 / (R1 + R2) ) * U

We always check that U1 + U2 = U (additivity law of voltages in series).

Concrete example

R1 = 1 kOhm, R2 = 3 kOhm, U = 8 V.

U1 = (1 / (1+3)) * 8 = 1/4 * 8 = 2 V

U2 = (3 / 4) * 8 = 6 V

Indeed 2 + 6 = 8 V. The larger resistor receives the larger share of the voltage.

What is it used for?

The voltage divider is widely used in electronics: potentiometers (volume control of an amplifier), resistive sensors (photoresistor, thermistor), setting a reference voltage level for a microcontroller.

Common pitfall

Don't swap R1 and R2 in the numerator: the voltage across R1 depends on R1 in the numerator, not R2. A frequent mistake is writing U1 = R2/(R1+R2)*U, confusing it with the current divider (seen in chapter 2).