Voltage divider

Resistor divider

Two resistors are connected as shown in the following diagram:

The output voltage V_out is related to V_in as follows: :
As a simple example, if R₁ = R₂ then
:

Any ratio between 0 and 1 is possible.

Note that this rule only works if the divider is unloaded, i.e. the load resistance is infinite and all of the current flowing through R₁ goes into R₂. If current flows into a load resistance (through V_out), that resistance must be considered in parallel with R₂ (see resistor) to determine the voltage at V_out.

Impedance divider

A voltage divider is usually thought of as two resistors, but capacitors, inductors, or any combined impedance can be used. For general impedances Z₁ and Z₂, the voltage becomes

Since the capacitor's impedance is

(where j is the imaginary number, and ω is frequency in radians per second) and the resistor's impedance is simply

this divider will have the voltage ratio:

The ratio then depends on frequency, in this case decreasing as frequency increases. This circuit is, in fact, a basic lowpass filter, or, in the world of audio, a treble-cut filter.

See also