Chemistry - Voltage divider

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In electronics, a voltage divider or resistor divider is a design technique used to create a voltage (V_out) which is proportional to another voltage (V_in). This is also known as the voltage divider rule.

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Resistor divider

Two resistors are connected as shown in the following diagram:

The output voltage V_out is related to V_in as follows:

$V_{out} = \frac{R_2}{R_1+R_2} \cdot V_{in}$

As a simple example, if R₁ = R₂ then

$V_{out} = \frac{1}{2} \cdot V_{in}$

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

$V_{out} = \frac{Z_2}{Z_1+Z_2} \cdot V_{in}$

For instance, for a divider can be made with a resistor and capacitor:

Since the capacitor's impedance is

$Z_C = {1 \over j \omega C}$

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

$Z R = R$

this divider will have the voltage ratio:

${V_{out} \over V_{in}} = {{1 \over j \omega C} \over {1 \over j \omega C} + R} = {1 \over 1 + R j \omega C}$

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.

External links

Calculator: voltage divider - loaded and open circuit

Categories: Electronic circuits