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Voltage Division





RESISTOR DIVIDER


Two Resistor s are connected as shown in the following diagram:

The output voltage ''V''out is related to ''V''in as follows:
:
V_\mathrm{out} = rac{R_2}{R_1+R_2} \cdot V_\mathrm{in}


As a simple example, if ''R''1 = ''R''2 then
:
V_\mathrm{out} = rac{1}{2} \cdot V_\mathrm{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 ''R''1 goes into ''R''2. If current flows into a load resistance (through ''V''out), that resistance must be considered in ''parallel'' with ''R''2 (''see Resistor '') to determine the voltage at ''V''out.


IMPEDANCE DIVIDER


A voltage divider is usually thought of as two resistors, but Capacitor s, Inductor s, or any combined Impedance can be used. For general impedances ''Z''1 and ''Z''2, the voltage becomes

:
V_\mathrm{out} = rac{Z_2}{Z_1+Z_2} \cdot V_\mathrm{in}


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

The resistor's impedance is simply its resistance:


Z_R = R


The capacitor's impedance is a large resistance at low Frequencies and a low resistance at high frequencies. The exact formula is:


Z_C = {1 \over j \omega C}


where ''j'' is the Imaginary Unit , and ''ω'' is Frequency in Radian s per second. This divider will then have the voltage ratio: