Voltage Divider

Written by Srijan Sood

The Main Idea

Voltage Dividers are real-life applications of resistors that are used in circuits when the input voltage is different than the output voltage required, and also have applications in voltage and sensor measurement .

The output voltage is directly proportional to the input voltage, and the ratio of [math]\displaystyle{ R_1 }[/math] and [math]\displaystyle{ R_2 }[/math]:

[math]\displaystyle{ V_\mathrm{out} = \frac{R_2}{R_1+R_2} \cdot V_\mathrm{in} }[/math]

Figure 1. Examples of Voltage Divider Schematics.

Proof

This can be arrived at by using Ohm's Law.

[math]\displaystyle{ R_\mathrm{T} = R_1 + R_2 }[/math]

[math]\displaystyle{ V_\mathrm{in} = I\cdot(R_T) }[/math]

[math]\displaystyle{ V_\mathrm{in} = I\cdot(R_1+R_2) }[/math]

[math]\displaystyle{ V_\mathrm{out} = I\cdot(R_2) }[/math]

[math]\displaystyle{ I = \frac {V_\mathrm{in}}{R_1+R_2} = \frac {V_\mathrm{out}}{R_2} }[/math]

[math]\displaystyle{ V_\mathrm{out} = \frac {R_2}{R_1+R_2} \cdot V_\mathrm{in} }[/math]