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Potential dividers

Potential dividers

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Summary

Potential dividers

​​In a nutshell

Potential dividers are a type of circuit that can vary the potential difference across an output.


Equations

Description

equation

Ratio of resistances
​V1V2=R1R2\dfrac{V_1}{V_2}=\dfrac{R_1}{R_2}​​
Potential divider equation 
​Vout=R2R1+R2VinV_{out}=\dfrac{R_2}{R_1+R_2} V_{in}​​


Variable definitions

quantity name

symbol

derived units

alternate units

si base units

​resistanceresistance​​
​RR​​
​Ω\Omega​​
​V A−1V\ A^{-1}​​
​kg m2 s−3 A−2kg\ m^2\ s^{-3}\ A^{-2}​​
​potential differencepotential\ difference​​
​VV​​
​VV​​
​J C−1J\ C^{-1}​​
​kg m2 s−3 A−1kg\ m^2 \ s^{-3}\ A^{-1}​​


Ratio of resistances

Take a simple circuit as shown below:


Physics; Electrical circuits; KS5 Year 12; Potential dividers


According to Kirchhoff's second law, the potential difference across R1R_1 and R2R_2 (which you can call V1V_1​ and V2V_2) is equal to the e.m.f. of the power source. These potential differences are split between the resistors according to the ratio of their resistances. Therefore one can write:


V1V2=R1R2\dfrac{V_1}{V_2}=\dfrac{R_1}{R_2}​​


Potential dividers

When you need a specific amount of potential difference for a task but you have a power source with a higher e.m.f., you can use a potential divider. This is a type of circuit that can vary the potential difference across an output by using the ratio of resistances. 


Below is a diagram of a simple potential divider:


Physics; Electrical circuits; KS5 Year 12; Potential dividers


By considering the total potential difference VinV_{in} and the ratio between R1R_1  and R2R_2, it is possible to know the output voltage VoutV_{out} across R2R_2 through the equation:


​Vout=R2R1+R2VinV_{out}=\dfrac{R_2}{R_1+R_2} V_{in}​​


You can then change resistors and regulate the output voltage. This can also be done through a potentiometer which is a type of variable resistor with three terminals that allows you to regulate voltage more freely. Potential dividers that use such components are for example used to control volume on a stereo. 


Note: ​VinV_{in} does not necessarily need to be the e.m.f. of the power source.


Example

A potential divider is composed of a battery and two resistors. The total potential difference is 12 V12\ V and the resistors have resistance 5 Ω5\ \Omega and 10 Ω10\ \Omega. What is the voltage output from the 10 Ω10\ \Omega resistor?


Firstly, identify all the variables:


Vin=12 VR1=5 ΩR2=10 Ω\begin{aligned}V_{in}&=12\ V \\R_1&=5\ \Omega \\R_2&=10\ \Omega\end{aligned}​​


Next, write down the equation for potential dividers:


Vout=R2R1+R2VinV_{out}=\dfrac{R_2}{R_1+R_2} V_{in}​​


Substitute all the numbers into the equation and calculate the output voltage:


Vout=105+10×12=8 VV_{out}=\dfrac{10}{5+10}\times12=8\ V​​


The output voltage of this potential divider is 8 V‾\underline{8\ V}.

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Learn with Basics

Length:
Measuring current and potential difference

Measuring current and potential difference

Potential difference and resistance

Potential difference and resistance

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Potential dividers

Potential dividers

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FAQs - Frequently Asked Questions

How can you regulate the output voltage in a potential divider?

How does potential difference split between resistors?

What is a potential divider?