# 5.3.4 Potential Divider Circuits

### Potential Divider Circuit

• When two resistors are connected in series, through Kirchhoff’s Second Law, the potential difference across the power source is divided between them
• Potential dividers are circuits which produce an output voltage as a fraction of its input voltage
• Potential dividers have two main purposes:
• To provide a variable potential difference
• To enable a specific potential difference to be chosen
• To split the potential difference of a power source between two or more components
• Potential dividers are used widely in volume controls and sensory circuits using LDRs and thermistors
• Potential divider circuits are based on the ratio of voltage between components. This is equal to the ratio of the resistances of the resistors in the diagram below, giving the following equation:
• The input voltage Vin is applied to the top and bottom of the series resistors
• The output voltage Vout is measured from the centre to the bottom of resistor R2
• The potential difference V across each resistor depends upon its resistance R:
• The resistor with the largest resistance will have a greater potential difference than the other one from V = IR
• If the resistance of one of the resistors is increased, it will get a greater share of the potential difference, whilst the other resistor will get a smaller share
• In potential divider circuits, the p.d across a component is proportional to its resistance from V = IR

#### Worked Example

The circuit is designed to light up a lamp when the input voltage exceed a preset value.
It does this by comparing Vout with a fixed reference voltage of 5.3 V. Vout is equal to 5.3
Calculate the input voltage Vin. #### Exam Tip

Always make sure the correct resistance is in the numerator of the potential divider equation. This will be the resistance of the component you want to find the output voltage of.

### Variable Resistance Components

• Variable and sensory resistors are used in potential dividers to vary the output voltage
• This could cause an external component to switch on or off e.g. a heater switching off automatically when its surroundings are at room temperature
• Sensory resistors used are Light Dependent Resistors (LDRs) and thermistors
• Recall that the resistance of an LDR varies with light intensity
• The higher the light intensity, the lower the resistance and vice versa
• The resistance of a thermistor varies with temperature
• The hotter the thermistor, the lower the resistance and vice versa

• From Ohm’s law V = IR, the potential difference Vout from a resistor in a potential divider circuit is proportional to its resistance
• If an LDR or thermistor’s resistance decreases, the potential difference through it also decreases
• If an LDR or thermistor’s resistance increases, the potential difference through it also increases

#### Worked Example

A potential divider consists of a fixed resistor R and a thermistor. What happens to the p.d through resistor R and the thermistor when the temperature of the thermistor decreases? • Due to Ohm’s Law (V = IR), both the resistor and thermistor are connected in series and have the same current I
• If resistance R increases, the potential difference across the thermistor also increases
• In series, the potential difference is shared equally amongst the components. Their sum equals the e.m.f of the supply (Kirchhoff’s second law)
• If the potential difference across the thermistor increases, the potential difference across the resistance R must decreases, to keep the same overall total e.m.f
• This is row D ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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