Potential Dividers (Cambridge O Level Physics)

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Input Sensors

Thermistors

  • A thermistor is a non-ohmic conductor and sensory resistor whose resistance varies with temperature
  • Most thermistors are negative temperature coefficient (NTC) components.
    • This means that if the temperature increases, the resistance of the thermistor decreases (and vice versa)

    Resistance-Temperature Graph for a NTC Thermistor

Thermistor graph, downloadable AS & A Level Physics revision notes

A graph of temperature against resistance for a thermistor shows that as temperature increases, resistance decreases

  • Thermistors are temperature sensors and are used in circuits in ovens, fire alarms and digital thermometers
    • As the thermistor gets hotter, its resistance decreases
    • As the thermistor gets cooler, its resistance increases

    Relationship Between Resistance and Temperature for a Thermistor

Thermistor diagram, downloadable AS & A Level Physics revision notes

The resistance through a thermistor is dependent on the temperature of it

Light-Dependent Resistors

  • A light-dependent resistor (LDR) is a non-ohmic conductor and sensory resistor
  • Its resistance automatically changes depending on the light energy falling onto it (illumination)
  • As the light intensity increases, the resistance of an LDR decreases

Resistance-Temperature Graph for a Light-Dependent Resistor

LDR graph, downloadable AS & A Level Physics revision notes

A graph of resistance against light intensity for an LDR shows that as light intensity increases, resistance decreases

  • LDRs can be used as light sensors, so, they are useful in circuits which automatically switch on lights when it gets dark, for example, street lighting and garden lights
    • In the dark, its resistance is very large (millions of ohms)
    • In bright light, its resistance is small (tens of ohms)

LDR diagram, downloadable AS & A Level Physics revision notes

Resistance of an LDR depends on the light intensity falling on it

Variable Potential Dividers

  • When two resistors are connected in series, the potential difference across the power source is shared between them

Potential Divider

Potential divider, IGCSE & GCSE Physics revision notes

A potential divider splits the potential difference of a power source between two components

 

  • The potential difference across each resistor depends upon its resistance:
    • The resistor with the largest resistance will have a greater potential difference than the other one
    • 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
  • A potentiometer is a single component that (in its simplest form) consists of a coil of wire with a sliding contact, midway along it

 Potentiometer

Potentiometer, IGCSE & GCSE Physics revision notes

A potentiometer is a kind of variable resistor

  • The sliding contact has the effect of separating the potentiometer into two parts – an upper part and a lower part – both of which have different resistances

Circuit Diagram Using a Potentiometer

Potentiometer circuit diagram, IGCSE & GCSE Physics revision notes

Moving the slider (the arrow in the diagram) changes the resistances (and hence potential differences) of the upper and lower parts of the potentiometer

 

  • If the slider in the above diagram is moved upwards, the resistance of the lower part will increase and so the potential difference across it will also increase

Resistors as Potential Dividers

  • 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:

Diagram Illustrating the Potential Divider Equation

Potential divider diagram and equation, downloadable AS & A Level Physics revision notes

Potential divider diagram and 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.

WE - potential divider question image, downloadable AS & A Level Physics revision notes

Vout is equal to 5.3 V

Calculate the input voltage Vin.

Answer: 

Step 1: List the known quantities

  • Resistance of resistor 1, R1 = 20 kΩ
  • Resistance of resistor 2, R2 = 12 kΩ
  • Input voltage, Vout = 5.3 V

Step 2: State the potential divider equation

V subscript o u t end subscript space equals space open parentheses fraction numerator R subscript 1 over denominator R subscript 1 space plus space R subscript 2 end fraction close parentheses V subscript i n end subscript

Step 3: Rearrange to make input voltage the subject

  • Divide both sides by fraction numerator R subscript 1 over denominator R subscript 1 plus space R subscript 2 end fraction

V subscript i n end subscript space equals space V subscript o u t end subscript space divided by space open parentheses fraction numerator R subscript 1 over denominator R subscript 1 plus R subscript 2 end fraction close parentheses space

V subscript i n end subscript space equals space V subscript o u t end subscript cross times open parentheses fraction numerator R subscript 1 plus R subscript 2 over denominator R subscript 1 end fraction close parentheses

Step 4: Substitute in the known values to calculate

V subscript i n end subscript space equals space 5.3 space cross times space open parentheses fraction numerator 12 space plus space 20 over denominator 20 end fraction close parentheses

V subscript i n end subscript space equals space 8.5 space straight V space open parentheses 2 space straight s. straight f. close parentheses

Examiner Tip

When thinking about potential dividers, remember that the higher the resistance the more energy it will take to 'push the current through' and therefore the higher the potential difference.

This means that if a component (often shown as a voltmeter in questions) needs to be switched on by a change such as increased light or temperature, then the resistor it is in parallel with needs to become larger compared to the other resistor.

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Leander

Author: Leander

Expertise: Physics

Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.