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LDR & Thermistor in Potential Dividers

Key idea: Learn how LDRs and NTC thermistors work in potential divider circuits, and practise O Level questions on how Vout changes with light and temperature.

  • SEC G3 Physics 2027
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Learning objectives

  • Recognise and interpret circuit symbols for cells, batteries, switches, lamps, LEDs, resistors, fuses, ammeters and voltmeters
  • Draw circuit diagrams with cells, batteries, switches, lamps, LEDs, fixed and variable resistors, fuses, ammeters and voltmeters
  • Recognise and interpret circuit symbols for d.c. and a.c. supplies, potentiometers, bells, light-dependent resistors and thermistors
  • Draw circuit diagrams with d.c. and a.c. supplies, potentiometers, bells, light-dependent resistors and thermistors
  • Apply the same-current rule in series circuits
  • Apply the potential-difference sum in series circuits
  • Apply current conservation at parallel junctions
  • Apply equal potential difference across parallel branches
  • Calculate effective resistance in series
  • Calculate effective resistance in parallel
  • Solve whole-circuit problems using consistent quantities
  • Describe variable-potential-divider action
  • Describe NTC thermistor action as an input transducer
  • Describe light-dependent resistor (LDR) action as an input transducer
  • Solve simple NTC and LDR potential-divider problems

1. Definition

A. LDR

A light-dependent resistor (LDR) is a resistor whose resistance decreases when light intensity increases.

B. NTC thermistor

A negative temperature coefficient (NTC) thermistor is a resistor whose resistance decreases when temperature increases.

Using an LDR or NTC thermistor in a potential divider makes the output p.d. change with light or temperature, so it acts as an input transducer (physical change → voltage change).

What you need for this course

You should be able to explain how LDRs and NTC thermistors act as input transducers in potential-divider circuits and solve simple circuit problems involving them.

2. Key Ideas

A. The divider relationship (output across the bottom resistor)

For a two-resistor divider (top R₁, bottom R₂), the output across R₂ is:

Vₒᵤₜ = Vₛ(R₂/(R₁ + R₂))

B. Sensor behaviour (must memorise)

  • LDR: brighter → R smaller; darker → R larger
  • NTC thermistor: hotter → R smaller; colder → R larger

C. Always state the arrangement

  • which resistor is the sensor
  • where Vₒᵤₜ is measured (across which part)
  • use limiting cases (sensor resistance very large / very small) as a check

3. Detailed Explanations

A. A sensor in a potential divider

If a sensor is one of the resistors, changing its resistance changes the ratio, so Vₒᵤₜ changes.

Potential divider with a sensor

An LDR sensor and fixed resistor are connected in series across a supply. The output potential difference is measured from their junction to the zero-volt end of the fixed resistor.

A potential divider with an LDR above a fixed resistor and output measured from their junction to the zero-volt endA potential divider with an LDR above a fixed resistor and output measured from their junction to the zero-volt end
A sensor in a potential divider: changing sensor resistance changes the output p.d.
View figure data
Sensor potential-divider topology
PartConnection
LDRUpper component in the divider
Fixed resistor RLower component; output is measured across it
NTC alternativeMay replace the LDR in the same series position

Potential divider with a sensor: how Vout depends on sensor resistance

With a sensor on top and a fixed resistor at the bottom, Vout can increase or decrease depending on which part you measure across.

Scroll across the graph to read all labels.

With a sensor on top and a fixed resistor at the bottom, Vout can increase or decrease depending on which part you measure across.With a sensor on top and a fixed resistor at the bottom, Vout can increase or decrease depending on which part you measure across.
Schematic values using Vs = 10 V and bottom fixed resistor = 10 kΩ. Brighter/hotter usually means smaller sensor resistance (move left).
Open full-size graph
View figure data
Values for Potential divider with a sensor: how Vout depends on sensor resistance
Sensor resistance (kΩ)Vout across bottom fixed resistorVout across the sensor
19.09090.9091
28.33331.6667
56.66673.3333
1055
203.33336.6667
501.66678.3333

B. LDR example (light sensor)

Assume the LDR is on top and Vₒᵤₜ is taken across the bottom fixed resistor.

  • brighter → R_LDR decreases → Vₒᵤₜ increases
  • darker → R_LDR increases → Vₒᵤₜ decreases

If you measure Vₒᵤₜ across the LDR instead, the trend reverses.

C. NTC thermistor example (overheating alarm)

Assume the NTC thermistor is on top and Vₒᵤₜ is taken across the bottom fixed resistor.

  • hotter → R_NTC decreases → Vₒᵤₜ increases
  • colder → R_NTC increases → Vₒᵤₜ decreases

4. Common Mistakes

  • Describing how Vₒᵤₜ changes without stating where it is measured.
  • Mixing up sensor behaviour (both LDR and NTC thermistor decrease R when the stimulus increases).
  • Forgetting limiting-case checks (e.g. “if sensor R is very large, what happens?”).

5. Exam Tips

  1. Copy the circuit and label Vₛ, the sensor, and the two points for Vₒᵤₜ.
  2. Write the sensor rule first (e.g. “more light → R_LDR decreases”).
  3. Use the divider fraction (or limiting cases) to decide whether Vₒᵤₜ increases or decreases.

6. Worked Examples

Modelled example 1

LDR (qualitative)

Core

Problem

An LDR is above a fixed resistor in a potential divider, with Vₒᵤₜ across the bottom fixed resistor. What happens to Vₒᵤₜ when light intensity increases?
Study the worked solution

  1. Translate the stimulus

    Method

    State that R_LDR decreases.

    Reason

    An LDR has lower resistance in brighter light.

    Working

    light intensity↑ ⇒ R_LDR↓

  2. Track the divider output

    Method

    Conclude that Vₒᵤₜ increases.

    Reason

    The fixed resistor stays in the numerator while the total resistance in the denominator falls.

    Working

    Vₒᵤₜ = Vₛ(R_fixed/(R_LDR + R_fixed))

Guided practice 2

LDR (numerical)

About 6 min

Problem

An LDR is above a 6.0 kΩ fixed resistor across 12 V, with Vₒᵤₜ across the fixed resistor. The LDR is 12 kΩ in darkness and 3.0 kΩ in bright light. Find both output p.d.s.

Keep the output resistance fixed in both ratios

Hints

Hint 1: dark state
Use 6.0/(12 + 6.0) for darkness.
Hint 2: bright state
Only replace the LDR resistance with 3.0 kΩ.
View solution step by step

  1. Calculate the dark output

    Method

    Use the 12 kΩ LDR value.

    Reason

    The output remains across the 6.0 kΩ fixed resistor.

    Working

    V_(out,dark) = 12(6.0/(12 + 6.0)) = 4.0 V

  2. Calculate the bright output

    Method

    Substitute the smaller LDR resistance.

    Reason

    More light lowers the LDR resistance and raises the bottom resistor’s voltage fraction.

    Working

    V_(out,bright) = 12(6.0/(3.0 + 6.0)) = 8.0 V

Common misconception 3

NTC thermistor (qualitative)

Find and correct the mistake

Learner response

An NTC thermistor is above a fixed resistor and Vₒᵤₜ is across the fixed resistor. A learner says heating raises thermistor resistance, so the output falls. Diagnose both parts of the claim.

Start with what NTC means

View solution step by step

  1. Correct the sensor rule

    Method

    State that R_NTC decreases as temperature rises.

    Reason

    NTC means negative temperature coefficient.

    Working

    T↑ ⇒ R_NTC↓

  2. Correct the voltage trend

    Method

    Conclude that Vₒᵤₜ across the fixed resistor increases.

    Reason

    The fixed numerator is unchanged while the denominator decreases.

    Working

    Vₒᵤₜ = Vₛ(R_fixed/(R_NTC + R_fixed))

Examiner practice 4

NTC thermistor (numerical)

4 marks

Examination question

An NTC thermistor is above a 5.0 kΩ fixed resistor across 10 V, with Vₒᵤₜ across the fixed resistor. The thermistor is 15 kΩ cold and 2.5 kΩ hot. Find both outputs. [4 marks]

Use the same output numerator in each state

View solution step by step

  1. Cold output

    2 marks

    Method

    Use 15 kΩ for the thermistor.

    Reason

    The 5.0 kΩ fixed resistor remains the output resistance.

    Working

    V_(out,cold) = 10(5.0/(15 + 5.0)) = 2.5 V

  2. Hot output

    2 marks

    Method

    Replace the thermistor resistance with 2.5 kΩ.

    Reason

    Heating an NTC thermistor reduces its resistance.

    Working

    V_(out,hot) = 10(5.0/(2.5 + 5.0)) ≈ 6.7 V

Challenge 5

Same sensor, different measurement points

Minimal support

Output-terminal transfer

An LDR is above a fixed resistor. When light intensity increases, compare the output trend when Vₒᵤₜ is measured across (a) the bottom fixed resistor and (b) the LDR.

Hold the sensor change fixed, then move the output leads

Hints

Hint 1: sensor response
Brighter light makes R_LDR smaller.
Hint 2: complementary outputs
The two series p.d.s add to the fixed supply p.d.
View solution step by step

  1. Output across the fixed resistor

    Method

    State that the output increases.

    Reason

    A smaller top resistance gives the bottom fixed resistor a larger fraction of the supply.

    Working

    V_fixed = Vₛ(R_fixed/(R_LDR + R_fixed))↑

  2. Output across the LDR

    Method

    State that the output decreases.

    Reason

    The LDR’s own share becomes smaller as its resistance falls.

    Working

    V_LDR = Vₛ(R_LDR/(R_LDR + R_fixed))

7. Mind Stretchers

Mind stretcher 1: Make output larger in the darkExtension

You want Vₒᵤₜ to be larger in the dark (when an LDR has a higher resistance). Should you measure Vₒᵤₜ across the LDR or across the fixed resistor?

Show Answer

Measure Vₒᵤₜ across the LDR, because:

Vₒᵤₜ = Vₛ(R_LDR/(R_LDR + R_fixed))

In the dark, R_LDR increases, so the fraction increases and Vₒᵤₜ increases.

Mind stretcher 2: Limiting case checkExtension

In a divider, the sensor is on top and Vₒᵤₜ is across the bottom fixed resistor. If the sensor resistance becomes extremely large, what happens to Vₒᵤₜ?

Show Answer

If the top sensor resistance is extremely large, almost the whole supply p.d. is across the sensor, so the p.d. across the bottom resistor is very small. Therefore Vₒᵤₜ is close to 0 V.

8. Practice and next step

  • For each sensor problem, state the stimulus change, resistance change, sensor position and output measurement points before deciding the voltage trend.
  • Predict each output direction, then test it in the lab below.

Concept Explorer: Potential Divider Lab

Vary supply, resistor values, sensor placement, and output loading to track voltage trends and checkpoint your divider reasoning.

BetaO LevelA LevelElectricityBest for: O Level practical electricity
  • Divider Ratio
  • Sensor Placement
  • Trend Analysis
  • Source and Branch Current

Open the full interactive simulation on its own page

Use the standalone simulation page for the live controls, SVG scene, run modes, and scoring flow.

Open Interactive Simulation

The lesson stays lightweight and links out to the dedicated simulation page.

Finish with the D.C. Circuits Structured Practice, then continue to the Practical Electricity Hub.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027