Use thermistors and LDRs in potential dividers
Predict how a sensor's resistance change affects divider output as temperature or light changes.
Section 10 · D.C. circuits
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 10. These original circuit diagrams and calculations are study aids; full timed assessment, supervised practical competence and human subject-teacher review remain outstanding.
Before you begin
- Use current, potential difference, resistance, energy and charge with consistent circuit directions.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What happens to NTC thermistor resistance as temperature rises?
What you will learn
- Explain sensor potential-divider use for temperature-dependent output
- Explain sensor potential-divider use for light-dependent output
- Trace whether the output rises or falls from the sensor's position
A sensor changes a divider's resistance ratio
An NTC thermistor's resistance decreases as temperature increases. An LDR's resistance decreases as light intensity increases. Placing either sensor in series with a fixed resistor across a supply creates a potential divider whose output depends on the measured condition.
The output trend depends on which resistor is connected across the output terminals. If the output is across the sensor, a falling sensor resistance reduces its share of the total p.d.; if output is across the fixed resistor, the fixed resistor's share rises.
Explain the circuit, not just the sensor
A divider translates a sensor resistance change into an output p.d. that changes with temperature or light and can be measured or supplied to another circuit stage. State the supply, which element changes, the output connection and the direction of the output change.
The ideal ratio assumes the output is not significantly loaded. Numerical output needs the supply voltage and both resistor values at the condition; a qualitative sensor trend alone is not enough for a voltage calculation.
Pause and explain
A sensor resistance falls and output is measured across that sensor in a simple divider. What happens to its p.d. share?
Worked example
An NTC thermistor is in series with a fixed resistor across 10 V. Output is across the thermistor. Predict output when temperature rises.
Show the worked solution
- The thermistor resistance decreases as temperature rises.
- Its output fraction is Rthermistor/(Rfixed + Rthermistor).
- A smaller thermistor resistance gives a smaller fraction and lower output p.d.
Answer The output across the thermistor decreases as temperature increases.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A divider has an LDR in series with a fixed resistor. Output is across the LDR. Predict output when light intensity increases.
Give me a hint
First use the LDR's resistance trend, then apply the output fraction.
Compare my reasoning
- Increasing light intensity decreases LDR resistance.
- The LDR output fraction is RLDR/(Rfixed + RLDR).
- The smaller fraction gives lower output p.d.
Output across the LDR decreases as light intensity increases.
Look for these in your work
- Sensor trend stated
- Output terminals identified
- Ratio trend derived
An NTC thermistor and a fixed resistor form a divider. Output is across the fixed resistor. Predict output when temperature increases.
Give me a hint
A falling thermistor resistance changes the total denominator while fixed output resistance stays constant.
Compare my reasoning
- Temperature rise reduces thermistor resistance.
- Vout across fixed resistor is Vs × Rfixed/(Rfixed + Rthermistor).
- The denominator falls, so the output fraction rises.
Output across the fixed resistor increases as temperature rises, for the unloaded divider.
Look for these in your work
- NTC trend applied
- Correct output fraction used
- Direction derived
A designer wants the output across a sensor to rise as it warms, but uses an NTC thermistor in a divider. Explain how to alter the output connection to obtain a rising output trend.
Give me a hint
The same falling thermistor resistance gives complementary p.d. shares across the two series elements.
Compare my reasoning
- With output across the NTC sensor, its falling resistance makes its p.d. share fall.
- Measure output across the fixed series resistor instead.
- The fixed resistor's share rises as the thermistor resistance falls.
Connect output across the fixed resistor; its divider share rises as the NTC resistance falls with warming.
Look for these in your work
- Current sensor trend used
- Output terminals changed
- Desired trend explained
Common mistakes
- Predicting an output trend before identifying output terminals
- Using an LDR trend for a thermistor or vice versa
- Claiming a numerical divider output without resistance and supply values
What can you explain now?
What happens to NTC thermistor resistance as temperature rises?
Compare with the explanation
It decreases
The assumed thermistor has a negative temperature coefficient.
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Make it stick
How can the same thermistor resistance change make one divider output fall but the other rise?
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