K323 / 2027
D.C. circuits overview

Lesson 6 of 6

Thermistor and LDR circuits

  • I can describe NTC thermistors and LDRs and explain their use as divider input transducers.Syllabus

    Syllabus K323, 15(i). Describe NTC thermistors and LDRs and explain their use as divider input transducers.

  • I can solve simple circuits involving both NTC thermistors and LDRs.Syllabus

    Syllabus K323, 15(j). Solve simple circuits involving both NTC thermistors and LDRs.

A sensor changes resistance when its surroundings change. In a powered potential divider, that resistance change produces a changing output voltage.

For an unloaded divider, the output is the supply voltage multiplied by the fraction of the total resistance across the chosen output. Check which terminals are used before predicting whether the voltage rises or falls.

NTC thermistor
Its resistance decreases as temperature increases. NTC means negative temperature coefficient. This behaviour differs from the rising resistance of a hotter ordinary metallic conductor.
Light-dependent resistor: LDR
Its resistance decreases as the light falling on it increases. Its symbol's incoming arrows represent illumination.

These trends do not establish a straight-line or inverse-proportional relationship. Use supplied resistance values or a given characteristic for a calculation.

As an input transducer, the sensor lets a physical input such as temperature or light affect an electrical signal. The sequence is: surroundings change, sensor resistance changes, voltage sharing changes, output voltage changes. The source supplies the circuit's energy; the sensor does not provide a universal on/off voltage by itself.

A sensor changes the voltage share across a named output

Both supplied divider circuits keep the source at 6.0 V and take negligible output current. Read the output between B and C; the sensor is in a different arm in each case.

NTC thermistor below a fixed upper resistor

NTC thermistor below a fixed upper resistorA fixed 6.0 V source is across A and C. A fixed 3.0 kilohm resistor is the upper arm from A to B; an NTC thermistor is the lower arm from B to C. The thermistor has a diagonal temperature-dependent symbol without an adjustment arrowhead. The ideal output voltmeter is between B and C, across the NTC. When the supplied NTC resistance falls from 6.0 to 2.0 kilohm as temperature rises, V_BC falls from 4.0 to 2.4 V.+-6.0 VVA: 6.0 VBC: 0 V reference+-Fixed3.0 kohmNTC

Supplied 20 deg C condition: NTC 6.0 kohm, output 4.0 V. At 40 deg C: NTC 2.0 kohm, output 2.4 V. The series current changes between conditions.

LDR above a fixed lower resistor

LDR above a fixed lower resistorA fixed 6.0 V source is across A and C. An LDR is the upper arm from A to B; a fixed 4.0 kilohm resistor is the lower arm from B to C. Incident-light arrows point towards the LDR symbol. The ideal output voltmeter is between B and C, across the fixed resistor, not across the sensor. When the supplied LDR resistance falls from 12.0 to 2.0 kilohm, V_BC rises from 1.5 to 4.0 V.+-6.0 VVA: 6.0 VBC: 0 V reference+-LDRFixed4.0 kohm

Supplied dim condition: LDR 12.0 kohm, output 1.5 V. Brighter condition: LDR 2.0 kohm, output 4.0 V. Output is across the fixed lower resistor.

Both supplied circuits use a fixed 6.0 V source and negligible output current. The NTC is the lower arm in the first circuit; the LDR is the upper arm in the second. In both, VBC is measured across the lower arm.

An NTC in the lower arm

A fixed 3.0 kΩ resistor connects A/B. The NTC connects B/C, and output is across the NTC. Its supplied resistance is 6.0 kΩ at 20 °C and 2.0 kΩ at 40 °C.

Temperature to output voltage

Warm the NTC from 20 °C to 40 °C

At 20 °C: total resistance is 3.0 + 6.0 = 9.0 kΩ. Current is 6.0/9000 = 0.000667 A, or 0.667 mA. Output VBC = 6.0 x 6.0/(3.0 + 6.0) = 4.0 V.

At 40 °C: total resistance is 3.0 + 2.0 = 5.0 kΩ. Current is 6.0/5000 = 0.00120 A, or 1.20 mA. Output VBC = 6.0 x 2.0/(3.0 + 2.0) = 2.4 V.

Warming reduces the lower arm's resistance and its share of the supply voltage. The output falls even though the series current rises. The fixed upper resistor's p.d. rises from 2.0 V to 3.6 V, keeping the total at 6.0 V.

This changing voltage could be an input to a temperature monitor or alarm. The controller's required input and switching condition would need to be specified; the thermistor alone does not determine them.

An LDR in the upper arm

The LDR now connects A/B, with a fixed 4.0 kΩ resistor at B/C. Output is across the fixed lower resistor. The supplied LDR resistance is 12.0 kΩ in a dim condition and 2.0 kΩ in a brighter condition.

Light to output voltage

Increase the illumination

Dim: total resistance is 12.0 + 4.0 = 16.0 kΩ. Current is 6.0/16 000 = 0.000375 A = 0.375 mA. Output VBC = 6.0 x 4.0/(12.0 + 4.0) = 1.5 V.

Brighter: total resistance is 2.0 + 4.0 = 6.0 kΩ. Current is 6.0/6000 = 0.0010 A = 1.0 mA. Output VBC = 6.0 x 4.0/(2.0 + 4.0) = 4.0 V.

More light lowers the upper resistance, giving the fixed lower resistor a larger share of the supply. The output rises. The LDR's own p.d. instead falls from 4.5 V to 2.0 V.

Try it step by step

Work it out in steps: Total resistance in ohm, then Output p.d. across the fixed resistor in V, then Output when the sensor resistance falls.

  1. Problem 1. A thermistor of resistance 8.0 kilo-ohm (cold) is the upper resistor of a divider. The lower resistor is a fixed 4.0 kilo-ohm, and the output is across it. The supply is 6.0 V. Find the output and say what happens to it when the thermistor warms.
  2. Problem 2. The same thermistor has warmed to 2.0 kilo-ohm. The fixed lower resistor is still 4.0 kilo-ohm and the supply is 6.0 V. Find the output, then say what happens if it warms further.
  3. Problem 3. An LDR of resistance 12 kilo-ohm (dark) is the upper resistor. The fixed lower resistor is 3.0 kilo-ohm, and the output is across it. The supply is 9.0 V. Find the output, then say what happens when light shines on the LDR.
Show the answer

Problem 1.

Total resistance in ohm: R = 8000 + 4000 = 12000 ohm

Output p.d. across the fixed resistor in V: V out = 6.0 x 4000 / 12000 = 2.0 V

Output when the sensor resistance falls: Warming lowers the thermistor resistance, so the fixed resistor takes a larger share of the 6.0 V: the output rises.

Problem 2.

Total resistance in ohm: R = 2000 + 4000 = 6000 ohm

Output p.d. across the fixed resistor in V: V out = 6.0 x 4000 / 6000 = 4.0 V

Output when the sensor resistance falls: Warming further lowers the thermistor resistance again, so the output rises further.

Problem 3.

Total resistance in ohm: R = 12000 + 3000 = 15000 ohm

Output p.d. across the fixed resistor in V: V out = 9.0 x 3000 / 15000 = 1.8 V (2 sf)

Output when the sensor resistance falls: Light lowers the LDR resistance, so the fixed resistor takes a larger share: the output rises.

A light-level controller can use this voltage as its input. Moving the sensor to the other arm, or measuring across the other component, can reverse the output trend. Name the resistance that changes and the terminals being measured.

Compare readings under controlled conditions

Use supplied data or a suitable low-voltage arrangement with the output meter across the named terminals. Keep the source voltage fixed. Allow the sensor's response to settle before recording the input condition and output voltage.

For an NTC comparison, measure temperature with a suitable thermometer and keep other conditions consistent. Electrical current can also warm the thermistor, so do not attribute every change to the intended external temperature alone. A voltage response needs calibration before it can be read as a temperature scale.

For an LDR comparison, change the illumination while limiting unwanted heating and keeping other light sources consistent. These supplied resistance values describe the example; they are not a calibration for every LDR or thermistor.

The current can change between conditions. Both arms carry the same current within one unloaded-divider state, but changing a sensor's resistance changes the total resistance and therefore the current. Recalculate it or use the correctly referenced voltage ratio.

Check your understanding

A 6.0 V divider has an NTC thermistor as its upper arm and a fixed 3.0 kilohm resistor as its lower arm. Output is across the fixed lower resistor. Warming reduces the NTC resistance from 6.0 to 2.0 kilohm. What happens to the unloaded output?

  1. It falls from 4.0 V to 2.4 V.
  2. It stays at 2.0 V because the output resistor has not changed.
  3. It rises from 2.0 V to 3.6 V.
Show the answer

It rises from 2.0 V to 3.6 V.

Across the fixed lower arm, V_out = 6.0 x 3.0/(R_NTC + 3.0), using the same resistance units. Initially this is 2.0 V; afterwards it is 3.6 V. The falling upper resistance gives the fixed lower resistor a larger share of the supply.

Practise an exam question

Write your answer first, then tick the mark points it makes.

Exam-style question

A potential divider is made from a fixed resistor and a thermistor (NTC) in series across a constant supply. The output is taken across the fixed resistor and switches on a fan when it is high enough. Explain why the fan switches on when the room gets warmer. [3]

Saved on this browser only. Anyone using this browser can see it.