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Potential dividers with thermistors and LDRs

Key idea: An LDR's resistance falls in brighter light, and an NTC thermistor's falls as it warms. In a potential divider, the sensor's share of supply voltage falls and the fixed resistor's rises.

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  • GCE A-Level H2 Physics 2027
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Enlarged diagram

A thermistor’s resistance changes with temperature and an LDR’s with light, but a control circuit needs a changing voltage, not a changing resistance. Put the sensor in series with a fixed resistor across a supply and the p.d. across either one changes with the temperature or the light. That arrangement is a potential divider.

The potential divider

Two resistors R₁ and R₂ in series across a supply p.d. Vₛ carry the same current, I = Vₛ/(R₁ + R₂). The p.d. across R₂ is then

Vₒᵤₜ = VₛR₂/(R₁ + R₂)

The supply p.d. is shared in the ratio of the resistances: the larger resistor takes the larger share. The resistance on top of the fraction is the one the output is measured across. This assumes no current is drawn from the output.

Fixed and variable potential-divider circuits

The upper circuit has resistors R1 and R2 in series across a supply, with output voltage measured across the lower resistor R2. The lower circuit has a three-terminal potentiometer across a supply, with output measured from its slider to the zero-volt end.

Scroll across the figure to read all labels.

A fixed two-resistor potential divider beside a three-terminal variable potential dividerA fixed two-resistor potential divider beside a three-terminal variable potential divider
In the fixed divider, the output is measured across R₂. The second diagram shows a variable resistor (potentiometer) used as an adjustable divider.
View figure data
Potential-divider topology
CircuitConnection
Fixed dividerR₁ and R₂ are in series; output is across R₂
Variable dividerThe potentiometer track is across the supply; output is taken from its wiper

Sensors in a divider

The resistance of an NTC thermistor falls as its temperature rises. The resistance of an LDR falls as the light falling on it gets brighter.

Suppose the output is measured across the lower resistor:

  • With the sensor in the upper position, its resistance falls as the temperature or light increases, so the lower, fixed resistor takes a larger share: the output rises.
  • With the sensor in the lower position, its own share falls: the output falls.

So the position of the sensor decides whether the output rises or falls. The graph shows how the output depends on the ratio of the two resistances; it does not tell you the temperature or the light level without the sensor’s own calibration.

Sensor placement in a potential divider

Two divider curves showing how Vₒᵤₜ/Vᵢₙ changes with sensor resistance depending on whether the sensor is placed at R₁ (top) or R₂ (bottom).

Scroll across the figure to read all labels.

Two divider curves showing how Vₒᵤₜ/Vᵢₙ changes with sensor resistance depending on whether the sensor is placed at R₁ (top) or R₂ (bottom).Two divider curves showing how Vₒᵤₜ/Vᵢₙ changes with sensor resistance depending on whether the sensor is placed at R₁ (top) or R₂ (bottom).
Output is across the lower arm of an unloaded divider with fixed input. Sensor resistance falls as an NTC warms or an LDR receives more light, so read the curve towards the left: upper-arm sensor gives rising output; lower-arm sensor gives falling output.
Open full-size graph
What to noticeAs sensor resistance falls, follow the curve towards the left. Output direction depends on which arm contains the sensor.
View figure data
Figure data: Sensor placement in a potential divider
Sensor resistance / fixed resistance (1)Sensor in lower armSensor in upper arm
0.2500.20000.8000
0.2750.21570.7843
0.3000.23080.7692
0.3250.24530.7547
0.3500.25930.7407
0.3750.27270.7273
0.4000.28570.7143
0.4250.29820.7018
0.4500.31030.6897
0.4750.32200.6780
0.5000.33330.6667
0.5250.34430.6557
0.5500.35480.6452
0.5750.36510.6349
0.6000.37500.6250
0.6250.38460.6154
0.6500.39390.6061
0.6750.40300.5970
0.7000.41180.5882
0.7250.42030.5797
0.7500.42860.5714
0.7750.43660.5634
0.8000.44440.5556
0.8250.45210.5479
0.8500.45950.5405
0.8750.46670.5333
0.9000.47370.5263
0.9250.48050.5195
0.9500.48720.5128
0.9750.49370.5063
1.0000.50000.5000
1.0250.50620.4938
1.0500.51220.4878
1.0750.51810.4819
1.1000.52380.4762
1.1250.52940.4706
1.1500.53490.4651
1.1750.54020.4598
1.2000.54550.4545
1.2250.55060.4494
1.2500.55560.4444
1.2750.56040.4396
1.3000.56520.4348
1.3250.56990.4301
1.3500.57450.4255
1.3750.57890.4211
1.4000.58330.4167
1.4250.58760.4124
1.4500.59180.4082
1.4750.59600.4040
1.5000.60000.4000
1.5250.60400.3960
1.5500.60780.3922
1.5750.61170.3883
1.6000.61540.3846
1.6250.61900.3810
1.6500.62260.3774
1.6750.62620.3738
1.7000.62960.3704
1.7250.63300.3670
1.7500.63640.3636
1.7750.63960.3604
1.8000.64290.3571
1.8250.64600.3540
1.8500.64910.3509
1.8750.65220.3478
1.9000.65520.3448
1.9250.65810.3419
1.9500.66100.3390
1.9750.66390.3361
2.0000.66670.3333
2.0250.66940.3306
2.0500.67210.3279
2.0750.67480.3252
2.1000.67740.3226
2.1250.68000.3200
2.1500.68250.3175
2.1750.68500.3150
2.2000.68750.3125
2.2250.68990.3101
2.2500.69230.3077
2.2750.69470.3053
2.3000.69700.3030
2.3250.69920.3008
2.3500.70150.2985
2.3750.70370.2963
2.4000.70590.2941
2.4250.70800.2920
2.4500.71010.2899
2.4750.71220.2878
2.5000.71430.2857
2.5250.71630.2837
2.5500.71830.2817
2.5750.72030.2797
2.6000.72220.2778
2.6250.72410.2759
2.6500.72600.2740
2.6750.72790.2721
2.7000.72970.2703
2.7250.73150.2685
2.7500.73330.2667
2.7750.73510.2649
2.8000.73680.2632
2.8250.73860.2614
2.8500.74030.2597
2.8750.74190.2581
2.9000.74360.2564
2.9250.74520.2548
2.9500.74680.2532
2.9750.74840.2516
3.0000.75000.2500
3.0250.75160.2484
3.0500.75310.2469
3.0750.75460.2454
3.1000.75610.2439
3.1250.75760.2424
3.1500.75900.2410
3.1750.76050.2395
3.2000.76190.2381
3.2250.76330.2367
3.2500.76470.2353
3.2750.76610.2339
3.3000.76740.2326
3.3250.76880.2312
3.3500.77010.2299
3.3750.77140.2286
3.4000.77270.2273
3.4250.77400.2260
3.4500.77530.2247
3.4750.77650.2235
3.5000.77780.2222
3.5250.77900.2210
3.5500.78020.2198
3.5750.78140.2186
3.6000.78260.2174
3.6250.78380.2162
3.6500.78490.2151
3.6750.78610.2139
3.7000.78720.2128
3.7250.78840.2116
3.7500.78950.2105
3.7750.79060.2094
3.8000.79170.2083
3.8250.79270.2073
3.8500.79380.2062
3.8750.79490.2051
3.9000.79590.2041
3.9250.79700.2030
3.9500.79800.2020
3.9750.79900.2010
4.0000.80000.2000

Check your understanding 1 Predict the sensor direction

Before using the lab, predict the output across the bottom arm when an NTC thermistor at the top is warmed. Then predict the change when the thermistor is instead at the bottom. Keep the supply and fixed resistor unchanged; draw no current from the output.

Thermistor at the top, warming
Thermistor at the bottom, warming
Show answer

Top thermistor: the output rises. Bottom thermistor: the output falls. Identify which component the output is across before using the sensor’s resistance change.

Test both sensor positions

Select Two components, set Supply p.d. to 6.0 V and leave the load off. Choose Thermistor for Top arm and Resistor for Bottom arm; set the bottom resistor to 2.0 kΩ. Increase Temperature from 25 to 50°C and read the output. Swap the arm types, set the top resistor to 2.0 kΩ, and repeat.

A 6.0 volt supply across a resistor R₁ of 1.00 kΩ and a resistor R₂ of 1.00 kΩ. The output p.d. across R₂ is 3.00 volts.

Divider
V
Top arm, R₁
Bottom arm, R₂
kΩ
kΩ
More settings
Vout
3.00 V
R₁ now
1.00 kΩ
R₂ now
1.00 kΩ
Vout as a fraction of the supply
0.50
How Vout responds

Try this

0 of 4 done

  1. With two resistors and a 6.0 V supply, make Vout = 2.0 V. (not done yet)

  2. Make a sensor whose Vout is high in the dark and low in bright light. (not done yet)

  3. Make a sensor whose Vout rises as it gets hotter. (not done yet)

  4. Connect a load across Vout that pulls Vout down by more than a fifth. (not done yet)

Check your understanding 2 Explain the two traces

Record whether the output rises or falls in each arrangement. Use the R₁ now and R₂ now readouts to explain the change. Why does the output remain between zero and the supply p.d.?

Show answer

Check for a rising output with the top thermistor and a falling output with the bottom thermistor. In the first case only the denominator R₁ + R₂ falls; in the second the bottom resistance loses a share of the total. With positive resistances, 0 < R₂/(R₁ + R₂) < 1, so the unloaded output lies between zero and 6.0 V. The model’s sensor calibration determines the exact readings.

Worked example 1

An output that rises with temperature

Problem

A potential divider across a 12 V supply has a fixed 4.0 kΩ resistor and an NTC thermistor whose resistance falls from 8.0 kΩ when cold to 2.0 kΩ when warm. Arrange it so the output rises with temperature, and find the output when cold and when warm.

Show full solution

  1. Arrangement

    Method

    Put the thermistor in the upper position and take the output across the fixed resistor.

    Reason

    As the thermistor’s resistance falls, the fixed resistor takes a larger share of the supply p.d.

    Working

    Answer

    Output across the 4.0 kΩ resistor.

  2. Cold

    Reason

    The fixed resistor is on top of the fraction.

    Working

    Answer

    Vₒᵤₜ = 12 × 4.0/(8.0 + 4.0) = 4.0 V

  3. Warm

    Working

    Answer

    Vₒᵤₜ = 12 × 4.0/(2.0 + 4.0) = 8.0 V

Guided practice 2

An LDR in the lower position

About 3 min

Problem

A potential divider across 9.0 V has a fixed 2.0 kΩ resistor at the top and an LDR at the bottom. The LDR’s resistance is 4.0 kΩ in dim light and 1.0 kΩ in bright light. Find the output across the LDR in each case.

Find both outputs

Show the steps Optional working
Unit: kΩ
Unit: V
Show the steps Optional working
Unit: kΩ
Unit: V

Hints

Hint 1

numerator

Which component is the output measured across?

Show full solution

  1. Both outputs

    Working

    Answer

    Dim: 9.0 × 4.0/(2.0 + 4.0) = 6.0 V. Bright: 9.0 × 1.0/(2.0 + 1.0) = 3.0 V. The output falls in bright light.

Try it yourself 3

Dimmer light, higher output

Minimal support

Problem

A street-light controller needs an output that rises as the light gets dimmer. It uses the same LDR and fixed resistor, but this time the output is taken across the upper component. Where should the LDR go? With a 9.0 V supply and 2.0 kΩ fixed resistor, calculate the upper-component output when the LDR changes from 1.0 to 4.0 kΩ.

Choose the position

Show the steps Optional working
Unit: kΩ
Unit: V
Show the steps Optional working
Unit: kΩ
Unit: V
LDR position

Hints

Hint 1

dim light

Which component is the output measured across, and how does its resistance change?

Show solution step by step

  1. Dim light

    Reason

    A larger resistance takes a larger share of the supply p.d.

    Working

    Answer

    As it gets darker, the p.d. across the LDR rises.

  2. Position

    Working

    Answer

    The output must be taken across the LDR itself, so the LDR goes in the upper position. Bright output: 9.0(1.0)/(2.0 + 1.0) = 3.0 V. Dim output: 9.0(4.0)/(2.0 + 4.0) = 6.0 V.

Exam-style question 1

Thermistor resistance from an output

5 marks

Examination question

A potential divider across a 10.0 V supply has a fixed 2.00 kΩ resistor at the top and an NTC thermistor at the bottom. The output across the thermistor is 6.00 V.

(a) Calculate the resistance of the thermistor. [3 marks]

(b) State and explain what happens to the output when the thermistor is warmed. [2 marks]

Write your answer before viewing the mark scheme

Show solution step by step

  1. (a) Resistance

    3 marks

    Method

    Use the ratio of the p.d.s.

    Reason

    The two resistors carry the same current, so their p.d.s are in the ratio of their resistances; the fixed resistor has 10.0-6.00 = 4.00 V.

    Working

    Answer

    RT/2.00 = 6.00/4.00, so RT = 3.00 kΩ

  2. (b) Warming

    2 marks

    Working

    Answer

    The thermistor’s resistance falls, so it takes a smaller share of the supply p.d.: the output falls.

Common mistakes

  • Putting the wrong resistance on top of the fraction; it must be the one the output is measured across.
  • Assuming a sensor always makes the output rise, whatever position it is in.
  • Mixing up the two sensors: an NTC thermistor’s resistance falls with temperature; an LDR’s falls with light.
  • Using the divider equation when the output is connected to a load that draws current.

Spotted an error? Report a correction

Syllabus and review details

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