Thermistor graphs

A thermistor graph shows how a thermistor's resistance changes with temperature. For the thermistors in GCSE and A-level Physics, the resistance falls as the temperature rises, steeply at first and then more gently, so the graph is a downward curve that levels off. That makes a thermistor a simple temperature sensor.

Thermistor resistance against temperature graph

AQA's GCSE specification states that the resistance of a thermistor decreases as the temperature increases. The graph below is for a typical thermistor: x is the temperature in °C and y is the resistance in kΩ.

Three things to notice:

• It goes down. Hotter means lower resistance. This kind of thermistor is called NTC, for negative temperature coefficient, and AQA's A-level specification says only NTC thermistors are considered.
• It is a curve, not a straight line. The resistance changes most at low temperatures. Here it drops from 8.0 kΩ to 4.4 kΩ between 0 °C and 20 °C, but only from 1.3 kΩ to 0.73 kΩ between 60 °C and 80 °C.
• It never reaches zero. The curve levels off towards the temperature axis.

Why does the resistance fall?

A thermistor is made from a semiconductor. Heating it releases more charge carriers that are free to move, so a bigger current can flow for the same potential difference. That increase outweighs the extra vibration of the atoms, which on its own would raise the resistance, as it does in a metal wire.

Reading values from a thermistor graph

1. Find the temperature on the horizontal axis.
2. Go straight up to the curve.
3. Go straight across to the resistance axis and read the value, checking the units (Ω or kΩ).

Example 1: current from the graph

Use the graph above. The thermistor is at 40 °C, with 3.0 V across it. Find the current.

• From the graph, the resistance at 40 °C is 2.4 kΩ = 2400 Ω.
• I = V ÷ R = 3.0 ÷ 2400 = 0.00125 A = 1.25 mA.

Going the other way, you can measure a thermistor's resistance and read off the temperature. A resistance of 0.73 kΩ means the thermistor is at about 80 °C.

Try one: find a resistance from a graph, then press Mark to check it in the Electricity course.

Investigating a thermistor

AQA's GCSE specification asks you to investigate the relationship between the resistance of a thermistor and temperature. A typical method:

1. Connect the thermistor to an ohmmeter, or in series with an ammeter and a supply, with a voltmeter across it.
2. Put the thermistor in a beaker of water with a thermometer, keeping the leads dry.
3. Heat the water in steps, stirring, and record the temperature and resistance (or V and I, then R = V ÷ I) at each step.
4. Plot resistance against temperature and draw a smooth curve of best fit.

Waiting a minute at each temperature lets the thermistor reach the temperature of the water before you take a reading.

The I-V graph of a thermistor

At a fixed temperature, a thermistor behaves like an ordinary resistor, so its I-V graph is straight and passes through the origin. If the current is large enough to warm it, its resistance falls as it heats, and the graph curves upwards: the current rises faster than the potential difference. The I-V characteristics guide compares this with resistors, filament lamps and diodes.

Using a thermistor as a temperature sensor

AQA lists a thermostat as an application you need to know. The usual circuit is a potential divider: a thermistor in series with a fixed resistor across a supply. AQA's A-level specification names thermistors and LDRs as examples to use in potential dividers.

With the output taken across the fixed resistor, warming the thermistor lowers its resistance, so it takes a smaller share of the supply and the output voltage rises. That output can switch on a fan or an alarm when it gets hot. Swap the two components round and the output rises when it gets cold instead, which suits a heating thermostat.

Example 2: a temperature sensor

A thermistor with the graph above is in series with a 1.0 kΩ fixed resistor across a 5.0 V supply. Find the output voltage across the fixed resistor at 20 °C and at 80 °C.

The output rises from about 0.9 V to 2.9 V as the temperature goes up. You can build this circuit and watch the voltages change in the circuit builder, or work out other values with the voltage divider calculator.

Thermistor vs LDR

The two graphs have the same falling, curved shape. The light dependent resistor guide covers the LDR side.

Common mistakes

• Drawing a straight line. The resistance against temperature graph is a curve.
• Getting the direction wrong. For an NTC thermistor, resistance goes down as temperature goes up.
• Ignoring the units on the axis. Convert kΩ to Ω before using V = IR.
• Mixing up the sensor output. Decide which component the output is across before saying whether it rises or falls.
• Saying a thermistor has no resistance when hot. It is lower, never zero.

Resistance and Ohm's law are in the Electricity course. For practice in a short timed paper, try today's GCSE Physics Higher or A-level Physics: Year 1 paper.

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Physics · Electricity and magnetismI-V characteristics: resistor, filament lamp and diodeI-V characteristic graphs for a resistor, a filament lamp and a diode: what each shape means, how to find resistance from them, and the circuit you use.