GCSE Physics Tutorial: Relationship of a Thermistor's Resistance with Temperature

A thermistor is a type of temperature-sensitive resistor that exhibits changes in resistance with variations in temperature. Understanding the relationship between a thermistor's resistance and temperature is crucial for various applications, including temperature measurement and control in electronic circuits. In this tutorial, we will explore the characteristics of a thermistor and the mathematical relationship that describes its resistance-temperature behaviour.

1. What is a Thermistor?

• A thermistor is a semiconductor device made from metal oxides, such as manganese, nickel, or cobalt. These materials possess temperature-dependent electrical properties, which make thermistors highly sensitive to changes in temperature.

• Thermistors come in two types: Positive Temperature Coefficient (PTC) and Negative Temperature Coefficient (NTC). In this tutorial, we will focus on NTC thermistors, which exhibit a decrease in resistance as temperature increases.

2. Resistance-Temperature Relationship:

• NTC thermistors follow an exponential relationship between their resistance (R) and temperature (T). This relationship can be expressed mathematically as:

R = R₀ * e^(β * (1/T - 1/T₀))

where:

• R: The resistance of the thermistor at temperature T (measured in ohms, Ω).

• R₀: The resistance of the thermistor at a reference temperature T₀ (usually specified at 25°C).

• β: The material constant (in Kelvin, K) that characterises the thermistor's temperature sensitivity. It determines the rate of change of resistance with temperature.

• T: The absolute temperature of the thermistor in Kelvin (K).

3. Key Points:

• As the temperature increases, the resistance of an NTC thermistor decreases exponentially. Conversely, as the temperature decreases, the resistance increases.

• The resistance-temperature relationship of a thermistor is nonlinear, unlike the linear behaviour of standard resistors.

• The material constant β is specific to each thermistor and is provided by the manufacturer. It is essential for accurately predicting the thermistor's resistance at different temperatures.

4. Practical Applications:

• NTC thermistors are widely used in temperature sensing and control applications. For example:

  • Temperature sensors in thermostats, weather stations, and temperature-controlled systems.

  • Over-temperature protection in electronic devices to prevent damage due to excessive heat.

  • Temperature compensation in circuits to ensure accurate performance of components over a range of temperatures.

5. Safety Precautions:

• Handle thermistors and other electronic components with care to avoid damage.

• When applying a voltage or current to a thermistor, ensure that the power supply is set to safe and suitable levels.

6. Summary: The resistance of an NTC thermistor decreases exponentially as the temperature increases. This nonlinear relationship is a key characteristic of thermistors, allowing them to be highly sensitive temperature sensors used in a wide range of electronic applications.

By understanding the resistance-temperature relationship of thermistors, you can design and implement accurate temperature sensing and control systems. NTC thermistors offer a practical and reliable solution for temperature-related tasks, making them valuable components in various electronic devices and systems.

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