Thermistor temperature sensitivity

In summary, in Section 15.3, it was mentioned that semiconductors have a high temperature sensitivity of conductivity, making them advantageous for precise temperature measurements compared to traditional thermocouples. These devices are called thermistors. For example, a 0.5 mm diameter and 10 mm long wire made of intrinsic silicon can have its temperature sensitivity calculated at 300 K if its resistance can be measured within 10^-3 Ω. To do this, an expression for dσ/dT can be developed using the equation relating temperature and conductivity, σ=σ_0e^(-E_g/2kT), and the formula for conductivity, σ=l/RA, where l is the length,
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Homework Statement


. (a) It was pointed out in Section 15.3 that the temperature sensitivity of conductivity in semiconductors make them superior to traditional thermocouples for certain high-precision temperature measurements. Such devices are referred to as thermistors. As a simple example, consider a wire of 0.5 mm in diameter × 10 mm long made of intrinsic silicon. If the resistance of the wire can be measured to within 10^-3 Ω, calculate the temperature sensitivity of this device at 300 K. (hint: The very small differences here may make you want to develop an expression for dσ/dT.)

Homework Equations


The Attempt at a Solution


I know the equation relating temperature and conductivity is

σ=σ_0e^(-E_g/2kT)

So I integrate the formula to get dσ/dT = [σ_0(E_g/2k)e^(-E_g/2kT)]/T^2

and I know the formula for conductivity
σ=l/RA
where l is the length, R resistance, and A area.

My problem is that I don't know how to relate resistance sensitivity to temperature sensitivity
 
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problem has been solved, disregard
 

What is a thermistor and how does it measure temperature?

A thermistor is an electronic component that changes its resistance in response to changes in temperature. It measures temperature by detecting the changes in its resistance and converting them into a corresponding temperature reading.

What is the temperature sensitivity of a thermistor?

The temperature sensitivity of a thermistor refers to its ability to accurately measure small changes in temperature. It is typically represented by the term "beta" (β) and is measured in degrees Celsius per ohm (°C/Ω). Higher values of beta indicate a more sensitive thermistor.

How is the temperature sensitivity of a thermistor calculated?

The temperature sensitivity (β) of a thermistor is calculated by taking the natural logarithm of the resistance ratio at two different temperatures (T1 and T2) and dividing it by the difference in temperature (T1-T2). This can be represented by the formula: β = ln(R1/R2) / (T1-T2)

What factors can affect the temperature sensitivity of a thermistor?

The temperature sensitivity of a thermistor can be affected by several factors, including the material it is made of, its physical size and shape, the circuit it is used in, and the operating temperature range. Additionally, the accuracy and precision of the manufacturing process can also impact the temperature sensitivity of a thermistor.

How can the temperature sensitivity of a thermistor be improved?

The temperature sensitivity of a thermistor can be improved by using a material with a higher beta value, choosing a smaller and more precise thermistor, and using a well-designed circuit that minimizes external influences on the thermistor's resistance. Additionally, proper calibration and testing of the thermistor can also help improve its temperature sensitivity.

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