Explicit Relationship Between Resistance and Temperature

However, it is important to note that this only works for certain temperature ranges, as mentioned in the original formula.In summary, the formula R=R_{0}[1+\alpha(T-T_{0})] can be used for calculating certain temperature ranges, but it can also be turned into a differential equation and solved explicitly. The resulting equation is R=\sqrt{2 \alpha T+C}, where alpha is the same as in the original formula and C is a constant of integration. This method has been successful in all examples attempted.
  • #1
marschmellow
49
0
Hi folks. So I've found in multiple places the formula

R=R[itex]_{0}[/itex][1+[itex]\alpha[/itex](T-T[itex]_{0}[/itex])]

with qualifications that for a given material it will only work for certain temperature ranges. However, I've never seen it turned into a differential equation and solved explicitly. It seems like a perfectly natural thing to do, and the result seems to be

R=[itex]\sqrt{2 \alpha T+C}[/itex]

where the alpha is the same alpha as in the previous equation and C is a constant of integration. Is there something wrong with what I'm doing?
 
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  • #2
It seems to work for me in all the examples I've tried. Thanks.No, there is nothing wrong with what you are doing. This equation is a special case of the general equation for a line, which when solved gives the result you have derived.
 

Related to Explicit Relationship Between Resistance and Temperature

1. What is the relationship between resistance and temperature?

The relationship between resistance and temperature is an inverse one. This means that as the temperature of a material increases, the resistance of that material decreases. Similarly, as the temperature decreases, the resistance increases.

2. Why does resistance change with temperature?

The change in resistance with temperature is due to the behavior of the atoms in a material. As the temperature increases, the atoms vibrate more vigorously, making it more difficult for electrons to flow through the material. This increased resistance is known as thermal resistance.

3. How is temperature coefficient of resistance (TCR) related to the resistance-temperature relationship?

The temperature coefficient of resistance (TCR) is a measure of how much the resistance of a material changes with temperature. It is directly related to the resistance-temperature relationship, as a material with a higher TCR will have a more significant change in resistance with temperature.

4. What is the significance of the resistance-temperature relationship in electronic devices?

The resistance-temperature relationship is essential in electronic devices as it can affect their performance. For example, if a material with a high TCR is used in a circuit, it may lead to a change in the circuit's resistance and cause issues with the device's functionality. Understanding this relationship is crucial in designing and selecting appropriate materials for electronic devices.

5. Can the resistance-temperature relationship be used to measure temperature?

Yes, the resistance-temperature relationship can be utilized to measure temperature. This is known as resistance temperature detectors (RTDs) and is commonly used in various industrial and scientific applications. RTDs work by measuring the change in resistance of a material with temperature, and this can provide an accurate and precise measurement of temperature.

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