Dependence of resistance on temperature

The value for t has a bigger impact on the accuracy of the formula, but the value for α also plays a role. By expanding the approximation to include more terms, it can be made more accurate, but as long as t is small and the coefficient for the additional terms is not large, the original formula is still a reasonable approximation.
  • #1
Karol
1,380
22

Homework Statement


The book says the formula is accurate as long as t and α are small. i understand about t but why also α?

Homework Equations


Resistance R: ##R=R_0(1+\alpha t)##

The Attempt at a Solution


According to the graph (see picture) α is the slope and is suited for every material, so only t makes a difference, because of the limited linear approximation
 

Attachments

  • 5-15.jpg
    5-15.jpg
    4.3 KB · Views: 379
Physics news on Phys.org
  • #2
I agree with you. We could expand the approximation to more terms to make it more accurate: ##R=R_0(1+\alpha t + \beta t^2 + ...)##. The approximation ## R=R_0(1+\alpha t)## is reasonable if t is small and ##\beta## not large; it has nothing to do with ##\alpha##.
 
  • #3
Thanks
 

1. How does temperature affect resistance?

As temperature increases, the resistance of a material typically increases as well. This is because the atoms in a material vibrate more at higher temperatures, causing more collisions with electrons and making it harder for them to flow through the material.

2. What is the relationship between temperature and resistance?

The relationship between temperature and resistance is typically linear. This means that as temperature increases, resistance also increases in a predictable and proportional manner.

3. Why does resistance increase with temperature?

The increase in resistance with temperature is due to the increase in collisions between atoms and electrons. This phenomenon is known as thermal agitation and it makes it more difficult for electrons to flow through the material, resulting in higher resistance.

4. How does the type of material affect the dependence of resistance on temperature?

The type of material can greatly affect the dependence of resistance on temperature. Some materials, such as metals, have a positive temperature coefficient, meaning their resistance increases with temperature. Other materials, like semiconductors, have a negative temperature coefficient, meaning their resistance decreases with temperature.

5. How is the dependence of resistance on temperature used in practical applications?

The dependence of resistance on temperature is used in a variety of practical applications. For example, it is used in thermistors, which are temperature-sensitive resistors used for temperature measurement and control. It is also used in circuit protection devices, such as fuses and circuit breakers, which use the increase in resistance with temperature to prevent damage to electronic components.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
616
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
817
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
4K
  • Introductory Physics Homework Help
Replies
14
Views
488
Back
Top