Temperature dependence of Resistance

In summary, the conversation discusses a question about finding the temperature coefficient of resistance for a wire with given resistances at two different temperatures. Two methods are proposed and compared, with the first method giving a mean temperature coefficient and the second method giving the actual coefficient. It is determined that the actual temperature coefficient is measured with respect to the resistance at 0 C.
  • #1
zorro
1,384
0

Homework Statement


A wire has a resistance of 2 ohm at 25 C and 2.5 ohm at 100 C . Find the temperature coefficient of resistance of the wire.

The Attempt at a Solution



This question is a very easy one, but I had a doubt -
R=Ro(1 + αθ)
Here θ is the change in temperature.

I proceed in 2 ways:
1) We can take Ro = 2 ohm at 25 C so that the equation becomes
2.5 = 2 [1 + α(100-25)]
On solving, α=3.33 x 10-3

2) Take Ro as the resistance at 0 C

2 = Ro(1 + 25α)
2.5 = Ro(1 + 100α)

On solving, α = 3.64 x 10-3

Which one is correct and why?
 
Physics news on Phys.org
  • #2
How do you know the resistance at 0C?
 
  • #3
R1 = Ro( 1 + αθ1)

R2 = Ro(1 + αθ2)

When you solve for α, you will get

α = (R2 - R1)/(R1θ2 - R2θ1)

Now find α.
 
  • #4
rock.freak667 said:
How do you know the resistance at 0C?

I don't know the resistance. On dividing the two equations, Ro gets cancelled.
 
  • #5
rl.bhat said:
R1 = Ro( 1 + αθ1)

R2 = Ro(1 + αθ2)

When you solve for α, you will get

α = (R2 - R1)/(R1θ2 - R2θ1)

Now find α.

Why can't we use just one equation as I showed?...thats my doubt.
 
  • #6
In the first case, we get mean temperature coefficient of resistance for a selected pair of temperatures.

In the second case, it is the actual α for particular temperature.
 
  • #7
rl.bhat said:
In the first case, we get mean temperature coefficient of resistance for a selected pair of temperatures.

In the second case, it is the actual α for particular temperature.

Is it that the actual temperature coefficient of resistance is measured w.r.t. the resistance at 0 C?
 
  • #8
Abdul Quadeer said:
Is it that the actual temperature coefficient of resistance is measured w.r.t. the resistance at 0 C?

Yes. In the table of constants, α for different materials is given for 20oC.
 

1. What is the temperature coefficient of resistance?

The temperature coefficient of resistance (TCR) is a measure of how much a material's resistance changes with temperature. It is typically expressed in units of ohms per degree Celsius (Ω/°C) or ohms per degree Kelvin (Ω/K).

2. How does temperature affect resistance?

As temperature increases, the resistance of most materials also increases. This is because higher temperatures cause atoms to vibrate more and disrupt the flow of electrons through the material, resulting in higher resistance.

3. What is the relationship between temperature and resistance?

The relationship between temperature and resistance can be described by the following equation: R = R0(1 + α(T - T0)), where R is the resistance at temperature T, R0 is the resistance at reference temperature T0, and α is the temperature coefficient of resistance. This equation shows that resistance increases linearly with temperature.

4. How do different materials respond to changes in temperature?

Different materials have different TCR values, which means they respond differently to changes in temperature. For example, metals typically have positive TCR values, while semiconductors and insulators can have positive or negative values.

5. Why is temperature dependence of resistance important?

Understanding the temperature dependence of resistance is important in many fields, such as electronics, materials science, and engineering. It allows us to predict how a material will behave at different temperatures and design systems that can operate reliably under varying temperature conditions.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
665
  • Introductory Physics Homework Help
Replies
7
Views
503
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
294
  • Introductory Physics Homework Help
Replies
16
Views
917
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
1K
Back
Top