Temperature coefficient of resistance calculation

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  • #1
Preksha
5
0


When we are supposed to calculate the value of "temperature coefficient of resistance " i.e. α , how are we supposed to choose between the following two formulae :

α = (R2 - R1) / (R1*T2 - R2* T1 )

or

α = (R2 - R1)/ [ R1 *( T2-T1) ]

I have attached scanned pictures of two similar questions . I can't understand as to why diff. formulae are being used in both of them
 

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  • #2


I am new to this forum, so I have no idea as to how things work here. I wanted to know, till when , can I expect a reply to my question?
 
  • #3


Its not a linear function.
http://img405.imageshack.us/img405/9383/co3wv.jpg
 
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  • #4


Preksha,

When we are supposed to calculate the value of "temperature coefficient of resistance " i.e. α , how are we supposed to choose between the following two formulae :

My physics book agrees with this link, which is a different formula than what you submitted.

Ratch

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html
 
  • #5


Ratch said:
Preksha,



My physics book agrees with this link, which is a different formula than what you submitted.

Ratch

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html

My second formula is the same as yours.

The first one can be derived as
R1 = R0(1 + aT1) ...(i)
R2 = Ro (1 +aT2)... (ii)

Divide (i) by (ii)
And you'll get the 1st formula.
Both formulae are correct.
The difference in their usage is that When T1 is 0deg. The 1st formula changes to the second one. But when I came across this particular question where T1 =20 deg (the one I've posted before) and still they are using the second formula, i got thoroughly confused. So, if you have any idea, please help.
 
  • #6


azizlwl said:
Its not a linear function.
http://img405.imageshack.us/img405/9383/co3wv.jpg

I didnt get you :O How does linearity play a role in this question?
 
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  • #7


Does anybody else know how to go about it?
 
  • #8


Preksha,

When we are supposed to calculate the value of "temperature coefficient of resistance " i.e. α , how are we supposed to choose between the following two formulae :

α = (R2 - R1) / (R1*T2 - R2* T1 )

or

α = (R2 - R1)/ [ R1 *( T2-T1) ]

Use the one that is correct. The second formula agrees with the link I posted, so use that. The first formula can be arranged to R=Ro(1+αT)/(1+α*To). Does that make sense compared to the first formula, which is R=Ro(1+α(T-To))?

My second formula is the same as yours.

Yes, that is the correct one.

The first one can be derived as
R1 = R0(1 + aT1) ...(i)
R2 = Ro (1 +aT2)... (ii)

Divide (i) by (ii)
And you'll get the 1st formula.

Your derivation is wrong. R1 = Ro(1+α(T1-To))

Both formulae are correct.

They both can't be correct.

The difference in their usage is that When T1 is 0deg. The 1st formula changes to the second one. But when I came across this particular question where T1 =20 deg (the one I've posted before) and still they are using the second formula, i got thoroughly confused. So, if you have any idea, please help.

In order for the formula to be correct, it must be correct across the whole temp range, not just one temperature. Use the one proven to be correct.

Ratch
 
  • #9


Preksha said:
I am new to this forum, so I have no idea as to how things work here. I wanted to know, till when , can I expect a reply to my question?
Hello Preksha. Welcome to PF !

Be patient. While you're waiting, read the rules for this Forum, particularly the section regarding Homework Help.

Rules
 

What is the temperature coefficient of resistance?

The temperature coefficient of resistance is a measure of how much the resistance of a material changes with temperature. It is typically represented by the symbol alpha (α) and is expressed in units of ohms per degree Celsius (Ω/°C).

How is the temperature coefficient of resistance calculated?

The temperature coefficient of resistance is calculated by taking the change in resistance (ΔR) over the change in temperature (ΔT) and dividing it by the initial resistance (R0) multiplied by the initial temperature (T0). This can be expressed mathematically as α = (ΔR/R0)/(ΔT/T0).

What is a positive temperature coefficient of resistance?

A positive temperature coefficient of resistance means that as the temperature increases, the resistance of the material also increases. This is common in metals and is due to the increased thermal vibration of atoms which makes it more difficult for electrons to flow through the material, resulting in a higher resistance.

What is a negative temperature coefficient of resistance?

A negative temperature coefficient of resistance means that as the temperature increases, the resistance of the material decreases. This is often seen in semiconductors and is due to the increased number of free electrons available for conduction at higher temperatures.

Why is the temperature coefficient of resistance important?

The temperature coefficient of resistance is important because it allows us to predict how the resistance of a material will change with temperature. This is essential for designing electronic circuits that are stable and reliable over a range of temperatures. It also helps in selecting the right materials for specific applications where temperature changes are expected.

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