temperature coefficient of resistance

Preksha

1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

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

Attached Thumbnails

   

Preksha

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?

azizlwl

Its not a linear function.

Ratch

Preksha,

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

Ratch

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

Preksha

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.

Preksha

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

Preksha

Does anybody else know how to go about it?

Ratch

Preksha,

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))?

Yes, that is the correct one.

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

They both can't be correct.

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

SammyS

Hello Preksha. Welcome to PF !

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

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