Transposition

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Paulh

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Jan 21, 2022
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Hello,

I'm trying to transpose the following Thermal Coefficient formula

R=Rref(1+a(t-Tref))

• R= New value of resistance
•Rref = Initial resistance
•a= Thermo Coefficient of material
•t= New temperature

I'm looking to rearrange formula in order to have Tref as the subject. I've tried different way, expanding brackets etc but the closest I've got to is finding minus Tref. I understand you can multiply each side by -1 to make it Tref but I was looking to find the step by step way of finding Tref without having to do that.

If anyone could show me how they would transpose it, it would be massively appreciated.

Thanks,
Paul
 
Last edited by a moderator:
Paulh said:
I'm looking to rearrange formula in order to have Tref as the subject.
Click to expand...
What is Tref? You didn't define it.
Paulh said:
I've tried different way, expanding brackets etc but the closest I've got to is finding minus Tref. I understand you can multiply each side by -1 to make it Tref but I was looking to find the step by step way of finding Tref without having to do that.
Click to expand...
Please share your work.
 
Paulh said:
Hello,

I'm trying to transpose the following Thermal Coefficient formula

R=Rref(1+a(t-Tref))

• R= New value of resistance
•Rref = Initial resistance
•a= Thermo Coefficient of material
•t= New temperature

I'm looking to rearrange formula in order to have Tref as the subject. I've tried different way, expanding brackets etc but the closest I've got to is finding minus Tref. I understand you can multiply each side by -1 to make it Tref but I was looking to find the step by step way of finding Tref without having to do that.

If anyone could show me how they would transpose it, it would be massively appreciated.

Thanks,
Paul
Click to expand...
Please show us your work regarding -Tref.
 
There are several ways to do it, including getting an expression for -Tref first. Why are you so reluctant to simply multiply both sides by -1?
 
Harry_the_cat said:
There are several ways to do it, including getting an expression for -Tref first. Why are you so reluctant to simply multiply both sides by -1?
Click to expand...
Hi, I guess I would just like to learn different methods and broaden my knowledge on transposition. If would be appreciated if anyone could help
 
Paulh said:
Please find my work attached. ThanksView attachment 30813
Click to expand...
That's exactly the way i would have done it. The last line would be to multiply both sides by -1 to get

Tref = t - (the fraction bit).

BTW where you have said you have "cross-mulitplied" what you have really done is got a common denominator and also divided both sides by 'a'.
The term "cross-multiply" is used when :
\(\displaystyle \frac{a}{b}=\frac{c}{d} \) becomes \(\displaystyle a.d = b.c\), ie you "cross-muliply" across an = sign.
 
Paulh said:
Hi, I guess I would just like to learn different methods and broaden my knowledge on transposition. If would be appreciated if anyone could help
Click to expand...
In this case, there is no "significantly" different method.
 
If you really don't like multiplying by -1 (which can be valid to avoid having to rewrite at the end), then after
1642858259151.png
you could add Tref to both sides (to make its coefficient positive), and then subtract the rest.
 
[math]R=R_{ref}(1+a(t-T_{ref}))\\ \frac{R}{R_{ref}}=1+a(t-T_{ref})\\ \frac{\frac{R}{R_{ref}}-1}{a}=t-T_{ref}\\ T_{ref}=t-\frac{\frac{R}{R_{ref}}-1}{a}\\ T_{ref}=t-\frac{R}{aR_{ref}}+\frac{1}{a}[/math]
 
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