Re: A little help with some basic calculus
From: Ari (NOaristotlepolonium_at_yahoo.comSPAM)
Date: 02/06/05
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Date: Sat, 5 Feb 2005 23:40:21 -0600
"Steven O." <null@null.com> wrote in message news:b68b011nureekgu9ghd8hfgbrbcmvqkt9q@4ax.com...
> Okay, this is a homework problem, but I'm middle-aged and already have
> my B.A., and just returning to school to pick up a little more
> knowledge. Besides, you can clearly see (below) that I'm giving this
> my best shot. So, someone please help me out here. For a basic
> electronics class, we are given that the temperature coefficient for
> the resistance of a material is given by:
>
> a (for alpha) = (1/R)(dR/dT), and we are asked to show that:
>
> R2 = {[ 1 + a(T1 - Ts) ] / [1 + a(T2 - Ts)]} R2
>
> where Ts is the "reference temperature".
>
> But here is how the math works out for me:
>
> a = (1/R)(dR/dT)
>
> dR/R = a dT Take indefinite integral of both sides....
>
> ln R = a T + Ts, where Ts is said reference temperature
>
> Assume R1 corresponds to T1, and R2 to T2, then....
>
> ln R1 = a T1 + Ts, and ln R2 = a T2 + Ts
>
> ln R1 - ln R2 = a (T1 - T2), so Ts is already gone.
>
> ln (R1/R2) = a (T1 - T2), exponentiate both sides...
>
> R1/R2 = exp (a [T1 - T2])
>
> exp x is approximately 1 + x, so we have,
>
> R1 = R2 { (1 + a [T1 - T2]) }, which is not the professor's desired
> result. Did the professor screw up, or have I forgotten some basic
> calculus or algebra in twenty years since college? Thanks in advance
> for all replies....
>
> Steve O.
>
>
> "Spying On The College Of Your Choice" -- How to pick the college that is the Best Match for a high school student's needs.
> www.SpyingOnTheCollegeOfYourChoice.com
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Is the equation
R2 = {[ 1 + a(T1 - Ts) ] / [1 + a(T2 - Ts)]} R2
correct? Should R2 appear on both sides of the equation?
Aristotle Polonium
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