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Equation not solving in Mathcad Prime

JH_9781973
6-Contributor

Equation not solving in Mathcad Prime

  1. T(R) -> Temperature is a function of resistance.  Therefore, if I want to find out a Temperature at a specific Resistance you can plug in a value of 10 kohms and get a corresponding value of Temperature -> degrees C.  -> This is Given.
  2. 3 Constants are provided and fixed.  They are givens.

JH_9781973_0-1631639967805.png

 

 

Goal -> Rewrite T(R) Equations so that Resistance is a function of Temperature -> i.e. R(T) := ???????

 

I would like the equation in a format where I plug in a temperature and get a corresponding resistance.

 

Again I am looking to rewrite T(R) as R(T):=

 

Can somebody help 

 

ACCEPTED SOLUTION

Accepted Solutions
LucMeekes
23-Emerald III
(To:JH_9781973)

Note that, due to the third power, you get three possible solutions of R for every value of T.

So here is the general solution:

LucMeekes_0-1631648926996.png

With x, y and z defined numerically, you can have:

LucMeekes_1-1631648963266.png

Only the first of the three solutions gives a real answer (the other two are complex).

Assuming you don't want the complex answers, you can set:

LucMeekes_2-1631649100418.png

which yields:

LucMeekes_3-1631649126153.png

and of course, with:

LucMeekes_4-1631649222638.png

you get:

LucMeekes_5-1631649236784.png

Success!

Luc

View solution in original post

7 REPLIES 7
Werner_E
25-Diamond I
(To:JH_9781973)

You may use a solve block or the "root" function.

Werner_E_1-1631644818670.png

 

 

The names T_ and R_ were chosen for the function arguments (and later for the abscissa variables) to avoid conflicts with the name of the two functions. Feel free to change them as you think is appropriate.

 

P6 sheet attached

 

StuartBruff
23-Emerald III
(To:Werner_E)

Hi Werner,

 

Does the OP's cube enclose the other ln(R) expression, as well?

 

(I think the question also asked for a rewrite.  I'm guessing that didn't mean "solve by any means that works"?)

 

2021 09 14 B.png

 

Stuart

StuartBruff
23-Emerald III
(To:StuartBruff)


@StuartBruff wrote:

Hi Werner,

 

Does the OP's cube enclose the other ln(R) expression, as well?

 


Forget the above. You are correct.  It's my eyes that are the problem.  Definitely time for new glasses.  And there goes my new laptop fund.  😞

 

Stuart

StuartBruff
23-Emerald III
(To:StuartBruff)

As partial penance for my earlier faux pas, here's a Prime 7 symbolic solution that seems to agree with Luc's but gives a slightly different approach that is, in principle, solvable by hand using the standard cubic solution. 

 

 

Stuart

LucMeekes
23-Emerald III
(To:StuartBruff)

So it is symbolically solvable with Prime as well. Can Prime do it from the original equation as well?

(I support your argument "for example, copying the wrong expressions, and failing to update the function definition after any changes to the original expression.", but you already used such an error prone action by copying the expression to the definition of rrexp...)

 

Success!
Luc

StuartBruff
23-Emerald III
(To:LucMeekes)


@LucMeekes wrote:

So it is symbolically solvable with Prime as well. Can Prime do it from the original equation as well?


It doesn't look like it, Luc.  I got the standard "no solution was found" error message. 

 


(I support your argument "for example, copying the wrong expressions, and failing to update the function definition after any changes to the original expression.", but you already used such an error prone action by copying the expression to the definition of rrexp...)

Welcome to the wonderful world of "Do as I say, not as I do".  🙂

 

It's actually just an exercise in risk vs performance management.   The symbolic processor (SP) is rather tardy on my PC and it was expedient to gamble on correct copy&paste for a one-time example.   Given that the SP is so reluctant to find a direct solution, any other method requires some form of manual manipulation, thus introducing risk, anyway.   The attached worksheet goes some way towards being a better example.

 

Stuart

LucMeekes
23-Emerald III
(To:JH_9781973)

Note that, due to the third power, you get three possible solutions of R for every value of T.

So here is the general solution:

LucMeekes_0-1631648926996.png

With x, y and z defined numerically, you can have:

LucMeekes_1-1631648963266.png

Only the first of the three solutions gives a real answer (the other two are complex).

Assuming you don't want the complex answers, you can set:

LucMeekes_2-1631649100418.png

which yields:

LucMeekes_3-1631649126153.png

and of course, with:

LucMeekes_4-1631649222638.png

you get:

LucMeekes_5-1631649236784.png

Success!

Luc

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