The resistance of a thermistor

[Mishal666]

Homework Statement

The resistance of thermistor over a limit range of temperature is given by equation R=c/(T-203). Where c is constant ant T is absolute temperature. What would be temperature on centigrade scale of thermistor at absolute temperature T=300k?

Homework Equations

i)R=c/(T-203)

ii) see pic

The Attempt at a Solution

See pic




But the answer is 47.3 degree. I don't know where am I doing this wrong. Please help.

 

[berkeman]

Welcome to the PF.

Sorry, your picture is not readable. Can you type your work into the forum for us to check? Thank you.

 

[Merlin3189]

I agree with the starting formulae:

$R_{300}=\frac {c} {97} \ \ \ R_{273}=\frac {c} {70} \ \ \ R_{373}=\frac {c} {170}$

and θ or $T_{300} = \frac {R_{300} -R_{273} } {R_{373} -R_{273} } \times {100^o C}$

Where it seems to go wrong is now as you put the numbers into the formula.
You seem to calculate $\frac {R_{300} } {R_{373}} - \frac {R_{273} } {R_{273} }$

 

[Merlin3189]

Edit: Oh! Missed a bit. $\left ( \frac {R_{300} } {R_{373}} - \frac {R_{273} } {R_{273} } \right ) \times {100}$

 

[Mishal666]

Edit: Oh! Missed a bit. $\left ( \frac {R_{300} } {R_{373}} - \frac {R_{273} } {R_{273} } \right ) \times {100}$

I don't know how to solve fractions

 

[berkeman]

I don't know how to solve fractions

Are you familiar with the term "common denominator"?

 

[Merlin3189]

Hold on a sec! The expression I wrote is the wrong method that OP did.
The correct calculation is the easy one!
Just do the sum on the top, do the sum on the bottom, then divide top by bottom and finally multiply by 100.

 

[Mishal666]

Are you familiar with the term "common denominator"?

Yup , but I got different denominators. T300= (c/97-c/70.15 ÷ c/170.15 - c/70.15) *100

 

[Merlin3189]

T300= (c/97-c/70.15 ÷ c/170.15 - c/70.15) *100

Just put in extra brackets T300= ( (c/97-c/70.15 ) ÷ (c/170.15 - c/70.15)) *100

 

[Mishal666]

I got your point. The problem is I can't solve unlike denominators.

 

[Merlin3189]

You haven't got unlike denominators. You've got a single denominator
$T_{300} = \frac {R_{300} -R_{273} } {R_{373} -R_{273} } \times {100^o C}$
So the denominator is simply $\left ( R_{373} -R_{273} \right )$
That big horizontal line in the fraction means, take all of the top (ie. work out the top into one number) and divide by all of the bottom (after first working that out to one number.)

 

[Mishal666]

T300= ( (c/97-c/70.15 ) ÷ (c/170.15 - c/70.15)) *100

I'm not supposed to solve this equation?

 

[Merlin3189]

I don't call that an equation: I call it a sum. Or more accurately, two takeaways, a division and a multiplication.

Most modern calculators will accept that as it's written, so long as you put in the correct brackets, or the big horizontal line.

I don't want to be unsympathetic, but I'm not sure how you can use any formulae if you can't put the numbers into a calculator correctly. Most people have their problems trying to work out the formula, or putting the right numbers into the formula. You did all that, no problem. It's just the easy bit you fell down on!

Edit: Ahh! I just noticed why you called it an equation: You've left the c in.
What you should notice is that all the numbers in the fraction are multiplied by c. So it does not matter what number c is, the result will be the same. So you can just "cancel" the c's, ie. rub them out, ignore them, call them 1, whatever. Try it with say, 10c / 5c Whatever number you say c is, you get the same answer, 10/5 = 2 If you had (12c - 4c)/(5c -3c) it works the same and you get (12-4)/(5-3)=4 even if you said c was 10 it would become (120-40)/(50-30)=80/20=4
Just be careful if every number doesn't have the same letter. It wouldn't work for (10-2c)/(4c) say : that would have different answers depending on what c was.

Edit2: Blimey! It's so easy to miss things. I should have said, you can make c any number except 0. Zero just gives you 0/0 and that's useless.

 

[kuruman]

What would be temperature on centigrade scale of thermistor at absolute temperature T=300k?

If the thermistor is at 300 K, then on the centigrade scale its temperature will be ... ? As per forum rules I cannot give the answer, but isn't it kinda obvious that one needs to convert from Kelvin to Celsius? I'm sorry, but am I missing something?

 

[Mishal666]

I don't call that an equation: I call it a sum. Or more accurately, two takeaways, a division and a multiplication.

Most modern calculators will accept that as it's written, so long as you put in the correct brackets, or the big horizontal line.

I don't want to be unsympathetic, but I'm not sure how you can use any formulae if you can't put the numbers into a calculator correctly. Most people have their problems trying to work out the formula, or putting the right numbers into the formula. You did all that, no problem. It's just the easy bit you fell down on!

Edit: Ahh! I just noticed why you called it an equation: You've left the c in.
What you should notice is that all the numbers in the fraction are multiplied by c. So it does not matter what number c is, the result will be the same. So you can just "cancel" the c's, ie. rub them out, ignore them, call them 1, whatever. Try it with say, 10c / 5c Whatever number you say c is, you get the same answer, 10/5 = 2 If you had (12c - 4c)/(5c -3c) it works the same and you get (12-4)/(5-3)=4 even if you said c was 10 it would become (120-40)/(50-30)=80/20=4
Just be careful if every number doesn't have the same letter. It wouldn't work for (10-2c)/(4c) say : that would have different answers depending on what c was.

Edit2: Blimey! It's so easy to miss things. I should have said, you can make c any number except 0. Zero just gives you 0/0 and that's useless.
It seems helpful :)

 

[Mishal666]

If the thermistor is at 300 K, then on the centigrade scale its temperature will be ... ? As per forum rules I cannot give the answer, but isn't it kinda obvious that one needs to convert from Kelvin to Celsius? I'm sorry, but am I missing something?

If the thermistor is at 300 K, then on the centigrade scale its temperature will be ... ? As per forum rules I cannot give the answer, but isn't it kinda obvious that one needs to convert from Kelvin to Celsius? I'm sorry, but am I missing something?

i converted and got negative values. That messed up my mind.

 

[kuruman]

converted and got negative values. That messed up my mind.

Can you show your conversion and the value you got?

 

[Mishal666]

Can you show your conversion and the value you got?

I don't call that an equation: I call it a sum. Or more accurately, two takeaways, a division and a multiplication.

Most modern calculators will accept that as it's written, so long as you put in the correct brackets, or the big horizontal line.

I don't want to be unsympathetic, but I'm not sure how you can use any formulae if you can't put the numbers into a calculator correctly. Most people have their problems trying to work out the formula, or putting the right numbers into the formula. You did all that, no problem. It's just the easy bit you fell down on!

Edit: Ahh! I just noticed why you called it an equation: You've left the c in.
What you should notice is that all the numbers in the fraction are multiplied by c. So it does not matter what number c is, the result will be the same. So you can just "cancel" the c's, ie. rub them out, ignore them, call them 1, whatever. Try it with say, 10c / 5c Whatever number you say c is, you get the same answer, 10/5 = 2 If you had (12c - 4c)/(5c -3c) it works the same and you get (12-4)/(5-3)=4 even if you said c was 10 it would become (120-40)/(50-30)=80/20=4
Just be careful if every number doesn't have the same letter. It wouldn't work for (10-2c)/(4c) say : that would have different answers depending on what c was.

Edit2: Blimey! It's so easy to miss things. I should have said, you can make c any number except 0. Zero just gives you 0/0 and that's useless.

i got 47.1 degree. Thankyou so much

 

[kuruman]

You have a thermistor at temperature 300 K. What is its temperature in the centigrade scale?
http://www.rapidtables.com/convert/temperature/how-kelvin-to-celsius.htm