For the thermistor of Fig. 40 , determine the dynamic rate of change in specific resistance with

For the thermistor of Fig. 40 , determine the dynamic rate...

Key Concepts

Thermistor

A thermistor is a type of resistor whose resistance varies significantly with temperature, making it suitable for temperature sensing and control. Its response is typically non-linear, meaning that the relationship between temperature and resistance does not follow a simple straight line. This characteristic allows thermistors to be highly sensitive over specific temperature ranges, which is useful in precise temperature measurement and compensation applications.

Temperature Coefficient of Resistance

This concept refers to the rate at which a material's resistance changes with temperature. It is typically expressed as the derivative dR/dT. In devices like thermistors, understanding this coefficient is essential because it governs how the sensor will react to temperature variations, influencing design decisions in applications requiring precise thermal control or measurement.

Dynamic Rate of Change

The dynamic rate of change in resistance with temperature, represented by dR/dT, quantifies how rapidly the resistance of a thermistor changes with slight variations in temperature. This parameter helps in assessing the sensitivity of the thermistor at different temperatures and is crucial for applications where small temperature changes need to be detected accurately.

Logarithmic Scale Analysis

The use of a logarithmic scale in plotting data is significant when dealing with quantities that span several orders of magnitude, such as the resistance of a thermistor over a wide temperature range. A vertical log scale can reveal exponential trends and make it easier to compare relative changes in resistance at various temperature levels, highlighting which temperature ranges exhibit the greatest sensitivity.

Transcript

00:01 All right, this particular problem gives you a really nice formula.

00:06 So we're going to write it up here and it tells you t equals 1 over, and they say that's a plus b times the natural log of r plus c times the natural log of x that gets cubed minus 273 .15.

00:36 Okay, i think i copied that right.

00:41 All right, and this just becomes a big plug and chug problem, but you need to be able to actually plug it into your calculator.

00:51 The first trick that i'm going to teach here is to use the alpha y equals key.

00:56 So hit the alpha button on your graphing calculator and then the y equals, and that brings up a fraction option for you.

01:04 I think that's really important.

01:06 Now, if you want to just plug the number in there, you can do that, but i think it's easier to go into y sub one and we're going to graph this, and then you can grab both answers from the graph.

01:17 All right, so go into y equals, hit your alpha y equal button to get your fraction.

01:22 Your numerator is going to be one, and then you just hit your down arrow.

01:27 And then i want to show you something else here.

01:30 Start your denominator with a parentheses, and then type in the value of a that they give you, 8 .27153.

01:37 And then you want to hit second, the parentheses, or excuse me, apostrophe or comma, whatever they call that.

01:46 Second, and then this key.

01:48 And then that brings up what they call ee.

01:51 That's your exponent key.

01:52 All right, and then it'll give you an e, and then all you have to do is a negative four.

01:56 Instead of the times 10 to the negative fourth power and all that other stuff.

01:59 It's a little bit quicker and a little bit easier.

02:02 All right, we're going to do it again for b, 2 .08796.

02:10 Then you're going to hit second, that comma to get up the ee to the negative fourth power.

02:15 There you go.

02:16 And then start another parentheses, and then do your ln.

02:19 Your ln key is its own key on the side.

02:21 It's over by the four.

02:23 Then it starts a parentheses for you.

02:26 You're going to type in the x.

02:28 You're going to need to close that parentheses and the natural log parentheses.

02:33 You need them both closed.

02:34 Before you begin the plus, the c value, start with a parentheses 8 .060985.

02:44 Whoopsie, that's supposed to be a five.

02:46 That's my head working.

02:50 There we go.

02:51 Eight, five, and then e to the negative eighth power this time.

02:56 And then you want to start another parentheses ln.

03:00 It starts the parentheses.

03:03 You hit the hidden x.

03:05 You'll close that parentheses, close that next parentheses.

03:08 Then you'll do the up arrow and then not an a, an up arrow, and then that'll be a cubed, up arrow three.

03:17 It still won't let me scroll.

03:20 Then you'll have to hit your right arrow key a couple times to make sure that you get out of the denominator.

03:26 And then you'll hit the minus 273 .15.

03:31 But again, that needs to be flush and even.

03:34 This guy right here needs to be flush and even with the fraction, right? so that fraction is continuing over here.

03:40 And it needs to be even with that right there.

03:43 I'm sorry, there just isn't enough room on this little thing.

03:46 And it won't let me scroll.

03:48 All right? then don't hit graph because it's not going to fit.

03:54 So you'll have to go into your window.

03:56 I'll go back to black here.

03:58 Go into your window.

04:00 And then i found a nice window where this fits.

04:03 So the x min has to be negative 10.

04:08 I'm sure there are others, but this one i'll just get there a little bit quicker.

04:11 We know that we're going to have to put in 1 times 10 to the 5th power for the r value...

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