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(a) Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has $\alpha=-0.0600 /^{\circ} \mathrm{C}$ ) when it is at the same temperature as the patient. What is a patient's temperature if the thermistor's resistance at that temperature is 82.0$\%$ of its value at $37.0^{\circ} \mathrm{C}$ (normal body temperature)? (b) The negative value for $\alpha$ may not be maintained for very low temperatures. Discuss why and whether this is the case here. (Hint: Resistance can't become negative.)

(a) $T=40^{\circ} \mathrm{C}$(b) The temperature coefficient of resistivity must be greater than $-0.33^{\circ} \mathrm{C}$ for the resistance of the thermistor not to be negative.

Physics 102 Electricity and Magnetism

Chapter 20

Electric Current, Resistance, and Ohm's Law

Current, Resistance, and Electromotive Force

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

University of Winnipeg

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In this particular problem, we can find the patient's temperature by using the formula. I just write it down here. We can use the formula as our is equal to our zero bracket. It's one plus far times del dirty. The Stardust stands were changing the temperature, so we'll write Delta T as do you True, minus Stephen. That's right down the bottom. Accuse Israel, so are is equal to resistance. After the temperature change, Arzu is equal to in issue or original resistance. You that's talk about offer off as equal to temperature coefficient off resistive Really? And here, in this case, it is off to Mr Do. You do stands for final temperature on a divan. Is any sugar temperature Now? As for the given data, let's stick our easy quitter 82% off original resistance resisting arrest Ours. You therefore are is equal to 82 divided by hundreds of that, because seo 820.82 times are zero. No, here so far is giving us minus 0.6 for Gregory Senses. So there's a temperature coefficient offer the studio after Mr, and even that is initial temperature is given us 37 degree senses now, putting these values in the formula. We get 0.82 times are zero is a quitter are zero times one plus. But what the value of our fans minus 0.6 or did recesses times do you to minus 37 degrees is so we need to basically get the value of key to therefore are zero rt gets cancelled B minus off. I see your 0.18 Easy question my servicio 0.6 times do you do minus 37 and as we go further from here, therefore you don't 0.20 Do I did buy seed of porn 06 since minus signs get cancer, do you to minus 37 therefore three years equal to be to minus 30 70 dissonances. So you do. Is it going to 37 plus three and that is going to be 40 degrees into So here the final temperature that we get is 40 Digby senses. So for this party, we can write those hands. A patient's temperature is 40 legally senses If that they're misters registers at that temperature is 82% off its while you and 37 do the senses. Okay, this is our final answer for that. Also, for part B. Ask for the question. I asked if the value of the first negative rectal temperature then, so I'll write it as if value off for is negative that, you know, cam pictures. Then the term one plus four times D minus 37. Diggory senses becomes more negative. And which shoes That resistance has the oppose it sign do the initial resistance. So moving further. What we can, right is says it is not possible to have I'm negative. Sign off the resistance dead for at low temperature the temperature coefficient offer a festivity remains negative. So this will be our final answer for that.

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