Problem

What is the power of a $1.00 \times 10^{2} \mathr…

00:24

Problem 39 Hard Difficulty

Unreasonable Results
(a) To what temperature must you raise a resistor made of constantan to double its resistance, assuming a constant temperature coefficient of resistivity? (b) To cut it in half? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable, or which premises are inconsistent?

Answer

(a) $\Delta T=5.00 \times 10^{5} \circ \mathrm{C}$
(b) $\Delta T=-2.50 \times 10^{5 \circ} \mathrm{C}$
(c) The temperature changes are not reasonable.
(d) It is wrong to assume that the temperature coefficient of resistivity is constant.

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Physics 102 Electricity and Magnetism

College Physics for AP® Courses

Chapter 20

Electric Current, Resistance, and Ohm's Law

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Video Transcript

in this problem. The dependence off in the distance off the material on temperature is giving us the formula, which is our is equal to our issue. Multiply one plus are four times Delta T now here. In this case, Delta T is denoted as temperature change, which is two to minus Stephen. But you sense for find amber jerk even sense for the initial temperature. Next, our is equal to resistance after the temperature change are zero is known as origin A or in the short distance on first stands for temperature coefficient off festivity. As a Lear said he too is equal to finally temperature, and Steven is equal to initial temperature. No, to solve this problem. The relationship between the temperature and resistance is taken to be linear, So ask for the given data. When I write it down. When temperature change, he's denoted as deputy. Now, in this case, the finer resistance, which is generally are becomes twice the any share a distance. This is ask for the leader so right it is, therefore are is equal to two times ours. You So the original question becomes, as we can make sure he does two times are. Zero is equal to our zero times one plus on four times their dirty and in this case, were to find a body off temperature change that is your daddy. So are 00 gets cancer, so there's two minus. One is accorded to all four times Change in temperature. Therefore, one is equal to all four times Change in temperature. Find anywhere. So of this equation is there that is equal to one you wanted by other for and here the one you off I'm far is 0.2 into tennis, two minus three were degree Celsius which is the value of alpha for constant to therefore temperature change that we get it as fire into generous to five diggity Celsius. And this would be our answer, which will write it as so the resistance. But a couple when the temperature change is five into tennis to five times bigly census. This would be an answer for party. We'll start with Barbie. We need to find the temperature change required to cut the resistance in half. So in this case, are is equal. Joe are zero times one plus four times change in temperature. So As for the given condition are is quinto are zero by two Statistical toe are zero times one plus four times 10 30. Therefore, our CEO Arthur gets cancer. Certainly half is equal to one plus five times their daddy doing calculation further here. So if we take one to the left inside, it is going to be minus appalls you upon five is equal to or four times delta t. Therefore, change in temperature becomes minus. Solves your upon five divided by alpha. We know the value of off already, which is cedar 0.2 interventionist. You're minus tree. So we're just coming as 2.5 into generous to five degree Celsius, so we'll write dance for us. Hence the resistance. We'll double when the temperature he's decreased Bye 2.5 into tennis team fighting, since we have got the value as negative value. So there's a document in temperature. It's consider the Parsi asked for the party of the question. The we'll write it as the about temperature change. Valuing Barbie is so this change in back of you off temperature is very large, so it is actually even Could I do then the melting point off on Stanton. So the temperature change while you is unreasonable. This is what we can, right? It's an answer for part. See off the question. Moving ahead. Ask for the party of the question, the assumption that should write it down once again for party that assumption that the dependence off the resistance on temperature he's linear and seems to be in consistence inconsistent at the same time. So the brand new off registry really that is out for WAAS. Taking to be a constant, However, the Brazils are said to be on the reasonable, so the exemption that how far is a constant seems it could be wrong. This is what we can right for the question number gate.

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