Question
Of what material is a resistor made if its resistance is 40.0% greater at $100^\circ\textrm{C}$ than at $20.0^\circ\textrm{C}$ ?

Iron

Solution Video

# OpenStax College Physics Solution, Chapter 20, Problem 31 (Problems & Exercises) (1:38)

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Video Transcript
This is College Physics Answers with Shaun Dychko. So we have resistance of some unknown material is going to increase by 40 percent which means that its resistance will be the original resistance plus 40 percent of that which means we have 1.4 times the original resistance. The change in temperature is going to be 100 degrees Celsius final temperature, minus 20 degrees Celsius initial temperature, which is 80 Celsius degrees. These are the things we need to plug into our formula for the temperature dependence of resistance. So resistance equals the original resistance times one plus the temperature coefficient of resistivity multiplied by the change in temperature. Then we substitute 1.4 R naught in place of R and then divide both sides by R naught. You get one plus alpha delta t equals 1.4 after you switch the sides around. Then we'll subtract one from both sides and we get alpha delta t equals 0.4 and we're doing all this work because after we figure out what alpha is, we'll look up in our table of alpha for different materials and then we'll see which material has this particular alpha we've calculated. Then we divide both sides by delta t and we get 0.4 divided by delta t is the temperature coefficient of resistivity. So that's 0.4 divided by 80 Celsius degrees which is 0.005 reciprocal Celsius degrees. This is the temperature coefficient of resistivity of iron. So the material must be iron.