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

Iron.

Physics 102 Electricity and Magnetism

Chapter 20

Electric Current, Resistance, and Ohm's Law

Current, Resistance, and Electromotive Force

Rutgers, The State University of New Jersey

University of Washington

Hope College

Lectures

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Let us understand this particular equation: first, resistance of a conductor changes with the changes in the temperature of a conductor, so r is equal to 0 multiplied by 1, plus alpha times delta t where r is equal to resistance after temperature change. R 0 is initial resistance. Alpha stands for temperature coefficient of resistibility and delta. T denotes temperature change, which is denoted as t 2 minus 7. Here t 2 stands for final temperature and even stands for initial temperature. Now, in this case, final temperature is given us 100 degree celsius and initial temperature is 20 degree clad. As for the given data, the resistance of material is increased by 40 percent, so using r is equal to r 0 plus 40 percent increase of initial resistance. So write it as 40 percent of r 0, which is equal to r 0 plus 40, divided by 100 times, r 0, which is coming as r 0 plus 0.4 times, r 0, and that is coming as 1.4 times 0. Now, to find the material the resister is made up of, we need to find the value of temperature coefficient of resistivity, so we are using the same formula again, that is r 0 times 1 plus alpha times delta t. So now, in this case, value of r is 1.4 times. R o is equal to 01 plus alpha times 100 minus 20 point that is final temperature, minus initial, 1, so or 0 and 0 gets canceled. So 1.4 is equal to 1 plus alpha times 18 point, and we solve this further. Therefore, alpha is equal to .4 divided by at which is coming as 5 into 102 minus 34 degrees celsius. Now this callista temperature coefficient of resistivity, which is denoted by alpha now since iron, is made up of you, know having this kind of resistivity, which is fine to tend to minus 3 intherefore, this particular resistor. We can mention it as this particular resistor is made up of iron, since we testilyof iron is 5 point into 10 mnthnow. This will be our final answer.

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