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Physics Laboratory Experiments

Jerry D. Wilson, Cecilia A. Hernandez-Hall

Chapter 25

The Temperature Dependence of Resistance - all with Video Answers

Educators


Chapter Questions

03:00

Problem 1

What is the value of $\alpha$ for copper in terms of Fahrenheit degrees? If the resistance is a linear function on the Celsius scale, will it be a linear function on the Fahrenheit scale? Explain.

Mike Gaerlan
Mike Gaerlan
Numerade Educator
05:22

Problem 2

Replot the copper data for $R_{\mathrm{c}}$ versus $T$ with a smaller temperature scale extending to $-300^{\circ} \mathrm{C}$, and extrapolate the line to the temperature axis. At what temperature would the resistance go to zero? What are the practical electrical implications for a conductor with zero resistance? [It is interesting to note that the value of $\alpha$ is roughly the same for many pure metals:
approximately $\frac{1}{273}$, or $0.004^{\circ} \mathrm{C}^{-1}$. This is the same as the value of the coefficient of expansion of an ideal gas. Also, some metals and alloys do become "superconductors" or have zero resistance, at low temperatures. Some "high-temperature" ceramic materials show superconductivity at liquid nitrogen temperatures $\left(77 \mathrm{~K}\right.$, or $-196^{\circ} \mathrm{C}$, or $-321{ }^{\circ} \mathrm{F}$ ).]

Jacquelinne S. Mejia Sandoval
Jacquelinne S. Mejia Sandoval
Numerade Educator
02:07

Problem 3

A coil of copper wire has a resistance of $10.0 \Omega$, and a coil of silver wire has a resistance of $10.1 \Omega$, both at $0{ }^{\circ} \mathrm{C}$. At what temperature would the resistance of the coils be equal?

Shahab Ullah
Shahab Ullah
Numerade Educator
02:02

Problem 4

Explain why the ambient temperature $T_{\mathrm{a}}$ for the thermistor cannot be taken as $T_{\mathrm{a}}=0^{\circ} \mathrm{C}$, and why the expression for the resistance is written $R=R_{0} e^{\beta / T}$, where $T$ is in degrees Celsius.

Manik Pulyani
Manik Pulyani
Numerade Educator
02:02

Problem 5

Assuming that $\beta$ remained constant, what would be the resistance of the thermistor in the experiment as the temperature approached absolute zero?

Manik Pulyani
Manik Pulyani
Numerade Educator
02:02

Problem 6

Assume the temperature coefficient of resistance $\alpha$ to be defined over the temperature range $\Delta T=T-T_{\mathrm{a}}$, where $T_{\mathrm{a}}>273 \mathrm{~K}\left(0{ }^{\circ} \mathrm{C}\right)$, by $R-R_{\mathrm{a}}=-R_{\mathrm{a}} \alpha\left(T-T_{\mathrm{a}}\right)$. Show that for
a thermistor, $\alpha$ is a function of temperature given by:
$$
\alpha=\frac{\left.1-e^{\beta\left(1 / T-1 / T_{\mathrm{o}}\right.}\right)}{T-T_{\mathrm{a}}}
$$

Manik Pulyani
Manik Pulyani
Numerade Educator