Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 30 - Current and Resistance - Exercises and Problems - Page 888: 39

Answer

$ 2.25\times 10^5\;\rm \Omega^{-1}\cdot m^{-1}$

Work Step by Step

We know, from Ohm's law, that $$\Delta V=IR$$ So if this material is an ohmic one, the graph $\Delta V-I$ will give us a straight line that has a slope of $R$. And if the material is not an ohmic one, then the graph will not be linear. We plugged the 4 points into the $\Delta V-I$ graph, as we see below. And the best-fit line is already a straight line and it started from the origin as expected, so the material is an ohmic one. As we can see the slope is 0.4 which is $R$ $${\rm Slope}=R=\bf 0.4\;\rm \Omega$$ Now we need to find the conductivity of this material. Recalling that the resistance is given by $$R=\dfrac{\rho L}{A}$$ where $\rho$ is the resistivity which is given by $\rho=1/\sigma$ where $\sigma$ is the conductivity. $$R=\dfrac{ L}{\sigma A}$$ Thus, $$\sigma=\dfrac{ L}{R A}$$ Plug the known; $$\sigma=\dfrac{ (45\times 10^{-3})}{(0.4)(0.5\times 1.0\times 10^{-6}) }$$ $$\sigma=\color{red}{\bf 2.25\times 10^5}\;\rm \Omega^{-1}\cdot m^{-1}$$
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