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 890: 65

Answer

$ {\bf 1.79\times 10^8}\;\rm A/m^2$

Work Step by Step

We know, according to Ohm's law, that $$\Delta V=IR$$ where $R=\rho L/A$ $$\Delta V=I\dfrac{\rho L}{A}$$ where $I/A$ is the current density $J$ Thus, $$\Delta V=\left(J\rho \right)L$$ Replacing $L$ by $s$ to match the given graph, $$\Delta V=\left(J\rho \right)s$$ This is a formula of a straight line where $\left(J\rho\right)$ is the slope of the given graph. $${\rm Slope}=J\rho_{\rm tungsten} $$ Hence, $$J=\dfrac{{\rm Slope}}{\rho_{tungsten}}$$ Plug the known from the figure and Table 30.3; $$J=\dfrac{\dfrac{3-0}{0.3-0}}{5.6\times 10^{-8}}$$ $$J=\color{red}{\bf 1.79\times 10^8}\;\rm A/m^2$$
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