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: 68

Answer

${\bf 2.8}\;\rm mA$

Work Step by Step

Let's assume that the muscle and fat are ohmic resistors. We know, according to Ohm's law, that $$\Delta V=IR$$ where $R=\rho L/A$ and $A=\pi r^2=\pi D^2/4$ where $D$ is the diameter. $$\Delta V=I\dfrac{4\rho_{\rm } L}{\pi D^2}$$ Thus, Solving for $I$; $$I=\dfrac{\pi D^2\Delta V}{4\rho L}\tag 1$$ We know that the upper leg consists of 82% muscle and 18% fat, so $$\rho=0.82\rho_{\rm muscle }+0.18\rho_{\rm fat}$$ Plug into (1), $$I=\dfrac{\pi D^2\Delta V}{4L (0.82\rho_{\rm muscle }+0.18\rho_{\rm fat})} $$ Plug the known; $$I=\dfrac{\pi (0.12)^2(1.5)}{4(0.40) (0.82[13]+0.18[25])} $$ $$I=\color{red}{\bf 2.8}\;\rm mA$$
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