Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 27 - Current and Resistance - Stop to Think 27.1 - Page 744: 1

Answer

$i_{e,3} > i_{e,2} > i_{e,1} > i_{e,3}$

Work Step by Step

Recall $i_e = n_eA_{\perp}v_d$ and $A_{\perp} = \pi r^2$ Since all of the wires are made of the same material, we don't need to worry about $n_e$. That is, $i_e \propto A_{\perp}v_d = \pi r^2v_d$ The electron current for each wire is: $i_{e,1} = \pi (r)^2(v_d) = \pi r^2 v_d$ $i_{e,2} = \pi (r)^2(2v_d) = 2\pi r^2 v_d$ $i_{e,3} = \pi (2r)^2(v_d) = 4\pi r^2 v_d$ $\displaystyle i_{e,4} = \pi (\frac{1}{2}r)^2(2v_d) = \frac{1}{2}\pi r^2 v_d$ So in ranking from largest to smallest, the order is $i_{e,3} > i_{e,2} > i_{e,1} > i_{e,3}$.
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