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 - Conceptual Questions - Page 886: 6

Answer

We can rank the currents in order from largest to smallest: $I_a = I_d \gt I_b = I_c$

Work Step by Step

Since all the wires have the same diameter and they are made of the same material, the resistivity of each wire is the same. Since the currents $I_b$ and $I_c$ move through wires of the same total length, the resistance is the same. Since the potential difference is the same across both branches of the middle section, $I_b = I_c$ $I_a$ and $I_d$ are equal to the total current flowing through the wire since there is only one path at these sections. Therefore, $I_a = I_d$. $I_b$ and $I_c$ are both equal to half the total current since there are two equal paths at this section. We can rank the currents in order from largest to smallest: $I_a = I_d \gt I_b = I_c$
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