University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 25 - Current, Resistance, and Electromotive Force - Problems - Exercises - Page 842: 25.19

Answer

a) $ 0.047 μΩ$ (Side to side) b) $R=672 μΩ$ (End to end)

Work Step by Step

The formula for resistance is : $R=\frac{ρL}{A}$ a) This shows that resistance is inversely proportional to the area and when area increases, the resistance decreases. Therefore the resistance of 120 wires placed side to side to create a single strand is: $R = \frac{Resistance of Wire}{Number Of Wires}$ $R = \frac{5.60 μΩ}{120}$ Thus, The resistance is $ 0.047 μΩ$ b) However, if the wires are connected end by end, the area is the same but the length increases by a factor of 120 and since length is proportional to the resistance, the resistance increases by a factor of 120 as well. Thus the resistance is $R= (Resistance of One wire)\times(Number of Wires)$. $R = (5.60 μΩ)\times(120)$ $R=672 μΩ$
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