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 31 - Fundamentals of Circuits - Exercises and Problems - Page 916: 18

Answer

The resistance of the two connected wires is $~~\frac{R}{4}$

Work Step by Step

We can write an expression for the resistance of the original wire: $R = \frac{\rho~L}{A}$ We can write an expression for the resistance of each half of the wire after it has been cut: $R' = \frac{\rho~(L/2)}{A}$ $R' = \frac{\rho~L}{2A}$ $R' = \frac{R}{2}$ We can find the resistance $R_{eq}$ of the connected wires: $\frac{1}{R_{eq}} = \frac{1}{R/2} + \frac{1}{R/2}$ $\frac{1}{R_{eq}} = \frac{2}{R} + \frac{2}{R}$ $\frac{1}{R_{eq}} = \frac{4}{R}$ $R_{eq} = \frac{R}{4}$ The resistance of the two connected wires is $~~\frac{R}{4}$
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