Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 27 - Circuits - Questions - Page 794: 11c

Answer

The equivalent resistance $R_{12}$ of $R_1$ and $R_2$ is less than $R_1$

Work Step by Step

We can find the equivalent resistance when the resistors are in parallel: $\frac{1}{R_{12}} = \frac{1}{R_1}+\frac{1}{R_2}$ $\frac{1}{R_{12}} = \frac{R_2}{R_1~R_2}+\frac{R_1}{R_1~R_2}$ $\frac{1}{R_{12}} = \frac{R_1+R_2}{R_1~R_2}$ $R_{12} = \frac{R_1~R_2}{R_1+R_2} \lt \frac{R_1~(R_1+R_2)}{R_1+R_2} = R_1$ The equivalent resistance $R_{12}$ of $R_1$ and $R_2$ is less than $R_1$.
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