Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 19 - DC Circuits - Problems - Page 552: 21

Answer

The other resistor is identical, and also has a value of $4.8\;k\Omega$.

Work Step by Step

When the resistors are in series, the power used is one-fourth the power used when they are in parallel. The applied voltage is the same in each case. $$\frac{V^2}{R_{series}}=\frac{1}{4}\frac{V^2}{R_{parallel}}$$ $$R_{series}=4R_{parallel}$$ $$R_1+R_2=4\frac{R_1R_2}{R_1+R_2}$$ $$(R_1+R_2)^2=4R_1R_2$$ $$R_1=R_2$$ The other resistor is identical, and also has a value of $4.8\;k\Omega$.
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