Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 23 - Alternating Current Circuits - Problems - Page 669: 3

Answer

$36\,\Omega$

Work Step by Step

Capacitive reactance $X_{C}=\frac{1}{2\pi fC}$ Given $X_{C}=68\,\Omega = \frac{1}{2\pi \times(460\,Hz)\times C}$ $\implies C=\frac{1}{2\times \pi\times460\,Hz\times68\,\Omega}=5.1\times10^{-6}F$ When frequency $f=870\,Hz$, $X_{C}=\frac{1}{2\times\pi\times870\,Hz\times5.1\times10^{-6}\,F}=36\,\Omega$
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