Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 28 - Fundamentals of Circuits - Exercises and Problems - Page 792: 35


$t = 6.9\times 10^{-3}~s$

Work Step by Step

We can find the time when the charge is $10~\mu C$: $Q(t) = Q_0~e^{-t/RC}$ $\frac{Q(t)}{Q_0} = e^{-t/RC}$ $ln(\frac{Q(t)}{Q_0}) = -t/RC$ $t = -RC\times ln(\frac{Q(t)}{Q_0})$ $t = -(1.0\times 10^3~\Omega)(10\times 10^{-6}~F)\times ln(\frac{10~\mu C}{20~\mu C})$ $t = 6.9\times 10^{-3}~s$
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