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 555: 54

Answer

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Work Step by Step

a. The time constant is RC. $$\tau=RC$$ Solve for the capacitance. $$C=\frac{\tau}{R}=\frac{18.0\times10^{-6}s}{15.0\times10^{3}\Omega}=1.20\times10^{-9}F$$ b. The battery has an emf of 24.0 V. When the voltage across the resistor is 16.0 V, the voltage across the capacitor will be 8.0 V. Use the equation, 19-7a, for the voltage across a charging capacitor. $$V_C=\epsilon(1-e^{-t/\tau})$$ $$t=-\tau\; ln(1-\frac{V_C}{\epsilon})=-(18.0\times10^{-6}s) ln(1-\frac{8V}{24V})=7.30\times10^{-6}s $$
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