Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 35 - AC Circuits - Exercises and Problems - Page 1053: 42

Answer

a) ${\bf 25}\;\rm mA$ b) ${\bf 6.63}\;\rm V$

Work Step by Step

$$\color{blue}{\bf [a]}$$ To find the peak current, we need to find the equivalent capacitance, as we did in the figure below. $$I_{\rm peak}=\dfrac{\varepsilon_0}{X_C}=2\pi f C_{eq,2} \varepsilon_0$$ Plug the known (see the figure below); $$I_{\rm peak}= 2\pi (200) (2\times 10^{-6}) (10)$$ $$I_{\rm peak}= \color{red}{\bf 25}\;\rm mA$$ $$\color{blue}{\bf [b]}$$ To find the peak voltage across the $3\;\mu$F capacitor, we need to use the second circuit below. It is obvious now that all the current passes through this capacitor. So, $$V_{1}=IX_{C1}=\dfrac{I}{2\pi f C_1}$$ Plug the known; $$V_{1}= \dfrac{(25\times 10^{-3})}{2\pi (200)(3\times 10^{-6})}$$ $$V_{1}=\color{red}{\bf 6.63}\;\rm V$$
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