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 34 - Electromagnetic Fields and Waves - Exercises and Problems - Page 1031: 39

Answer

See the graph below,

Work Step by Step

The displacement current through the capacitor is given by $$I_{\rm disp }=\dfrac{dQ}{dt}$$ Recalling that $V_C=Q/C\Rightarrow Q=V_CC$, $$I_{\rm disp }=C\dfrac{dV_C}{dt}$$ where $dV_C/dt$ is the slope of the given graph where we have three stages there. $$I_{\rm disp }=C \cdot{\rm slope}$$ Plug the known; $$I_{\rm disp }=(0.10\times 10^{-6}) \cdot{\rm slope}\tag 1$$ $*$ For the first stage, the slope is 100, Plug into (1), $$I_{\rm disp }=(0.10\times 10^{-6}) \cdot (100)=\bf 10\;\rm \mu A$$ $**$ For the second stage, the slope is 0, Plug into (1), $$I_{\rm disp }=(0.10\times 10^{-6}) \cdot (0)=\bf 0\;\rm \mu A$$ $***$ For the third stage, the slope is -50, Plug into (1), $$I_{\rm disp }=(0.10\times 10^{-6}) \cdot (-50)=\bf -5.0\;\rm \mu A$$ Now we can draw the displacement current as a function of time. See the figure below
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