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What my professor is telling us that there is no conduction current through a parallel plate capacitor but the current that is passing through capacitor is the displacement current and this phenomena can be seen in one of the Maxwell's equation. What I know about displacement current is that there is no charge movement in displacement current but I am so confused with that. Can some one explain me the displacement current and how does it work in parallel plate capacitor?

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    \$\begingroup\$ Do check Dave's EEVblog with exactly that as a topic: EEVblog #486 - Does Current Flow Through A Capacitor? (link) \$\endgroup\$ – Josip Medved Jun 29 '14 at 16:23

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