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A parallel plate capacitor is charged by...

A parallel plate capacitor is charged by an exteranl ac source straight the displacement current inside the capacitor is the same as the current charging the capacitor.

Text Solution

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Electric field between the capacitor plates
`E = (sigma)/(epsilon_(0)) = (q)/(epsilon_(0)A)`
Where q is the charge accumulated on the positive plate.
The electric flux through this plate
`phi_(E ) = EA = (q)/(epsilon_(A))cdot A = (q)/(epsilon_(0))`
`therefore` Dispacement current
`I_(d) = epsilon_(0)cdot (d phi )/( dt ) = epsilon_(0) (d)/(dt) [(q)/(epsilon_(0))] = (dq)/(dt)`
`(dq)/(dt)` is the rate at which charge flows to positive plate through the conducting wire.
`I_(d) = I_(C )`
i.e., displacement current between the capacitor plates = conduction current through wire.
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