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Parallel plate capacitor - class-XII
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Choose the correct answer from the alternatives given.
The charge on a parallel plate capacitor varies as $q , = , q _0 , cos2\pi \nu t$. The plates are very large and close together (area = A, separation = d). The displacement current through the capacitor is then
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A
$-q _0 \, 2\pi \nu \, sin2\pi \nu t$
💡 Explanation:
Given: The charge on the parallel plate capacitor varies as $q=q _0cos2\pi\nu t$
To find: The displacement current through the capacitor.
The displacement current in a capacitor is equal to the conduction current of the capacitor.
Displacement current, $I _D , =I _C$
The conduction current in a capacitor is given by:
$I _C= \dfrac{dq}{dt}$
$I _C= \dfrac{dq}{dt}$
$\implies, \dfrac{d}{dt} , [q _0 , cos , 2\pi\nu t]$
$ ,=, -q _0 , 2\pi \nu, sin2\pi \nu,t$
Option $(B)$ is correct.