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  4. A large parallel plate capacitor, whose plates have an area of 1 m2 and are separated from each other by 1 mm , is being charged at a rate of 25 V s- 1 . If the dielectric between the plates has the dielectric constant 10 , then the displacement current at this instant is

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Q. A large parallel plate capacitor, whose plates have an area of $1 \, m^{2}$ and are separated from each other by $1 mm$ , is being charged at a rate of $25 \, V \, s^{- 1}$ . If the dielectric between the plates has the dielectric constant $10$ , then the displacement current at this instant is

NTA AbhyasNTA Abhyas 2022

Solution:

$C=\frac{\left(\epsilon \right)_{0} K A}{d}=\frac{\left(\right. 8.85 \times \left(10\right)^{- 12} \left.\right) \times 10 \times 1}{\left(10\right)^{- 3}}$
$=8.85\times 10^{- 8} \, F$
$i=\frac{d}{d t}\left(C V\right)=C\frac{d V}{d t}=8.85\times \left(10\right)^{- 8}\times 25$
$=2.2\times 10^{- 6}$ A