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  4. A large parallel plate capacitor, whose plates have an area of 1 m 2 are separated from each other by 1 . mm, is being charged at a rate of 25.8 V / s. 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 $1\, m ^{2}$ are separated from each other by $1 .\, mm$, is being charged at a rate of $25.8\, V / s$. If the dielectric between the plates has the dielectric constant $10$, then the displacement current at this instant is

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Solution:

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