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

Option: 1

25 \mu \mathrm{A}


Option: 2

11 \mu \mathrm{A}


Option: 3

2.2 \mu \mathrm{A}


Option: 4

1.1 \mu \mathrm{A}


Answers (1)

best_answer

\mathrm{\begin{aligned} & 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} \mathrm{~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} \mathrm{~A} \end{aligned}}

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