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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 1 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{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}}

\mathrm{I_D=\varepsilon_0 \frac{d \phi}{d t}=\varepsilon_0 \frac{d}{d t}\left[\frac{\sigma}{\varepsilon_0} \cdot A\right]=\varepsilon_0 \cdot \frac{d}{d t}\left[\frac{q}{\varepsilon_0}\right]}

\mathrm{=\varepsilon_0 \cdot \frac{1}{\varepsilon_0} \cdot \frac{d}{d t}[C V]=C \cdot \frac{d V}{d t}=8.85 \times 10^{-8} \times 25=2.2 \mu \mathrm{A}}

Posted by

Ritika Kankaria

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