A parallel plate capacitor consists of two circular plates each of radius \(2 \mathrm{~cm}\), separated by a…

1. \(5.56 \mathrm{~A}\)
2. \(5.56 \mathrm{~mA}\)
3. \(0.556 \mathrm{~mA}\)
4. \(2.28 \mathrm{~mA}\)

Solution

According to the question, a parallel plate capacitor is shown in the figure below,
Given, radius \(=2 \mathrm{~cm}\), distance between plates, \(d=0.1 \mathrm{~mm} \text { and } \frac{d V}{d t}=5 \times 10^6 \mathrm{Vs}^{-1}\) Displacement current in the capacitor, \(\begin{aligned} I_d=\varepsilon_0 \frac{d \phi}{d t} & =\varepsilon_0 \frac{d E}{d t} A \\ I_d & =\varepsilon_0 A \frac{d E}{d t} \\ \Rightarrow \quad I_d & =\varepsilon_0 \frac{A}{d} \frac{d V}{d t} \quad\left(\because E=\frac{V}{d}\right) \end{aligned}\) Putting the given values, we get \(\begin{aligned} & \Rightarrow \quad I_d=\frac{8.85 \times 10^{-12} \times \pi \times\left(4 \times 10^{-4}\right) \times 5 \times 10^6}{1 \times 10^{-4}} \mathrm{~A} \\ & \Rightarrow \quad I_d=556.28 \times 10^{-6} \mathrm{~A}=0.556 \mathrm{~mA} \end{aligned}\) Hence, the correct option is (c).

Asked in: AP EAMCET 2019 (23 Apr Shift 1)

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