Question

A parallel plate capacitor consists of two circular plates each of radius $2 \,cm$, separated by a distance of $0.1 \,mm$. If the potential difference across the plates is varying at the rate of $5 \times 10^{6} Vs ^{-1}$, then the value of displacement current is

• A. 5.56 A
• B. 5.56 mA
• C. 0.556 mA
• D. 2.28 mA

Answer 1

Answer: (C)

According to the question, a parallel plate capacitor is shown in the figure below,

Given, radius $=2\, cm$, distance between plates,
$d=0.1\, mm$ and $\frac{d V}{d t}=5 \times 10^{6}\, Vs ^{-1}$
Displacement current in the capacitor,
$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 \, I_{d}=\varepsilon_{0} \frac{A}{d} \frac{d V}{d t} $
$\left(\because \,E=\frac{V}{d}\right)$
Putting the given values, we get
$\Rightarrow \, I_{d}=\frac{8.85 \times 10^{12} \times \pi \times\left(4 \times 10^{4}\right) \times 5 \times 10^{6}}{1 \times 10^{-4}} A$
$\Rightarrow \, I_{d}=556 \cdot 28 \times 10^{-6} \,A$
$ =0.556 \,mA$