Question

A parallel plate capacitor consists of two circular plates each of radius $2cm$, separated by a distance of $0.1mm$. If the potential difference across the plates is varying at the rate of $5\times 10^{6}V{s}^{-1}$, 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 $=2cm$, distance between plates,
$d=0.1mm$ and $\frac{dV}{dt}=5\times 10^{6}V{s}^{-1}$
Displacement current in the capacitor,
$I_d={\epsilon }_0\frac{d\varphi }{dt}={\epsilon }_0\frac{dE}{dt}A$
$I_d={\epsilon }_{0}A\frac{dE}{dt}$
$\Rightarrow I_d={\epsilon }_0\frac{A}{d}\frac{dV}{dt}$
$\left(\because E=\frac{V}{d}\right)$
Putting the given values, we get
$\Rightarrow I_d=\frac{8.85\times 10^{12}\times \pi \times \left(4\times 10^4\right)\times 5\times 10^6}{1\times 10^{-4}}A$
$\Rightarrow I_d=556\cdot 28\times 10^{-6}A$
$=0.556mA$