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 `5xx10^(6) Vs^(-1)`, then the value of displacement current is

Options

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

Answer

C

Explanation

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 `(d V)/(dt) = 5 xx 10^(6) V s^(-1)`
Displacement current in the capacitor,
`I_(d) = epsilon_(0) (d phi)/(d t) = epsilon_(0)(d E)/(d t) A`
`I_(d) = epsilon_(0)A(dE)/(dt)`
`rArr I_(d) = epsilon_(0)(A)/(d) = (dV)/(dt) " "(because E = (V)/(d))`
Putting the given values, we get
`rArr I_(d) = (8.85 xx 10^(-12) xx pi xx (4 xx 10^(-4)) xx 5 xx 10^(6))/(1 xx 10^(-4)) A`
`rArr I_(d) = 556.28 xx 10^(-6)A = 0.556 mA`
Hence, the correct option is (c ).