Question

The capacity of a parallel plate air capacitor is $2\mu F$ and voltage between the plates is changing at the rate of $3V/S$. The displacement current in the capacitor is:

• A. $2\mu F$
• B. $3\mu F$
• C. $5\mu F$
• D. $6\mu F$

Answer 1

Answer: (D)

$6\mu F$

Displacement current in capacitor $i=A{ϵ}_o\frac{dE}{dt}$

Or $i=\frac{A{ϵ}_o}{l}\frac{d\left(El\right)}{dt}$ where $l$ is the separation between the two plates.

Potential difference between the two plates $V=El$

$⟹$ $i=C\frac{dV}{dt}$ where capacitance of the capacitor is $C=\frac{A{ϵ}_o}{l}$

$\therefore$ $i=2\mu F\times 3V/s=6\mu A$