Question

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

A
2μF
B
3μF
C
5μF
D
6μF

Solution

## The correct option is B $$6 \mu F$$Displacement current in capacitor $$i = A\epsilon_o \dfrac{dE}{dt}$$Or $$i = \dfrac{A\epsilon_o}{l} \dfrac{d(El)}{dt}$$ where $$l$$ is the separation between the two plates.Potential difference between the two plates $$V = El$$$$\implies$$ $$i = C \dfrac{dV}{dt}$$  where capacitance of the capacitor is $$C = \dfrac{A\epsilon_o }{l}$$$$\therefore$$ $$i = 2\mu F \times 3 V/s = 6\mu A$$Physics

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