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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
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B
3μF
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C
5μF
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D
6μF
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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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