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Q.

A parallel plate capacitor of plate separation 8.85 mm is connected in an electric circuit having source voltage 400V. What is the value of the displacement current for $10^{- 6}$ sec , if the plate area is $60 c m^{2}$ ?

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a

$2.4 m A$

b

$1 m A$

c

$4.2 m A$

d

$2.2 m A$

answer is A.

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Detailed Solution

Displacement current $I_{D} = \in_{o} \frac{{dϕ}_{E}}{dt}$

$since I_{D} = \frac{dq}{dt} and ϕ = \frac{q}{\in_{0}}$

$\begin{array}{rcl} \Rightarrow & I_{D} = \in_{o} \frac{EA}{t} \end{array}$

$\begin{array}{rcl} \Rightarrow & I_{D} = \in_{o} (V / d) \frac{A}{t} \\ \Rightarrow & I_{D} = \frac{8 .85 \times 10^{- 12} \times 400 \times 60 \times 10^{- 4}}{8 .85 \times 10^{- 3} \times 10^{- 6}} \\ \Rightarrow & I_{D} = 24 \times 10^{- 4} A = 2 .4 \times 10^{- 3} A = 2.4 mA \end{array}$

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A parallel plate capacitor of plate separation 8.85 mm is connected in an electric circuit having source voltage 400V. What is the value of the displacement current for10-6 sec , if the plate area is 60cm2 ?