First slide

Displacement current

Question

A parallel plate capacitor consists of two circular r plates each of radius z cm, separated by a distance-of 0.1 mm. If voltage across the plates is varying at the rate of 5 x 10 ¹³ V/s then the value of displacement current is

Moderate

A

5.50 A
B

5.56 x 10² A
C

5.56 x 10³ A
D

2.28 x 10⁴ A

Solution

$i_{d} = ϵ_{0} A \frac{dE}{dt} = \frac{ϵ_{0} A}{d} \frac{dV}{dt} (∵ E = V / d) i_{d} = \frac{(8 \cdot 86 \times 10^{- 12}) 3 \cdot 4 \times {(2 \times 10^{- 2})}^{2}}{0 \cdot 1 \times 10^{- 3}} \times (5 \times 10^{13}) = 5 \cdot 56 \times 10^{3} A$

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