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Q.

A parallel plate condenser consists of two circular plates each of radius 2 cm separated by a distance of 0.1 mm. A time varying potential difference of 5 × 10¹³ V/s is applied across the plates of the condenser. The displacement current is

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a

5.56 × 10² A

b

5.56 × 10³ A

c

5.50 A

d

2.28 × 10⁴ A

answer is C.

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Detailed Solution

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Displacement current

$\begin{array}{rcl} i_{d} & = & \in_{0} (\frac{{dϕ}_{E}}{dt}) \\ = & ε_{0} A (\frac{dE}{dt}) (∵ ϕ_{E} = EA) \\ = & \frac{ε_{0} A}{d} (\frac{dV}{dt}) (∵ E = \frac{V}{d}) \\ i_{d} & = & \frac{8.8 \times 10^{- 12} \times π (4 \times 10^{- 4})}{(10^{- 4})} \times 5 \times 10^{13} \end{array}$

= 5.56 × 10³A

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