AC voltage V(t) = 20sin ω t of frequency 50Hz is applied to a parallel plate capacitor. The separation between the plates is 2mm and the area is 1m2. The amplitude of the oscillating displacement current for the applied Ac voltage is__________. [Take ε 0 = 8 . 8 5 * 1 0 − 1 2 F / m ]

C = ε 0 A d ⇒ X C = 1 C ω = d ε 0 A ω ⇒ l 0 = V 0 X C = V 0 ε 0 A ω d = 2 π f V 0 ε 0 A d ⇒ l 0 = 2 * 3 . 1 4 * 5 0 * 2 0 * 8 . 8 5 * 1 0 − 1 2 * 1 2 * 1 0 − 3 = 2 7 . 7 9 * 1 0 − 6 A = 2 7 . 7 9 μ A

AC voltage V(t) = 20sin $ω t$ of frequency 50Hz is applied to a parallel plate capacitor. The separation between the plates is 2mm and the area is 1m². The amplitude of the oscillating displacement current for the applied Ac voltage is__________.

[Take $ε_{0} = 8.85 * 1 0^{- 12} F / m]$

Option 1 - 83.37 <math> <mrow> <mi>μ</mi> <mi>A</mi> </mrow> </math>

Option 2 - 55.58 <math> <mrow> <mi>μ</mi> <mi>A</mi> </mrow> </math>

Option 3 - 21.14 <math> <mrow> <mi>μ</mi> <mi>A</mi> </mrow> </math>

Option 4 - 27.79  <math> <mrow> <mi>μ</mi> <mi>A</mi> </mrow> </math>

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Alok Kumar Singh | Contributor-Level 10

7 months ago

Correct Option - 4

Detailed Solution:

$C = \frac{ε_{0} A}{d} \Rightarrow X_{C} = \frac{1}{C ω} = \frac{d}{ε_{0} A ω} \Rightarrow l_{0} = \frac{V_{0}}{X_{C}} = \frac{V_{0} ε_{0} A ω}{d} = \frac{2 π f V_{0} ε_{0} A}{d}$