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AC voltage V(t) = 20 sin ω t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m². The amplitude of the oscillating displacement current for the applied AC voltage is ______ . [Take ε₀ = 8.85 × 10⁻¹² F m⁻¹]

Asked in JEE Main 20th July 1st Shift 2021 · Capacitor on an a.c. source

Answer: (1) 27.29 μA

Step-by-step solution

C = ε₀A/d = (8.85 × 10⁻¹² × 1)/(2 × 10⁻³) = 4.425 × 10⁻⁹ F

ω = 2π × 50 = 314.2 rad s⁻¹

i_d0 = ω CV₀ = 314.2 × 4.425 × 10⁻⁹ × 20 = 2.78 × 10⁻⁵ A = 27.8 μA

Why the other options are wrong

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