The rms value of conduction current in a parallel plate capacitor is $6.9 \mu \mathrm{~A}$. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of $600 \mathrm{rad} / \mathrm{s}$, will be :

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Alternating Current

The rms value of conduction current in a parallel plate capacitor is

6.9 μ A

. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of

600 rad / s

, will be :

Answer: (B)

For a capacitor in AC circuit, the current is

I = V ω C

, where

V

is the rms voltage,

ω

is the angular frequency, and

C

is the capacitance. Rearranging:

C = \frac{I}{V ω} = \frac{6.9 \times 1 0 ^{- 6}}{230 \times 600} = \frac{6.9 \times 1 0 ^{- 6}}{138000} = 50 \times 1 0^{- 12} F = 50 pF

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Single correct option