The rms value of conduction current in a parallel plate capacitor is 6.9. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be: (a) 5 pF (b) 50 pF (c) 100 pF (d) 200 pF

Answer: (b). For a capacitor on ac: Irms = VrmsXC = Vrms ω C. C = Irmsω Vrms = 6.9 × 10⁻⁶600 × 230 = 6.9 × 10⁻⁶1.38 × 10⁵. C = 5 × 10⁻¹¹ F = 50 pF. So the answer is (b) 50 pF.

The rms value of conduction current in a parallel plate capacitor is… | JEE Main 2022 (25 Jul, Shift 1)

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Displacement Current, Maxwell's Equations & Production

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

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Answer: (b)

For a capacitor on ac: $I_{rms} = \dfrac{V_{rms}}{X_C} = V_{rms}\,\omega C$ .
$C = \dfrac{I_{rms}}{\omega V_{rms}} = \dfrac{6.9 \times 10^{-6}}{600 \times 230} = \dfrac{6.9 \times 10^{-6}}{1.38 \times 10^{5}}$ .
$C = 5 \times 10^{-11}$ F $= 50$ pF.
So the answer is (b) 50 pF.

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