Q 12-08-050JEE MainJEE Main 2024 (1 Feb, Shift 1)Easy
A parallel plate capacitor has a capacitance $C = 200\ \text{pF}$. It is connected to a $230\ \text{V}$ ac supply with an angular frequency of $300\ \text{rad s}^{-1}$. The rms value of the conduction current in the circuit and the displacement current in the capacitor respectively are
Answer: (D) $13.8\ \mu\text{A}$ and $13.8\ \mu\text{A}$
$$I_{rms} = \frac{V_{rms}}{X_C} = V_{rms}\,\omega C = 230\times300\times200\times10^{-12} = 1.38\times10^{-5}\ \text{A} = 13.8\ \mu\text{A}$$
The displacement current inside the capacitor always equals the conduction current in the wires, so both are $13.8\ \mu\text{A}$.
Solution by Sreeraj P, M.Sc Physics