A parallel plate capacitor has a capacitance $\mathrm{C}=200 \mathrm{pF}$. It is connected to 230 V ac supply with an angular frequency $300 \mathrm{rad} / \mathrm{s}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

(D) $13.8 \mu \mathrm{~A}$ and $13.8 \mu \mathrm{~A}$

(A) $1.38 \mu \mathrm{~A}$ and $1.38 \mu \mathrm{~A}$

(B) $14.3 \mu \mathrm{~A}$ and $143 \mu \mathrm{~A}$

(C) $13.8 \mu \mathrm{~A}$ and $138 \mu \mathrm{~A}$

JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Alternating Current

A parallel plate capacitor has a capacitance

C = 200 pF

. It is connected to 230 V ac supply with an angular frequency

300 rad / s

. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

(A) $1.38 μ A$ and $1.38 μ A$
(B) $14.3 μ A$ and $143 μ A$
(C) $13.8 μ A$ and $138 μ A$
(D) $13.8 μ A$ and $13.8 μ A$ ✓ Correct

Answer: (D)

Solution

The rms conduction current through the capacitor is

I_{r m s} = \frac{V _{r m s}}{X _{C}} = V_{r m s} ω C = 230 \times 300 \times 200 \times 1 0^{- 12} = 13.8 μ A

In a capacitor, the displacement current always equals the conduction current in magnitude (they are the same current in an AC circuit — one arises from the changing electric flux, the other from charge flow in the wires). So the displacement current is also

13.8 μ A

JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Single correct option

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JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Alternating Current

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