The potential difference between the plates of a parallel...

The potential difference between the plates of a parallel plate capacitor is charging at the rate of $10^{6} \mathrm{Vs}^{-1}$. If the capatance is $2 \mu \mathrm{F}$. The displacement current in the dielectric of the capacitor will be (A) $4 \mathrm{~A}$ (B) $3 \mathrm{~A}$ (C) $2 \mathrm{~A}$ (D) $1 \mathrm{~A}$

The potential difference between the plates of a parallel plate capacitor is charging at the rate of $10^{6} \mathrm{Vs}^{-1}$. If the capatance is $2 \mu \mathrm{F}$. The displacement current in the dielectric of the capacitor will be
(A) $4 \mathrm{~A}$
(B) $3 \mathrm{~A}$
(C) $2 \mathrm{~A}$
(D) $1 \mathrm{~A}$

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Key Concepts

Capacitance

Capacitance is a measure of a capacitor’s ability to store electric charge for a given potential difference. It is defined by the relation Q = CV, where Q is the stored charge, C is the capacitance, and V is the voltage across the capacitor.

Charging of a Capacitor

When a capacitor is charged by a time-varying voltage, the rate at which the potential difference increases determines the rate at which charge accumulates. The current flowing during charging is given by I = C dV/dt, linking the rate of change of voltage with the capacitance.

Displacement Current

The concept of displacement current arises in the context of Maxwell's equations and is used to account for the changing electric field in regions where no actual charge movement occurs, such as the dielectric of a capacitor. In charging capacitors, the displacement current in the dielectric is equal in magnitude to the conduction current in the wires and is calculated using the same formula, I_disp = C dV/dt.

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