A parallel plate capacitor consists of two circular plates...

A parallel plate capacitor consists of two circular plates each of radius $12 \mathrm{~cm}$ and separated by $5.0 \mathrm{~mm}$. The capacitor is being charged by an external source. The charging is being charged and is equal to $0.15 \mathrm{~A}$. The rate of change of potential difference between the plates will be (A) $8.173 \times 10^{7} \mathrm{~V} / \mathrm{s}$ (B) $7.817 \times 10^{8} \mathrm{~V} / \mathrm{s}$ (C) $1.873 \times 10^{9} \mathrm{~V} / \mathrm{s}$ (D) $3.781 \times 10^{10} \mathrm{~V} / \mathrm{s}$

A parallel plate capacitor consists of two circular plates each of radius $12 \mathrm{~cm}$ and separated by $5.0 \mathrm{~mm}$. The capacitor is being charged by an external source. The charging is being charged and is equal to $0.15 \mathrm{~A}$. The rate of change of potential difference between the plates will be
(A) $8.173 \times 10^{7} \mathrm{~V} / \mathrm{s}$
(B) $7.817 \times 10^{8} \mathrm{~V} / \mathrm{s}$
(C) $1.873 \times 10^{9} \mathrm{~V} / \mathrm{s}$
(D) $3.781 \times 10^{10} \mathrm{~V} / \mathrm{s}$

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Key Concepts

Charging Relationship

The process of the capacitor being charged involves the accumulation of charge over time, and the current charging the capacitor is defined by I = dQ/dt. Since the charge on a capacitor relates to its potential difference by Q = CV, the rate of change of the potential difference is given by dV/dt = I/C when the capacitance remains constant.

Parallel Plate Capacitor

A parallel plate capacitor consists of two conductive plates separated by a dielectric medium. Its operation is based on the storage of electrical energy in the electric field created between the plates. The geometry of the capacitor, largely determined by the area of the plates and the distance separating them, plays a crucial role in its capacitance.

Capacitance Calculation

The capacitance of a parallel plate capacitor is calculated using the formula C = ??A/d, where ?? is the permittivity of free space, A is the area of one plate, and d is the separation between the plates. The area is often computed using the formula for the area of a circle, A = ?r², when dealing with circular plates.

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