A parallel-plate capacitor is to be constructed by using, as...

A parallel-plate capacitor is to be constructed by using, as a dielectric, rubber with a dielectric constant of 3.20 and a dielectric strength of 20.0 $\mathrm{MV} / \mathrm{m}$ . The capacitor is to have a capacitance of 1.50 $\mathrm{nF}$ and must be able to withstand a maximum potential difference of 4.00 $\mathrm{kV} .$ What is the minimum area the plates of this capacitor can have?

Key Concepts

Dielectric Constant

The dielectric constant is a measure of a material's ability to increase the capacitance of a capacitor compared to a vacuum. In other words, it quantifies the material’s capacity to store electrical energy in an electric field by reducing the effective field within the capacitor. This concept is crucial when selecting and using a dielectric in capacitor design because it directly affects the overall capacitance when inserted between the plates.

Capacitance of a Parallel-Plate Capacitor

The capacitance of a parallel-plate capacitor is determined by the geometry of the plates and the properties of the dielectric material between them. The relationship is given by C = (???A)/d, where C is the capacitance, ? is the dielectric constant, ?? is the permittivity of free space, A is the area of the plates, and d is the distance between them. This formula connects the physical dimensions of the capacitor with its ability to store charge, making it essential for designing capacitors to meet specific requirements.

Dielectric Strength

Dielectric strength is the maximum electric field a material can withstand without breakdown, meaning without becoming electrically conductive. It is expressed in units of volts per meter and is critical in the design of capacitors because it determines the maximum potential difference that can be applied across the capacitor before the dielectric fails. This concept ensures that the capacitor operates safely under the intended voltage conditions.

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