# Parallel Plate Capacitor: Definition, Formula, and Applications

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A parallel plate capacitor is a device that can store electric charge and energy in the form of an electric field between two conductive plates. The plates are separated by a small distance and are connected to a voltage source, such as a battery. The space between the plates can be filled with air, a vacuum, or a dielectric material, which is an insulator that can be polarized by an electric field.

## What is a Parallel Plate Capacitor?

A parallel plate capacitor is defined as an arrangement of two metal plates of equal area A and opposite charge Q, separated by a distance d. The plates are connected to a voltage source V, which creates an electric potential difference between them. The electric field E between the plates is uniform and perpendicular to the plates, as shown in Figure 1.

The electric field E between the plates is given by:

where V is the voltage across the plates, d is the separation between the plates, σ is the surface charge density on each plate, and ϵ0​ is the permittivity of free space.

The electric field E induces a polarization P in the dielectric material, which is the dipole moment per unit volume of the material. The polarization P reduces the effective electric field E inside the dielectric and increases the capacitance C of the capacitor.

The capacitance C of a parallel plate capacitor is the ratio of the charge Q on each plate to the voltage V across the plates:

The capacitance C depends on the geometry of the plates and the dielectric material between them. For a parallel plate capacitor with air or vacuum between the plates, the capacitance C is given by:

where A is the area of each plate and d is the separation between the plates.

For a parallel plate capacitor with a dielectric material between the plates, the capacitance C is given by:

where k is the relative permittivity or dielectric constant of the material, which is a dimensionless quantity that measures how easily the material can be polarized by an electric field.

The relative permittivity k of a dielectric material is always greater than or equal to 1. The higher the value of k, the more charge can be stored on the capacitor for a given voltage, and thus the higher the capacitance.

## Applications of Parallel Plate Capacitors

Parallel plate capacitors have many applications in various fields of science and engineering. Some of them are:

• Filtering: Parallel plate capacitors can be used to filter out unwanted frequencies or noise from an electrical signal. For example, they can block direct current (DC) signals and allow alternating current (AC) signals to pass through. They can also be used to smooth out voltage fluctuations in power supplies.
• Tuning: Parallel plate capacitors can be used to tune electrical circuits to resonate at a desired frequency. For example, they can be used in radios, televisions, and other communication devices to select a specific channel or frequency band.
• Sensing: Parallel plate capacitors can be used to sense physical quantities such as pressure, temperature, humidity, displacement, etc. For example, they can be used in microphones, thermometers, hygrometers, accelerometers, etc. The capacitance of a parallel plate capacitor changes with these physical quantities due to changes in the distance between the plates or the dielectric material between them.
• Energy storage: Parallel plate capacitors can be used to store electrical energy in their electric fields. For example, they can be used in flashlights, cameras, defibrillators, etc. The energy stored in a parallel plate capacitor is given by:

where U is the energy stored in joules (J), C is the capacitance in farads (F), and V is the voltage in volts (V).

## Summary

• A parallel plate capacitor is a device that can store electric charge and energy in an electric field between two conductive plates separated by a distance.
• The capacitance of a parallel plate capacitor is proportional to the area of each plate and inversely proportional to the distance between them. It also depends on the dielectric material between the plates, which reduces the effective electric field and increases the capacitance.
• Parallel plate capacitors have many applications in filtering, tuning, sensing, and energy storage. They can be used to block or pass certain frequencies, select a desired frequency, measure physical quantities, and store electrical energy.

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