Capacitor. The energy of a charged capacitor

Since the beginning of the study of electricity, the problem of its accumulation and conservation was solved only in 1745 by Ewald Jürgen von Kleist and Peter van Mushenbruck. Created in the Dutch Leyden device allowed to accumulate electrical energy and use it if necessary.

The Leiden Bank is a prototype of a condenser. Its use in physical experiments has advanced the study of electricity far ahead, it has made it possible to create a prototype of an electric current.

What is a capacitor

Collecting electric charge and electricity is the main purpose of the capacitor. It is usually a system of two insulated conductors located as close as possible to each other. The space between the conductors is filled with a dielectric. The charge accumulated on the conductors is selected with a different charge. The property of unlike charges attracted contributes to its greater accumulation. The dielectric has a dual role: the greater the dielectric constant, the greater the electrical capacity, the charges can not overcome the barrier and become neutral.

The electrical capacity is the main physical quantity that characterizes the capacitor's ability to accumulate a charge. Conductors are called plates, the electric field of the capacitor centers between them.

The energy of a charged capacitor, apparently, should depend on its capacitance.

Electric capacity

The energy potential makes it possible to use (large electric capacitance) capacitors. The energy of a charged capacitor is used, if necessary, to apply a short-time current pulse.

What are the values of the electrical capacity? The process of charging the capacitor begins with the connection of its plates to the poles of the current source. The charge accumulated on one plate (the value of which is q) is taken as the charge of the capacitor. The electric field, concentrated between the plates, has a potential difference U.

The electrical capacity (C) depends on the amount of electricity concentrated on one conductor, and the field voltage: C = q / U.

This value is measured in Φ (farads).

The capacitance of the whole Earth does not go in comparison with the capacitance of a capacitor, the value of which is approximately from the notebook. The accumulated powerful charge can be used in engineering.

However, there is no possibility to accumulate an unlimited amount of electricity on the plates. When the voltage rises to the maximum value, a breakdown of the capacitor may occur. Plates are neutralized, which can lead to damage to the device. The energy of the charged capacitor is thus completely used to heat it.

The energy value

The heating of the capacitor is due to the transformation of the energy of the electric field into the internal one. The ability of the capacitor to perform work to move the charge indicates the availability of a sufficient supply of electricity. To determine how large the energy of a charged capacitor is, let us consider the process of its discharge. Under the action of an electric field by a voltage U, a charge of q flows from one plate to another. By definition, the work of the field is equal to the product of the potential difference by the amount of the charge: A = qU. This relationship is valid only for a constant value of the voltage, but in the process of discharge on the plates of the capacitor, it gradually decreases to zero. To avoid inaccuracies, let us take its average value U / 2.

From the formula for the electric capacity, we have: q = CU.

Hence the energy of the charged capacitor can be determined by the formula:

W = CU 2/2.

We see that its magnitude is greater, the higher the electrical capacity and the voltage. To answer the question of what is the energy of a charged capacitor, let us turn to their varieties.

Types of capacitors

Since the energy of the electric field concentrated inside the capacitor is directly related to its capacitance, and the operation of the capacitors depends on their design features, different types of storage devices are used.

1. The shape of the plates: flat, cylindrical, spherical, etc.
2. By changing the capacity: constant (capacity does not change), variables (changing physical properties, changing capacitance), trim. Changing the capacity can be carried out by changing the temperature, mechanical or electrical voltage. The electrical capacitance of trimmer capacitors varies with the area of the plates.
3. By type of dielectric: gas, liquid, with a solid dielectric.
4. By the type of dielectric: glass, paper, mica, metal, ceramic, thin-film from films of various composition.

Depending on the type, there are different capacitors. The energy of a charged capacitor depends on the properties of the dielectric. The main quantity is called the permittivity. The electrical capacity is directly proportional to it.

Flat capacitor

Consider the simplest device for collecting electric charge - a flat capacitor. This is a physical system of two parallel plates, between which there is a layer of dielectric.

The shape of the plates can be rectangular and round. If it is necessary to obtain a variable capacitance, then plates are taken in the form of half-discs. Turning one facing relative to the other leads to a change in the area of the plates.

We assume that the area of one plate is S, the distance between the plates is assumed equal to d, the permittivity of the filler is ε. The electrical capacity of such a system depends only on the geometry of the capacitor.

C = εε ₀ S / d.

The energy of a flat capacitor

We see that the capacity of the capacitor is directly proportional to the total area of one plate and is inversely proportional to the distance between them. The coefficient of proportionality is the electric constant ε ₀ . Increasing dielectric permittivity of the dielectric will increase the electrical capacity. Reducing the area of the plates makes it possible to obtain tuning capacitors. The energy of the electric field of a charged capacitor depends on its geometric parameters.

We use the calculation formula: W = CU 2/2.

Determination of the energy of a charged capacitor of a planar shape is carried out according to the formula:

W = εε ₀ SU ² / (2d).

Use of capacitors

The ability of capacitors to smoothly collect electric charge and give it up quickly enough in various fields of technology.

Connection with inductors allows the creation of oscillatory circuits, current filters, feedback circuits.

Flashbulbs, electric shock, in which an almost instantaneous discharge occurs, use the capacitor's ability to create a powerful current pulse. The capacitor is charged from a DC power source. The condenser itself acts as an element that tears the circuit. Discharge in the opposite direction occurs through a small ohmic resistance lamp almost instantaneously. In the electric shock, this element is the human body.

Condenser or battery

The ability to store accumulated charge for a long time gives an excellent opportunity to use it as a storage of information or energy storage. In radio engineering this property is widely used.

Replace the battery, unfortunately, the capacitor is not able to, because it has a feature to discharge. The energy accumulated by it does not exceed several hundred joules. The battery can save a large supply of electricity for a long time and practically without loss.