The energy of the charged capacitor

The energy of a charged capacitor - is the work spent on his charge.

From the history

The first capacitor is considered to be a Leyden jar. It developed independently once two scientists:

  1. Ewald Georg von Kleist (11 October 1745).
  2. Pieter van Musschenbroek (1745 - 1746 years).

Two decades later the light appeared elektroforus (1762), considered as the first planar capacitor. Then there were no terms, charge storage issues of little interest. Scientists yet fun give static charge. For example, van Pieter van Musschenbroek experienced Leyden jar too ambitious student, when he turned out to be one half-paralyzed electric charge.

Science did not go forward, even though the world, including Benjamin Franklin, does pushing locomotive. The current stage of development of physics began with Alessandro Volta. Scientist proved is attracted and intrigued design elektroforusa. Grated rubber could indefinitely charged metal plate. At that time, it was assumed that the electricity is transferred to the fluids of the atmosphere, and Volta thought similarly. Seeing that elektroforus able to store charge scientist decided to count the number.

The concept of the Volta

As the scientist notes, already in 1778 he got a glimpse of a potential difference, which he called tension - tension. Since 1775 Volta adheres capacitance concept - capacita, extended his teacher Beccaria. Volta already knows that elektroforus able to accumulate charge, calls the device a capacitor, and decides to confirm the theory of practice. Otherwise - to find the relationship of voltage, capacity and volume (quantita) charge.

Volta began with the Leyden jar. He charged it from the static generator and tried to determine the energy of the capacitor in three ways:

  1. Observed obtained spark of the electric arc by various design Leyden jars charged with the same voltage.
  2. Measured the amount of the electrostatic generators friction work until the electrometer readings did not grow to a certain level.
  3. Discharged a Leyden jar outdoors and tried to compare them produced an electric shock after time.

All of the above has led researchers to strange findings that high a Leyden jar roomy (under identical squares electrodes and other conditions being equal). This is probably related to the speed of the arc discharge in the air due to differences in the curvature of surfaces. Volta discharge force linked to the electric current the faster flowing fluid, the hotter (by sensations) effect. As a result, Volta found it, that the only potential difference defines the process of emergence of shock. He decided that the permissible voltage measured in two ways:

  1. After the amount of static charge generator speed.
  2. Comparing the effect of electric shock during the discharge of a Leyden jar.

Volta found that charging the Leyden jar empty of full, shock is twice as less. Slowly (1782) Volta concluded that the above values ​​relate to each other: tension x capacity ~ load, in the modern world looks like a U C = q or C = q / U.

Volta concluded that the capacity of greater where at a lower voltage hold more charge. Followed by the conclusion that the amount of accumulated fluid is directly proportional to the area of ​​the plates of a plane capacitor. Which is consistent with current formulas. Volta summarized knowledge to arbitrary conductor (experimented with rods Leyden jars). By varying the distance between the plates, found the following:

C ~ S / d.

What is actually an expression of the capacity of a plane capacitor. Volta explained by the presence of a dependence of resistance (resistance) between the electrodes, meaning the air. By changing the distance, this setting manages to be varied in both directions. It's a little inconsistent with the modern concepts, but Volta helped George Omu after 40 years to bring the relationship between current and voltage.

In fact, measurement is done based on the work field, exhibit only due to charge the capacitor. It is obvious that said energy value is - one of the first physical characteristics used to derive analytical expressions.


Energy and work is generally measured in joules, electrical voltage and potential - in volts.

It called volt potential difference, when moving a unit positive charge between which work is performed in 1 joule.

capacitance of the capacitor

Shown above, expressed Volta capacity capacitor. The formula will be needed when calculating the energy. The direction of the force lines determined by Coulomb, according to indications of a torsion balance, allowing physicists eventually bring own formula. Volta was close to the introduction of the concept of electric potential, can not deprive the mention of his mentors: Beccaria and Cavendish. Thanks to the people mentioned physics became closely to look closely to magnetism and electricity.

Employment of an electric field

The electric field is called potential. This means that the work of his strength does not depend on the trajectory of the charge, solely on the energy of the initial and final position. Recall, according to the definition:

Electric field - this matter, by which electric charges interact.

An electric field is applied only on electric charges. Created in two ways:

  1. Electric charges. Power lines begin on positive and end with negative charges.
  2. Changing magnetic field. This produces an electromagnetic wave that is used in a generator.

When they say that the radiation devices affects a person, and refers to the magnetic and electric components. Especially dangerous is the first one that is screened with great difficulty. The electric field is considered in a school course of physics, it is considered stationary and the strength of its lines are parallel. Two examples:

  1. Suppose the charge moves along the field lines by a distance l. Then the work is under the simplified formula A = Fl, where F - the force acting on the charge.
  2. Now assume that the charge has moved from the previous point on the bias. So that the projection path lb on the power line is again l. A rectilinear portion, the deflection angle - V. The work is calculated by the formula taking into account both geometrical relationships A = FlbcosB = Fl.

This simple case is easy to apply to any form of tension lines. These things means that in an electric field work does not depend on the trajectory and, hence, equal to the difference field potentials: A = P1 - P2. The formula is applicable for any field. To adapt expression, introduced the concept of electric potential as the power unit of positive charge - f = f / q1. Then the formula to work takes a different view.

Electric voltage between two points is called the potential difference between them. Multiplying said value by the amount of charge as the specific value, we obtain: A = (F1 - F2) q = U q. The potential across the field magnitude is:

p = q / 4 pi ε r,

wherein q - amount of charge generating field; ε - dielectric constant of the medium (air or vacuum is unity); Pi = 3.14; r - distance of the point from said charge. The formula is not suitable for all cases, are exemplary. Acceptable applied to the charge distributed on the surface of the sphere, and points that lie outside of said surface.

The field strength of the flat capacitor

In physics, the consideration is always conducted on the example of a plane capacitor, it just happens. Field flat capacitor corresponds exactly to that described above.

Let on the plates there is a certain charge. Obviously, the amount of it is the same, but different signs. Work on charge transfer between the electrodes is equal to A = F d, wherein a mean gap width d. Formula directly leads to an intensity due to: A = E q d = ​​U q (cm. above). Consequently, we can write that E = U / d.

The field strength shows the force with which the unit operates at a point charge.

The energy of the charged capacitor

Now consider how to calculate energy during charging of the capacitor. We need to remember formula potential created by a point charge. It can be seen that it decreases linearly distance. But in this case, the first and positive charge is located on a second plate and the second negative and located opposite. Therefore, as the movement in the direction of the line of force indicated the following picture:

  1. positive charge potential drops.
  2. Potential negative charge increases.

And the rate of change is the same. Consequently, the flat capacitor between the plates of the potential field does not change. Now remember, from which it depends. In case the investigated quantities are constant except charge accumulated on the plates after energization. So the potential is gradually increasing and linearly dependent on the charge, with no longer important schedule proper process. It turns a straight line.

This means that initially the potential is zero, and then increases to a certain limit. A graph of the number of potential charges would be a straight line (time goes exhibitor). Now explain why the conclusions were made:

  1. It is known that the energy is expressed by the work expended.
  2. So, it is permissible to write the formula W = U q. It looks easy, because the charge is related to capacity, but what is the voltage? It is recalled that the capacitor is growing exponentially during charging. Take the time integral? Physicists have already solved the problem.
  3. The potential (voltage) is linearly dependent on the charge, we conclude that the overall operation of averaging is that when a straight line is reduced to the division by 2.

The result: W = U q / 2. Now substitute here the expression obtained Alessandro Volta, and out: W = C U2 / 2. The resulting expression and used in the calculations.

measure of the energy of a charged capacitor

When calculating the power filter circuits and other electrical filters stands the problem of determining the denominations. It seems sufficient to take the formula of the frequency resonant circuit, but simplicity is deceptive. It is easy to verify that the same answer corresponds to a set of values. Which to choose?

The greater the power source, power device, the greater energy here takes place in unit time. For capacitor is dependent on the voltage and capacitance of a square, for a throttle - by the electric current and inductance. Hearing single period fluctuations this figure is easy to tie to power as the work performed per unit time.

As a result, the engineer will be able to say approximately how large capacity is required in a particular case. The calculation is carried out initially by the energy of a charged capacitor.

Similar occurs in any circuit. Capacitors are used to filter and galvanic isolation are required to easily pass the desired frequency and to be capacious, not to become a bottleneck in the system.

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