Capacitance

The electrical capacity (symbol, from the Latin capacitas = capacity; adjective capacitive) is a physical quantity in the field of electrostatics, electronics and electrical engineering.

The electrical capacitance between two insulated electrically conductive elements is equal to the ratio of the amount of charge that is stored on these conductors and the electrical voltage applied to them:

For accumulators and batteries to use the term " capacity " for the maximum amount of charge that can be stored in them. It is expressed in ampere-hours (Ah). This electric charge is not shown here electrical capacity.

Capacitance of a capacitor

A technically important application is the capacity in the form of electrical capacitors, which are characterized by specifying a certain capacity. The term "capacity" is used colloquially as a synonym for the electrical component capacitor itself used (English capacitor ).

Capacitors provide a conductor assembly having two electrodes for the separate storage of electrical charge and dar. In physical point of view occurs because the electrical flow of the separated electric charges, which are transported from the external power source to the voltage on the electrodes, which is:

Results. Formally, this relationship over the Gaussian law. The electrical capacity of a capacitor can be expressed as the ratio of the amount of charge to the applied voltage:

It usually is a constant parameter. It is like this, in simple terms, the volume of a compressed air tank at a constant temperature. The air pressure is analogous to voltage and the amount of air similar to the amount of charge. This analogy can realize easily that the amount of charge in the capacitor is proportional to the voltage.

This law applies to the so-called pseudo- capacitance, a voltage-dependent within narrow limits electrochemical or Faraday storing electrical energy which is connected to in a redox reaction, and a charge transfer of electrodes of double layer capacitors, however, unlike batteries the electrodes no chemical material change occurs.

Among other things, the Physikalisch -Technische Bundesanstalt ( PTB ) is concerned with capacity normals.

Unit

The electrical capacity is measured in the SI derived unit farad. A Farad ( F 1 ) is the capacity for storing the application of a voltage of 1 V, a charge amount of 1 Coulomb ( C 1 = 1 As):

A capacitor of capacitance 1 Farad charges at a constant charge current of 1 amp at 1 second for the voltage 1 volt. The SI unit farad, named in honor of the English physicist and chemist Michael Faraday, has now become internationally accepted everywhere.

Outdated unit

Until the mid-20th century, the capacity of capacitors was often labeled with the capacity unit cm. This in centimeters due to the fact that the capacity is expressed in today practically hardly used Gaussian system of units in the length dimension. Thus, a metal sphere with radius 5 cm with respect to a counter electrode is located at infinity to a capacity of 5 cm.

The figure shows a paper capacitor of the brand SATOR the former company Kremenezky, Mayer & Co of Johann Kremenezky from the year 1950 with a capacity of " 5000 cm " at a test voltage of " 2000 V". This would be a capacity of about 5.6 nF in the usual today the SI unit system. This corresponds to the capacity of a metal sphere of radius 5000 cm.

With a capacity of 1 cm in the Gaussian system of units corresponds to approximately 1.1 pF in the SI system of units, the conversion factor is 4πε0. This conversion is due to the definition of the field constant in the Gaussian system of units:

Capacity of certain conductor arrangements

For the capacity of a number of simple conductor arrangements, there are analytical solutions or convergent series expansions. The following table illustrates some examples:

D: distance between the spheres, d> 2a D: d/2a γ: Euler - Mascheroni constant

Herein, if necessary, A is the area of the electrodes, their distance d, l the length, and their radii. It is important where is the electric field constant of the vacuum and the permittivity of the dielectric. In the schematic representation of the head of light gray or dark gray and the dielectric are colored blue.

Calculations for capacity

General equations for the determination of capacity apply to current, voltage and charge to an electrical capacitance:

An expression for the capacity of any electrode array or charge distribution can be derived by means of the divergence theorem:

It is. For a vacuum, the above-mentioned simplified Equation due to:

A calculation of the capacity requires the knowledge of the electric field. For this, the Laplace's equation is a constant potential to solve the conductor surfaces. In more complicated cases, there is no closed form solution.

Measuring the capacitance

Measuring the capacity is not only the control of the capacitance of a capacitor (component ) but is used in, for example, capacitive distance sensor for determining the distance. Also, further sensors ( pressure, humidity, gases) are often based on a capacitance measurement.

According to the contexts mentioned above, the capacity can be determined as follows:

• Charging with a constant current and monitoring the voltage slew rate
• Measuring the resonant frequency of the capacitance formed by the LC resonant circuit
• Applying an AC voltage and measuring the current profile

In particular, the latter method is employed in measuring capacitance, wherein not only the magnitude of the current, but also its phase position is detected to the voltage. In this way, the loss angle, or the quality factor of the capacitor can be determined.