A capacitor is an electrical element that allows you to store a charge. Its simplest form is two plates separated by a dielectric layer. If voltage is applied to the plates, then it will remain for some time after it is removed. It is important to know where the capacitance is measured in order to properly build circuits with these elements.
Content
- Application in technology
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Formulas for calculating capacitors
- Determination of capacity
- Calculation of energy
- Dielectric leakage current
- Connecting elements
Application in technology
Capacitors are used in various electrical and radio equipment. These cells are capable of storing charge and maintaining the voltage (for example, mains) at the proper level during minor power outages. High-capacity capacitors are themselves used as power elements for small-sized mobile equipment. They are also called supercapacitors. Their disadvantage is the need for frequent recharging.
These elements are also of great importance in filtering devices, devices, the task of which is not to let interference into the useful signal, or to catch the desired signal in a constant voltage of an increased level.
No AC signal generator is complete without capacitors. Their purpose is to set the frequency of generation, period and other time parameters. Very precise elements are used here, with a nominal tolerance of no more than 1%.
Capacitors come in both fixed and variable capacities. Variable capacitance elements are used in equipment that requires tuning to different frequencies. For example, it is widely used in tuning radio frequencies in FM receivers.
Formulas for calculating capacitors
To solve technical problems and applied theoretical calculations, you need to know the laws by which electrical quantities interact with each other. These laws are expressed in formulas. For example, the voltage across a capacitor depends on its capacity and the charge it has accumulated.
Determination of capacity
This value depends on several parameters. To calculate it, you need to know what the capacitance of the capacitor is measured in. This value is equivalent to how much the coulomb of charge is accumulated by the cell when a voltage of 1 volt is applied to it. It is measured in farads. The capacity of these elements also depends on their shape.
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Flat capacitors are the simplest type of charge storage. How to find the capacitance of a capacitor that has a flat shape, you can find out if you determine all the parameters that affect this. Its capacitance is affected by the distance between its plates (conductive plates) d, the area of the plates themselves S, dielectric constant of the substance between the plates ε and electric constant ε0, which is equal to 8.85 ⋅ 10-12 farad per meter. The capacitor formula is as follows:
С = ε ⋅ ε0 ⋅ S / d
- A cylindrical capacitor also consists of two charged plates, both of which are in the form of cylinders located one inside the other. The inner cylinder is one-piece, the outer one is hollow. The distance between the plates is equal to the difference between the radii of these cylinders. The formula for the capacitance of a capacitor can be represented the same as in the previous case, with the difference that the area of the plates is calculated based on their height and radius:
С = 2 ⋅ π ⋅ ε ⋅ ε0 ⋅ h ⋅ R ext / (R ext - R ext) = ε ⋅ ε0 ⋅ S / d
where h is the height of the plate,
Rvn - inner radius, R bunk - outer radius,
π = 3,14.
- A charge can be possessed not only by a body with two plates, but also by a conducting spherical object. If you apply voltage to it, and then measure the potential between it and the ground, then the potential will be nonzero. Formula for calculating a spherical charge storage device:
С = 4 ⋅ π ⋅ ε ⋅ ε0 ⋅ R
where R is the radius of the ball.
If you substitute the radius of the Earth and the dielectric constant of air in the formula, you can get the value of the Earth's capacitance in farads. After calculations:
C (Earth) = 700 microfarads
Modern electrolytic capacitors can have such a capacity.
If we place one ball inside another and apply voltage between them, then the resulting structure will also accumulate charge between the surfaces of the balls. The determination of the capacity of such a design can be carried out according to the formula:
C =ε ⋅ ε0⋅4⋅π ⋅ R1 ⋅ R2 / (R2 - R1)
where R2 and R1 are the radii of the corresponding spherical surfaces.
The capacitance of a capacitor also depends on the type of dielectric used. The most common fillers are ceramic, electrolytic, paper, air and mica fillers.
Calculation of energy
Charge storage devices have other parameters as well. One of them is energy. When a capacitor is charged, potential energy accumulates on its plates.
It creates a force that attracts oppositely charged plates, as well as a current that feeds electrical appliances if you use a supercapacitor as a power source. Energy can be expressed as a dependence on the voltage of the plates and capacitance:
W = C ⋅ U 2 /2
Dielectric leakage current
A leakage current appears in an element if there are paths for the flow of electric current from one plate to another. The less insulating the dielectric has, the greater the leakage current will be. This is especially true for capacitors with an oiled paper dielectric. This parameter depends both on the design of the element and on the contamination of its body. If the cell is leaking, the leakage current can increase if moisture penetrates into the housing. This current can be calculated according to Ohm's law:
I ut = U / R d
where I ut is the leakage current,
U is the voltage on the plates,
R d - dielectric insulation resistance.
Connecting elements
When creating circuits, a different connection of elements is used. Schematic elements can be connected:
- Parallel;
- Consistently;
- Parallel - sequentially (mixed).
How to find the capacity of parallel connected elements? You need to understand what is common with this type of connection. Since the voltage is applied simultaneously to all plates, it is common. The charge will be different for everyone. According to the formula:
q = C ⋅ U, here q is the total charge, that is
q = ΣC i ⋅ U = U ⋅ ΣC i
C total will equal the sum of all C.
When the elements are connected in series, the charge will be common to all of them. At the same time, the stress will be different for each of them, and the total will be added up from all separately.
U = q / C, here U is the sum of voltages on all elements
U total = q ⋅ Σ (1 / C i)
1 / C total = 1 / C 1 + 1 / C 2 +... + 1 / C i
With this connection, the total capacitance value will be less than the smallest value of this value in the group.
In the case of using a mixed connection, it is necessary to calculate separately the total capacitance for the parallel connection and separately for the serial connection. After that, according to the formula of the serial connection, find the value common to the two resulting values.
