﻿ Capacitor — MecatrónicaLATAM

MecatrónicaLATAM

# CAPACITOR

## WHAT IS A CAPACITOR?

The condenser or capacitor is a passive component which is capable of storing energy in the form of an electric field. This field is the result of a separation of the electric charge. It is formed by a pair of conductive surfaces, generally of sheets or plates which are separated by a dielectric material or by vacuum. The plates subjected to a potential differential acquire a certain electric charge (positive in one of them and negative in the other), the total charge variation being zero. A capacitor is a two-terminal device and may have polarity at its terminals.

When a voltage source is connected to the capacitor, a positive charge + q is deposited on one plate and a negative charge –q on the other, in this way the capacitor stores the electric charge. The stored load is represented by the fact that it is directly proportional to the voltage applied between the plates by a constant that indicates the ability to store energy in the form of an electric field and depends on the dielectric material.

This can be expressed mathematically as:

q = CV

Where:

• q is the charge stored [Coulomb].
• C is the capacitance of the capacitor [Farad].
• V is the voltage applied to the capacitor [Volt].

Capacitance is the relationship between the electrical charge on a plate of a capacitor and the difference in voltage between the two plates, its value depends on the physical dimensions of the capacitor and the permittivity of the dielectric material with which it is constructed.

For a parallel conductor plate capacitor, the capacitance is expressed by:

C =
ε A /
d

Where:

• A is the surface area of each plate..
• d is the distance between the plates
• ε is the permittivity of the dielectric material between the plates.

The value of capacitance can increase by three factors:

1. A greater surface area of the plates.
2. Less spacing between the plates.
3. A better permittivity of the insulating material (dielectric).

The dielectric material is an insulator that increases the capacitance as a result of permanent or induced electrical dipoles in the material. Strictly speaking, the direct current (DC) does not flow through a capacitor, instead the charges move from one side of the capacitor through the conductor circuit to the other side, which establishes the electric field. The displacement of the charge is called the displacement current because the current seems to flow momentarily through the device.

## RELATIONSHIP VOLTAGE - CURRENT OF THE CAPACITOR

The voltage-current ratio of the capacitor is defined as:

V(t) =
1 /
C
t 0 idt =
q(t) /
C

Where q (t) is the amount of cumulative charge measured in coulombs and C is the capacitance measured in farads (F = coulombs / volts).

“The voltage on a capacitor cannot change abruptly.”

To differentiate this equation, you can relate this displacement current to the voltage change rate:

I(t) = C
dV /
dt

The capacitance is a property of the dielectric material and the geometry and separation of the plates. Typical capacitor values vary from 1 pF to 1000 uF. Since the voltage across a capacitor is the integral of the displacement current, the voltage can not change instantaneously. This feature can be used for timing purposes in electrical circuits as a simple RC circuit.

In experimental matters, the capacitor is capable of storing the electrical energy it receives during the charging period, the same energy that it yields later during the discharge period.

## POWER IN A CAPACITOR

The instantaneous power supplied to the capacitor is:

P = VI = CV
dV /
dt

The energy stored in the capacitor is:

W = t -∞ Pdt

V(-∞)=0, because the capacitor was discharged in t=-∞. The energy equation results:

W =
1 /
2
C V2

Based on the charge equation stored in the capacitor, the energy equation in the capacitor can be reformulated as:

W =
q2
/
2C

You can use any of the two previous equations to find the energy stored in the capacitor. This energy can be recovered since an ideal capacitor cannot dissipate energy.

## SIMBOLOGY OF THE CAPACITOR

The shape of a capacitor is rectangular, square, circular, cylindrical or spherical. As different types of capacitors are available, there are different symbols available to represent them that are shown below.

Just like the electric resistors, the capacitors can also be fixed or variable type, their symbology is presented in the following figure:

## VALUE OF A CAPACITOR

Theoretically, capacitors adopt any value such as electrical resistors, but in the market only certain values ​​that normally go in the range of picoFarad to microFarad are adopted, as well as the insulating material with which they are constructed as ceramics. Just like the electric resistors, the capacitors can also be fixed or variable type, their symbology is presented in the following figure:

“A non-ideal capacitor has a model with a leakage resistance in parallel, which can be up to 100Mohm and be neglected in most practical applications.”

## TYPES OF CAPACITORS

The main types of commercial capacitors are electrolytic capacitors, tantalum capacitors, ceramic disc capacitors and mylar capacitors. The electrolytic capacitors are polarized, which means that they have a positive and a negative end. The positive side of a polarized capacitor must be maintained at a higher voltage than the negative side; otherwise, the mechanism will usually be damaged.

## DIELECTRIC OF A CAPACITOR

The dielectric act as an insulating material between the plates. The dielectric can be any non-conductive material such as ceramic, waxed paper, mica, plastic or some form of liquid gel.

The dielectric also plays an important role in deciding the value of the capacitance. As the dielectric is introduced between the plates of the capacitor, its value increases.

The different dielectric materials will have different dielectric constants, however, this value is K>1.

The Table shows the value of the dielectric constant for some of the dielectric materials (approximate values).

Dielectric Table
Material Constant
dielectric
(K)
Vacuum 1
Air
(1 atm)
1.00059
Air
(100 atm)
1.0548
Polypropylene PP 2.2
Polyethylene 2.25
Benzene 2.28
Mica 5.4 to 8.0

Dielectric can be of two types

1. Polar dielectrics: These dielectrics will have permanent dielectric movement.
2. Non-polar dielectrics These will have a temporary dielectric moment. By placing them in an electric field, they can be induced with dipole moments.

Note: It should be considered that no dielectric is a perfect insulator because they have leakage current.

## VOLTAGE CLASSIFICATION OF A CAPACITOR

This is not voltage until the capacitor is charged but the maximum voltage to which the capacitor can operate safely. This voltage is called working voltage (WV) or DC working voltage (DC-WV).

If the capacitor is applied with a voltage greater than this voltage, it can be damaged by producing an arc between the plates due to the dielectric breakdown.

When designing circuits with condensers, care must be taken that the capacitance of the capacitor is greater than the voltage used in the circuit. For example; if the operating voltage of the circuit is 12 V, then it is necessary to choose a condenser with a nominal voltage of 12 V or higher.

This working voltage of a condenser depends on factors such as the dielectric material used between the capacitor plates, the dielectric thickness and also the type of circuit used.

## GENERAL TECHNICAL CHARACTERISTICS

• Rated capacity: It is the theoretical value expected at the end of the manufacturing process. It is marked on the body of the component by means of a color code or directly with its numerical value.
• Tolerance: Difference between deviations capacity, higher or lower depending on the manufacturer.
• Nominal voltage: It is the voltage that the capacitor can support in a continuous way without suffering deterioration.

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