### Condensator: old markings

To see the value of the capacity, the codes of markings evolved ⁄ moved with time, then to find nearest the value standardised.
To determine the technology of the component (chemical, mica, paper) and to find its equivalent current.

burst sight condensing filtering

burst sight condensing connexion
Units of capacity expressed in centimetres

structure of a condensator
Today the unit of capacity of a condensator paper and mica is the Farad (F). This unit is resulting system system internantional. The farad, badly adapted unit, are declined using its under multiples.
The table described opposite under the most current multiples in TSF:
The picofarad (pF): 1F ⁄ 1.000.000 000.000: agreement, decoupling and connexion high frequencies
The nanofarad (nF): 1F ⁄ 1.000.000 000: decoupling and connexion HF
The microfarad (µF): 1F ⁄ 1.000.000: decoupling low frequencies and filtering of food high voltages
 Old marking Unit Initials Value mF microfarad µF 10-6 F mmF ou µµF picofarad pF 10-12F 1 ⁄ 1000e nanofarad 1 ⁄ 1000 10-9F T (Tausend pF) nanofarad T(*) 10-9F
Some old models

One defines the capacity by the relation

### Q = C * U

Q is the load stored on its positive terminal and is expressed in Coulombs
U is the terminal voltage of the component
C is the electric capacity of the capacitor.
Algebraical expression of the law of behavior of the capacitor

### Q1 = C * (V1-V2)

Indices 1 and 2 locating each terminal. Qk being the load of the terminal K and Vk its electric potential (K = 1 or 2). The terminal with the highest potential (limits positive) is thus positively charged. The total load of a Qt capacitor = Q1 + Q2 is thus null
Proceeding by electrostatic induction, the penetrating current by a terminal arises with identical by the other limits, although the reinforcements are separated by an insulator.
If one directs the branch of circuit containing the capacitor in the direction: limit 1 to limits 2, thus fixing the positive direction of current I, one then defines algebraically the tension U in the opposite direction (convention receiver)

### U = V1 to V2

It then becomes possible algebraically to define a relation between the current circulating in the branch and the temporal derivative of the tension:

### I = dQ1 ⁄ dt = C * du ⁄ dt

A capacitor is made up basically of two electric conductors, or reinforcements, very close one to the other, but separated by an insulator or dielectric.
The electric charge stored by a capacitor is proportional to the tension applied between its two reinforcements. Also, such a component it is mainly characterized by its capacity, relationship between its load and the tension.
The electric capacity of a capacitor is determined primarily according to the geometry of the reinforcements and the nature of insulators; the following simplified formula is often used to estimate its value:

### C = ε S ⁄ e

S : surface reinforcements in glance
e : outdistance between the reinforcements
ε : permittivity of the dielectric one
The electric base unit of capacity, is the farad which represents a very high capacity, seldom reached (except for the supercondensateurs); thus, of very small capacitors can have capacities about the picofarad
One of the characteristics of the capacitors is their tension of limiting service, which depends on the nature and the thickness of insulator entering their constitution. This insulator has a certain dielectric rigidity, that is to say a tension beyond which it can appear a violent one running of breakdown which involves a destruction of the component (except for some of them, whose insulator is known as self-healing).
The search of the strongest capacity for weakest volume and coùt of manufacture results in reducing as much as possible the thickness of insulator between the two reinforcements; as the tension of breakdown also decreases in the same proportion, there is often favors to retain best insulators.
Many techniques, often resulting from chemistry, made it possible to appreciably improve the performances of the capacitors, which one connects to the quality of the dielectric employee. It is thus the nature of dielectric which makes it possible to classify the capacitors:
the nonpolarized capacitors, of low value nanofarad or microfarad are primarily of technology mylar or ceramics
the capacitors known as polarized are sensitive to the polarity of the electric tension which is applied to them: they have a negative terminal and positive. They are the capacitors of electrolytic technology and tantalum. An error of branch or an accidental inversion of the tension generally leads to their destruction, which can be very brutal, even explosive
the nonpolarized supercondensateurs have an enormous capacity but a low behavior in tension (a few volts). They were developed following search carried out to improve the accumulators. The capacity which can exceed the hundred farads is obtained thanks to the immense developed surface of electrodes on activated carbon support
capacitors with variable capacity, used for example for the realization of adjustable filters RLC.
When the plates are brought closer, the capacity increases quickly, just as the gradient of tension (that is to say, the electrostatic field). For example, the field in a capacitor subjected to only 5volts and whose plates are distant of 5 micrometers is of 1 million volts per meter! The insulator thus plays a key role. The ideal insulator would have an infinite resistance and a total transparency with the field, would not have any flash point (gradient of field or appears an arc), would not have any inductance (which limits the reaction to the high frequencies: an ideal capacitor would let pass the light for example) etc One must thus choose an insulator according to the sought-after goal, that is to say the use which one wants to make of the capacitor.
Electrolytique capacitors
The electrolytique capacitors are used:
when one needs a greater capacity of storage
when one does not have a need to have a perfect capacitor
great resistance in series
great tolerance
Contrary to any other capacitor, when they are manufactured, one does not put an insulator between the two conductors. Moreover, electrolytic nine conduit the D.C. current! In fact, one of the conductors is metal, the other is a conducting frost: the metal conductor is simply inserted in the frost. When one applies a tension for the first time, a chemical reaction electrolyzes takes place, which creates an insulating interface on the surface of metal. obviously, so early formed, this layer prevents the current from passing and thus its own training. It results a very thin insulating layer from it (some molecules thickness). However, the frost is not as good conducting as a metal: electrolytic thus has a considerable resistance series which creates one zero within the meaning of the transfer functions filters low-pass with the capacity. Moreover, one AC current passing in the frost deforms orbital electrons of the layers of valence which bind the frost, creating a small mechanical vibration in the frost
Capacitors with tantalum
There exist 2 technologies of capacitors to tantalum:
Capacitors with tantalum with solid electrolyte: They are capacitors or the first electrode is tantalum, and the second of dioxide MnO2 the manganese. The contact with the manganese dioxide is ensured by a layer of metallization containing money. This technology brings the following advantages:
resistance series (ESR) reduced
low inductances series
weak resonances
no degradation in time, in storage or of use
coùt weak.
Capacitors with tantalum with liquid electrolyte (WET Tantalum): They are capacitors or the first electrode is tantalum, and the second a conducting gel.
more resistance series (ESR) that solid models
low inductances series
weak resonances
capacity of raised car-cicatrization, of or a greater reliability
coùt higher.
Indeed, the liquid electrolyte is able to oxidize tantalum in the event of defect in the oxide coating, this regeneration in fact of the capacitors of greater reliability, they are often selected for applications or reliability is a decisive criterion
The capacitors with liquid electrolyte are coùteux, because of materials used: money or massive tantalum for the case (because of the acid electrolyte), as well as more complex manufactoring processes (leakproof assembly), they in fact is reserved for top-of-the-range applications.
The capacitors with solid tantalum have an extremely low resistance series, which makes of it a preferential component for decouplings of feeding on the cards.
The capacitors with tantalum have however a defect: it have a light non-linearity, this is why these capacitors are disadvised for the transmission of signals (creation of even harmonics) except when they are associated with other nonelectrolytic capacitors to form a composite capacitor.
The capacitors with solid tantalum also have another defect: tantalum is likely to take fire in the event of going beyond of the current or failure. This is why they are used little in applications or that presents a danger to the user (automobile for example).
Adjustable capacitor with air (used in the receiving sets of radio for the choice of the stations).
They consist of mobile reinforcements one compared to the other; surfaces in glance determine the value of the capacitor.
advantages of an extremely low inductance and a very great resistance series, this is why the capacitors with ceramics insulator are largely used:
in the high frequency applications (until hundreds of gigahertz
in the applications high voltage (circuits to valves tubes
for the components of surface, because they lend themselves well to a miniaturization.
to be mechanically fragile
to have a field of flash not very high. They require a certain distance between the plates and thus lend themselves badly to greater capacities (What does not have importance in the high frequencies).
They have a light hysteresis of load and generate very small little noise when the dV ⁄ dt (thus running) is high (great amplitude of signal or very high frequency). This noise being a white vibration has little effect on the circuits high frequency, those being generally granted syntonized on a narrow tape.
Several ceramics classes are defined according to their behavior in temperature:
ceramics C0G or NP0 has a great stability and is used for the high frequency applications, and each time a good stability in temperature is required. Unfortunately, this ceramics does not present a very great permittivity, which limits the value of the capacity: classically some nanofarads to the maximum, for the components of surface.
ceramics X 7R, of less stability: approximately 10% of variation between 10°C and 60°C. One holds this ceramics with the applications not requiring a high stability. The permittivity is raised, which makes it possible to reach out of standard CMS of the capacities of a few hundreds of nanofarads.
ceramics Y4T and Z5U, has drifts in temperature of about 50% in the ranges referred to above, and is thus reserved for the functions of decoupling. On the other hand one can obtain capacities in components of surface, several microfarads.
particular ceramics for the ultra high frequencies, of very high stability and very weak factor of loss. This ceramics has a definitely higher coùt, but is essential for certain applications.
The capacitors with plastic insulator polyethylene, polystyrene, polypropylene are most current) were designed specifically for ends of decoupling of signals and use in filters.
Their hysteresis of load is very low (no one for polypropylene) and, so they are invaluable for the processing of very weak signals radio µtelescopes, communications space and audio of reference). Polystyrene and the polypropylene do not have an effect of battery (polyethylene in has very weak).
Two methods are used: either by the use of conducting and insulating sheets (film ⁄ foil construction), or by aluminum deposit on the dielectric one (metallized film capacitor). The second method decreases the coùt, volume, the weight of the capacitors, but also decreases the acceptable current
The polyester is mainly used under 2 of its forms: polyethylene terephthalate (FART), and polyethylene naphtalate (PEN). The advantage of polyethylene is that it can be stretched or rolled very thin and can thus allow appreciable capacities in a small volume (not comparable with electrolytic, nevertheless). It is easy to manufacture and form, and these capacitors are thus not very coùteux. The capacitors with polyethylene are very used in the audio circuits of average to good quality and in circuits asking for a weak variation of capacity with the old one and moisture. They are easy to recognize with their yellow color canary.
Polystyrene is not as easy to manufacture with precision as polyethylene. It is not coùteux in oneself (pieces of furniture of patio and packing is made of polystyrene) but difficult to roll precisely in thin layers. For this reason, the polystyrene capacitors are relatively cumbersome for a given capacity one 0,01 micro farad being as bulky as electrolytic of micro farad). They are as definitely coùteux as polyethylenes.
The great advantage of the polystyrene capacitors is their quality. They are very stable. For this reason, they are employed there or the precision is necessary: syntonized circuits with narrow tape, time bases etc Their noise is practically undetectable and very near to the theoretical limit limits of Johnson). They are far from sensitive to the temperature and old and, in so far as one remains in on this side limits of current and tension of the manufacturer, insensitive with use. Their parasitic inductance depends on the assembly: some are done of two metal sheetings and two sheets of polystyrene rolled up in spiral: these present a good precision of the capacity to the price of a certain parasitic inductance (weak). Others are done plates moulded in a block of polystyrene: they are less precise for the capacitance (what is not a problem for the circuits of precision which always have an adjustable element) but have an inductance parasitizes extremely weak. Their behavior in audio is excellent.
The capacitors polypropylene (PP) are very much used in audio. Extreme resistance series, no effect of battery, no hysteresis of measurable load, noise almost as weak as polystyrene They are as less expensive as the capacitors with polystyrene.polypropylene is very known plastic manufacturers: many toys, pieces of furniture of patio, various cases, automobile parts, cellphones and other accessories, even the bags of grocer is done polypropylene). They are with all practical purposes as stable as polystyrene (the difference can take centuries before being appreciable). They are less precise in face value than the capacitors with polystyrene but, with share in the circuits of reference (ultra-precise time bases), this does not have any importance. They are large also enough for their capacity, the badly lending themselves polypropylene, him also, with a very fine rolling.
These capacitors generally of low value are used into high frequencies and on average and high voltage. They have a good stability, measuring rod etc; disadvantage they coùtent approximately twice expensive than a ceramic capacitor of tension and capacity equalizes for example.
One also finds polyphenylene sulfide (PS), polycarbonate (PC), polyimide (PI), Teflon (Polytetrafluoroethylene PTFE)
The capacitors with film paper were used in the old radio operator receivers. They were abandoned because of their bad ageing, involving an important leakage current. One can often find some in violin makers, the guitarists followers of his "vintage" sometimes use them on the electric guitars.
The multi-layer capacitors with dielectric out of glass are used for their stability in temperature, and lifespan
The value of the electronic capacitors is marked on their cases in three principal forms. It is in light on the capacitors of sufficient size to accommodate the inscription (example: 10 micro farad). The character is sometimes transformed into the letter U as in 10uF. The manufacturer can use the code of colors relatively little employed except on certain capacitors out of plastic case. Generally on the capacitors of modest size and normal precision, the value is noted in picofarads (pF) in format XXY or XX correspond to the first two digits of the value and Y to the value of the exhibitor of ten in scientific notation.

Two supercondensateurs
A supercondensator is a capacitor of particular technique allowing to obtain a density of power and a density of energy intermediate between the traditional batteries and electrolytique capacitors.
These components thus make it possible to store an intermediate amount of power between these two modes of storage, and to restore it more quickly than a battery.

### Principle of operation

The majority of the marketed supercondensateurs are carried out according to the electrochemical process double-layer from where Anglo-Saxon initials EDLC (electrochemical double to bush-hammer capacitator).
The supercondensator consists of two porous activated carbon electrodes, generally and impregnated electrolyte, which are separated by an insulating and porous membrane (to ensure ionic conduction). The electric double layer develops on each interface electrode-electrolyte, so that one can schematically see a supercondensator like association series of two capacitors, one with the positive electrode and the other with the negative electrode. The mobility of the anions, much less hydrated, is larger than those of the cations. They move more easily in the structure of the activated carbon and form a weaker layer thickness, so that one observes a value of capacity of anode higher than that of cathode. Because of the laws of association of the capacitors, the capacity of the whole in series is always lower than weakest of these two capacities.
It is known that the capacitance of a capacitor is primarily determined by the geometry of the reinforcements (specific surface S and distance E) and of the nature of the insulators (the dielectric one). The following formula is often used to estimate the value of it
C = ε * S ⁄ E
Here, the organic solvent molecules play the part of dielectric of permittivity. That corresponds to a low thickness E of insulator (lower than the nanometer) what involves than the capacity per unit of area of these components is high: from 0,1 F. m2 with 0,3 F. m2
In addition, thanks to the use of a deposit of activated carbon on an aluminum film which has surfaces specific S typical from 2.000 to 3.000 m2 per gram, the surface of contact between electrode and electrolyte is immense, which makes it possible to obtain considerable values of capacity.
The behavior in tension is limited by the decomposition of organic solvent. It is currently about 2,5 V.
The maximum tension by element is currently of approximately 2,7 V (record held by Maxwell)
This type of capacitor is not polarized.
Internal resistance is very low what authorizes a load or a discharge with strong currents
 Performance comparison (orders of magnitude) Combustible battery Battery Supercondensator Electrolytique capacitor Density of power (W ⁄ kg) 120 150 1 000 - 5 000 100 000 Density of energy (Wh ⁄ kg) 150 - 1500 50 -1500 4-6 0,1

### The capacitor:

The capacitor is one of the element of most interesting used in electricity. Composed of the two conducting plates (Al, Ag, Cu, With) separated by an insulator (dielectric: paper, mica, polyester etc.), it is able to accumulate electric charges. It thus presents one on one of its plates a defect of electrons (positive pole) and on the other an excess of electrons (negative pole).
The capacitance of a capacitor notes C and its unit is the farad F.
Marking of the plastic capacitors:
Like resistances, certain capacitors are marked with a code of colors (the colors correspond to the same coefficients).
 color 1er ring 2ème ring Multiplier Tolérance Insulation black 0 0 x 1 pF 20% chestnut 1 x 10 pF 1% 100 V red 2 2 x 100 pF 2% 250 V orange 3 3 x 1 nF yellow 4 4 x 10 nF 400 V green 5 5 x 100 nF blue 6 6 x 1 uF 630 V purple 7 7 gray 8 8 x 0,01 pF white 9 9 x 0,1 pF or x 0,1 pF 5% silver x 0,01 pF 10%

### Transitory mode of the capacitor supplied with continuous tension:

 Charge with the capacitor: The charge of a capacitor cannot be instantaneous. Its duration can be calculated. It is of 5 t (tau) .t is called time-constant. t = R. C [S] For the discharge, the voltage curve will be identical to that of the load current and for the discharge of the current the curve is the same one as that of the load while running but into negative. The shape of these curves are of exponential type discharge: U = U * E - t ⁄ t charge: I = I * E - t ⁄ t

### Coupling of the capacitors:

 in single-phase current: in three-phase current During use of several capacitors one can simplify the circuits by differentiating two mode from connections: in series: Q = Q1= Q2 = Q3 =. = Qn C = 1 (1 ⁄ C1 + 1 ⁄ C2 + + 1 ⁄ Cn) in parallel: Q = Q1 = Q2 = Q3 = . = Qn C = C1+ C2 + C3 +. + Qn The three-phase coupling is mainly used to make compensation (improvement of the power-factor). Theoretically, one can make: that is to say a coupling star that is to say a coupling triangle. However for an equivalent reactive power, the capacity in triangle can be three times smaller than out of star. Gifts one rather selected the casting triangle.

### Permanent mode of the capacitor:

 The ohmic value of the capacitor varies according to the frequency. This value is called the capacitive reactance Xc. Xc = 1 ⁄ (2 * PI * F * C) What brings us to two conclusions: with F = 0 (tension continues) Xc = infinite = I = 0 [has] (only one transient of load) with F = infinite Xc = 0 ohm note: on the graph opposite: C is in µF.
The unit of capacity is the farad F. the practice shows that the farad is a value too much large. One will thus use preferentially the microfarad 10-6F = 1 µF
For a capacitor, the capacity depends on its construction:
C = A * er * E0 ⁄ d
with
C: capacity out of F
At surface of one of the plates in m2
Er: relative permittivity [-]
E0: permittivity of the vacuum (4 * PI * 10-7 [F ⁄ m])
note : E is actually Epsilon
Values of relative permittivity:
Air : 1;
Paper paraffined 2;
Glass 4 to 6;
Mica 4 to 8.

The Farad is the unit of capacity.
C = 1 [F] if the terminal voltage of the capacitor is worth 1 [V] and that it is charged with Coulomb (Q = 1 [C])
C = Q ⁄ U
The capacitors of compensation of energy reactivates in order to raise the power-factor
Reactive energy
The electrical communications with AC current provide the apparent energy which corresponds to the apparent power (or power called). This energy breaks up into two forms of energy: energy activates, transformed into mechanical energy (work) and heat (losses), reactive energy, used to create magnetic fields. The consumers of energy reactivates are the asynchronous motors, the transformers, inductances (ballasts of fluorescent tubes) and the static inverters (rectifying).
The power-factor
It is the quotient of the consumed active power and the provided apparent power.
F = P (W) ⁄ S (VA) ≈ COS φ
The cos φ is the power-factor of fundamental and does not take into account the power conveyed by the harmonics. A power-factor close to 1 indicates a low power consumption reactivates and optimizes the operation of an installation.
Charts
S = √ P² + Q²
The tangent
Certain invoices of electricity indicate the value of tg J which corresponds to reactive energy that the distributer must deliver to provide a power activates given.
tg φ = Q (VAR) ⁄ P (W)
Improvement of the power-factor
reduction in the invoice of electricity by avoiding power consumption reactivates beyond the frankness allocated by the distributer (40% of consumed active energy) for the subscribers with the green tariff (S 250kVA)
reduction of the contractual demand for the subscribers to the yellow tariff (36kVA; S 250kVA)
reduction in the section of the cables
reduction in on-line losses
reduction of the voltage drop
increase in the power available of the transformer
To improve the power-factor, it is necessary to install capacitors (reactive energy source). This operation is called "compensation"
In precondition to the compensation, it is necessary to avoid the oversizing of the asynchronous motors and their idle run (the power-factor of an asynchronous motor is all the more weak as the engine functions in on this side its rated power).
The various types of compensation, the compensation of reactive energy can be done:
by fixed capacitors (if the power of the capacitors is lower than 15% of the power of the transformer)
by capacitor batteries to automatic regulation (if the power of the capacitors is higher than 15% of the power of the transformer), which allow the immediate adaptation of the compensation the radial forces
The compensation can be :
total, at the head of installation
partial, by sector, on the level of the switchboard
local, at the boundaries of each inductive receiver
The ideal compensation is that which makes it possible to produce reactive energy at the place even where it is consumed and in quantity adjusted with the request (local compensation).
Calculation of the power of the capacitors of compensation
On an installation of power Q reactivates, and of power connect S, one installs a capacitor battery of power Qc.La reactive power passes from Q to Q’ Q’ = Q - Qc the apparent power passes from S to S’.La apparent power after compensation thus decreased.
The capacity of the capacitors is calculated by: Qc = 3. U ². C. W
C = Qc ⁄ 3 * U² * ω
Harmonics
The presence of harmonics is translated
by an increase of the current in the capacitor which causes its heating and its premature ageing
by resonances which cause breakdown by overpressure.
To neutralize these phenomena, one uses coils anti-harmonics put in series and one on dimensions the capacitors in tension.
The protection of the capacitors
The startup of a capacitor is equivalent to a short-circuit during its time of load or discharge. The overload switches are thus selected with releases with high instantaneous threshold.
Examples of hardware

### Predimensioning of the condensers of compensation

Compensation of the transformers
The losses with vacuum and the pressure losses of a transformer represent a reactive power of inductive type.
One can compensate for them by condensers connected at the boundaries low tension of the transformer.
The data necessary to dimensioning of the capacitor battery are included in the data sheet of the transformer and on the electric invoice (case of the replacement of a transformer on an existing installation).
Compensation of the losses with vacuum: Po
Po = (no-load current X power) ⁄ 100 [kVAr]
Compensation of the pressure losses pc
PC = X ⁄ 100 X power
where
X² = Ucc² - R²
R = (Pcc ⁄ power) X 0,1
Centralized compensation of the whole of an installation
Known values
(values recorded on the meter during a time "T" and divided by "T", or values read on the monthly invoice)
the power activates P in kw
the power reactivates Q in kVAr
from where, the value of tg phi of the installation: Q ⁄ P called tg phi1
Reactive power necessary of the condensers:
Qc = P X p
where
p = coefficient being reproduced on the table below
 For the value Factor "p" for the calculation of the power of the condensers tg φ1 cos φ1 cos φ 0,70 0,75 0,80 0,82 0,84 0,86 0,88 0,90 0,92 0,94 0,96 0,98 1,00 4,90 0,20 3,88 4,02 4,15 4,20 4,26 4,31 4,36 4,42 4,48 4,54 4,61 4,70 4,90 3,88 0,25 2,86 2,99 3,13 3,18 3,23 3,28 3,33 3,39 3,45 3,51 3,58 3,67 3,88 3,18 0,30 2,16 2,30 2,42 2,48 2,53 2,59 2,65 2,70 2,76 2,82 2,89 2,98 3,18 2,68 0,35 1,66 1,80 1,93 1,98 2,03 2,08 2,14 2,19 2,25 2,31 2,38 2,47 2,68 2,29 0,40 1,27 1,41 1,54 1,60 1,65 1,70 1,76 1,81 1,87 1,93 2,00 2,09 2,29 1,98 0,45 0,97 1,11 1,24 1,29 1,34 1,40 1,45 1,50 1,56 1,62 1,69 1,78 1,99 1,73 0,50 0,71 0,85 0,98 1,04 1,09 1,14 1,20 1,25 1,31 1,37 1,44 1,53 1,73 1,64 0,52 0,62 0,76 0,89 0,95 1,00 1,05 1,11 1,16 1,22 1,28 1,35 1,44 1,64 1,56 0,54 0,54 0,68 0,81 0,86 0,92 0,97 1,02 1,08 1,14 1,20 1,27 1,36 1,56 1,48 0,56 0,46 0,60 0,73 0,78 0,84 0,89 0,94 1,00 1,05 1,12 1,19 1,28 1,48 1,41 0,58 0,39 0,52 0,66 0,71 0,76 0,81 0,87 0,92 0,98 1,04 1,11 1,20 1,41 1,33 0,60 0,31 0,45 0,59 0,64 0,69 0,74 0,80 0,85 0,91 0,97 1,04 1,13 1,33 1,27 0,62 0,25 0,39 0,52 0,57 0,62 0,67 0,73 0,78 0,84 0,90 0,97 1,06 1,27 1,20 0,64 0,18 0,32 0,45 0,51 0,56 0,61 0,67 0,72 0,78 0,84 0,91 1,00 1,20 1,14 0,66 0,12 0,26 0,39 0,45 0,49 0,55 0,60 0,66 0,71 0,78 0,85 0,94 1,14 1,08 0,68 0,06 0,20 0,33 0,38 0,43 0,49 0,54 0,60 0,65 0,72 0,79 0,88 1,08 1,02 0,70 0,14 0,27 0,33 0,38 0,43 0,49 0,54 0,60 0,66 0,73 0,82 1,02 0,96 0,72 0,08 0,22 0,27 0,32 0,37 0,43 0,48 0,54 0,60 0,67 0,76 0,97 0,91 0,74 0,03 0,16 0,21 0,26 0,32 0,37 0,43 0,48 0,55 0,62 0,71 0,91 0,86 0,76 0,11 0,16 0,21 0,26 0,32 0,37 0,43 0,50 0,56 0,65 0,86 0,80 0,78 0,05 0,11 0,16 0,21 0,27 0,32 0,38 0,44 0,51 0,60 0,80 0,75 0,80 0,05 0,10 0,16 0,21 0,27 0,33 0,39 0,46 0,55 0,75 0,70 0,82 0,05 0,10 0,16 0,22 0,27 0,33 0,40 0,49 0,70 0,65 0,84 0,05 0,11 0,16 0,22 0,28 0,35 0,44 0,65 0,59 0,86 0,06 0,11 0,17 0,23 0,30 0,39 0,59 0,54 0,88 0,06 0,11 0,17 0,25 0,33 0,54 0,48 0,90 0,06 0,12 0,19 0,28 0,48 0,43 0,92 0,06 0,13 0,22 0,43 0,36 0,94 0,07 0,16 0,36

Capacity:
The capacity C is the quantity of electricity Q (in Coulomb [C]; 1C = 1 As ampere second) that the capacitor can accumulate under a given tension.
C = Q ⁄ U
µF =

C ⁄ V

Q =

### Modify the values of Q and U!!

The unit of capacity is the farad F. The practice shows that the farad is a value too much large. One will thus use preferentially microfarad 10 -6 F = 1 µF
For a capacitor, the capacity depends on its construction:
C = A * E R * E 0 ⁄ d
with
C : capacity out of F
At surface of one of the plates in m2
E R : relative permittivity [-]
E 0 : permittivity of the vacuum (8,859 10-12 [F ⁄ m]) or constant of influence
note : E is actually Epsilon

### Values of relative permittivity:

Air : 1;
Paper paraffined 2
Glass 4 to 6
Mica 4 to 8

### The supercondensator FastCAP

Supercondensateur FastCAP ultra powerful and ultra resistant, stores 2 to 3 times more energy (15,6 Wh ⁄ kg) and resists 150°C : 5 world records.
The company FastCAP Systems was founded in 2008 by John Cooley and Riccardo Signorelli, former graduate students in electronic engineering and data processing, then associated post-doctorate in the laboratory for the electromagnetic and electronic systems with M.I.T.
The associates created this company with an aim of marketing the technology of supercondensator with high density of energy which they developed with MIT in 4 years of collaboratives research. A supercondensator containing electrodes of coated carbon nanotubes having the potential to store much more energy than the supercondensateurs with activated carbon of the trade.
A beginning of marketing of this powerful and ultra ultra supercondensator resistant began in March 2013 near the industry of gas and oil exploration. This industry is very interested by this means of storage which is not likely to explode in an environment of high temperature.
FastCAP obtained 5 world records for finalized supercondensateurs
High density of energy for a cell : 18.69 Wh ⁄ l - 15.66 Wh ⁄ kg (2 to 3 times more than the supercondensateurs commercial)
High density of power for a cell : 120.44 kW ⁄ L (117.32 kW ⁄ kg)
The highest operating temperature for a supercondensator : 150°C (2 times more than the supercondensateurs commercial)
The highest frequency for a supercondensator : 6,3V with a cut-off frequency of 500 Hz
High density of energy and power for the same cell : 14,93 Wh ⁄ l and 41,04 kW ⁄ L (13,50 Wh ⁄ kg and 37,12 kW ⁄ kg)
The last generation of supercondensateurs FastCAP stores two to three times thus more energy than its competitors and can provide 7 to 15 times more power. It is also less expensive, because it uses raw materials which are at the same time inexpensive and abundant in the United States. The material of the electrode, costs approximately one fiftieth that used in the conventional condensers.
The manufacturing process is based on the methods used for the production with large scales of photovoltaic solar components. Consequently, it is at the same time inexpensive and evolutionary, and precedes some, the equipment and the expertise necessary are very developed and easily available.
The key of the storage of energy, that it is in a battery or a supercondensator, is the capacity to transfer and store the particles charged called ions, explains Joel Schindall, professor at the department of electronic engineering and data processing of MIT. The two apparatuses have at their base an electrolyte, a mixture of positive and negative ions. In a pile, the chemical reactions move the ions of the electrolyte towards the interior or apart from the atomic structure of the matter composing the electrode according to whether the battery is charged or discharged. On the other hand, in a supercondensator, an electric field involves the ions to be moved towards or from the surface of the electrodes. Considering the ions nothing but do cling then to be detached from the electrodes without any chemical reaction, a supercondensator can be charged and discharged very quickly, still and still. But while the batteries store the ions with the center even of its electrodes with a great storage capacity, the supercondensateurs them store the ions only on the surface of the electrodes.
In theory thus, the solution for a good storage of energy by supercondensator is simple : to offer more surface of electrode so that a great quantity of ions can cling to it. In the commercial supercondensateurs of today, surfaces of the electrodes are covered with activated carbon, a material which is full with pores providing a surface so that the ions cling to it. But the storage of energy is still weak there.
In 2004, Schindall proposed a different solution : to cover the electrodes with nanotubes with carbon aligned vertically. A large and mean very tight network nanotubes on the electrode could provide much surface to hang the ions there. Moreover, whereas the pores of the activated carbon are irregular in the face and form, a forest of nanotube would offer right ways so that the ions can there enter and easily leave. It is like rather aspiring painting with a brush than with the surface of a sponge, known as Schindall. It started to explore the concept with collaborators, John G. Kassakian, professor of electronic engineering and Riccardo Signorelli, a graduate student in electronic engineering and data processing, then post-doctoral associate in the laboratory for the electromagnetic and electronic systems which now forms part of the research laboratory in electronics of MIT.
The concept and first steps
Diagram of a supercondensator with carbon nanotubes. One can see in top and bottom of the diagram the plates of electrodes with carbon nanotubes directed vertically. A liquid electrolyte fills space between the two electrodes, and a porous separator in the medium prevents the plates from electrically shorting-circuit between them. In this diagram, a tension through the two plates induced an excess of negative charge on the higher plate and an excess of positive load on the lower plate. It results from it that the nanotubes are covered by ions of opposite load. When the two plates are connected in external loop by an electric wire, the electrons run out through this circuit external starting from the negative electrode to the positive electrode by ensuring the food of a device consuming electricity in the course of road. To the wire of time, the two plates will lose their load, and the positive and negative ions will mix again in the electrolyte.
The team of MIT then carried out detailed studies of simulation which confirmed the potential advantages of the concept suggested. Simulations showed that the supercondensator with carbon nanotubes should be able to store more conventional ions than those with activated carbon, thus carrying out a storage of more effective energy.
Encouraged by these results, Schindall and Signorelli launched out on the following challenge : to produce electrodes of carbon nanotubes. In one year, they had learned how to make grow carbon nanotubes on silicon. But silicon is not a good driver. The growth of nanotubes on a conducting surface proved more difficult to make. After having tested many materials, various designs and methods, they found a combination which functions. They used a layer of tungsten, then a thin layer of aluminum like driver and finally iron oxide a roadbase, the catalyst for the process. By using a furnace especially designed, they heated their sample until the iron oxide separated in droplets. They then blew of acetylene gas diluted on surface. The iron oxide droplets caught the carbon of gas, and the carbon nanotubes started to push literally on the droplets. Each drop was used as follicule, almost like a pilous follicule, for the growth of the nanotubes, explains Schindall. The experiments showed that a very fine layer of iron oxide can be used to form small droplets from which it is possible to make grow large nanotubes, thin and tight. A configuration which maximizes surface available on the electrode.
The following stage consisted in integrating the electrodes of nanotubes in a device and to test their operation. We made grow nanotubes with good dimensions on a conducting substrate, but we did not know how they could function electrically, explains Schindall. A certain number of shelves could appear at the time when they were going to test the device. For example, was the electrolyte going to go down between the nanotubes and to cover their surface? The carbon nanotubes are known to be very damp-proof. Moreover, in this application, the nanotubes are very brought closer and thus that makes a very tight damp-proof whole of nanotubes between them.
The researchers succeeded in manufacturing a prototype of cell which alleviated these concerns. The ions could reach and to cover all surface with the nanotubes and the nanotubes were thus connected electrically. Other studies showed that the base of each nanotube was prolonged beyond the iron oxide droplets from where they grew. In the final analysis, the foot of each nanotube surrounds and includes the drop, consequently, it is directly connected to the aluminum substrate of the lower part. The prototype thus proved the practical viability of the supercondensator with carbon nanotubes.
Thereafter, the company FastCAP Systems succeeded in raising funds to improve the device and to create supercondensateurs able to store 2 times more energy than its competitors and able to provide densities of power 7 to 15 times more important.
A resistant ultra supercondensator
As we saw in our article research on the supercondensateurs advance very quickly, in spite of the fact that the supercondensator FastCAP beats already all the records of the other supercondensateurs commercial, still enormous possibilities for improvements its. In theory, technology containing carbon nanotubes used by FastCAP Systems can make it possible to reach the density of energy of the batteries Lithium-ion, that is to say 150 Wh ⁄ kg. The supercondensator FastCAP could in particular increase his density of energy by densifiant the forest of carbon nanotubes and by making them grow in a more monolithic way in order to hang there even more ions. The use of an ionic liquid can also strongly increase this density of energy.

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