Capacitor
Various types of capacitors
A capacitor (historically known as a "condenser") is a device that stores energy in an electric field, by accumulating an internal imbalance of electric charge.
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2 Practical capacitors 3 Applications 4 History 5 See also: 6 External links |
Typical designs consist of two electrodes or plates, each of which stores an opposite charge. These two plates are conductive and are separated by an insulator or dielectric. The charge is stored at the surface of the plates, at the boundary with the dielectric. Because each plate stores an equal but opposite charge, the total charge in the device is always zero.
The capacitor's capacitance (C) is a measure of the potential difference or voltage (V) which appears across the plates for a given amount of charge (Q) stored on each plate:
The above equation is only accurate for values of Q which are much larger than the electron charge e = 1.602·10-19 C. For example, if a capacitance of 1 pF is charged to a voltage of 1 µV, the equation would predict a charge Q = 10-19 C, but this is impossible as it is smaller than the charge on a single electron. However, recent experiments and theories (e.g. the fractional quantum Hall (FQH) effect) have suggested the existence of fractional charges.
The capacitance of a parallel-plate capacitor constructed of two identical plane electrodes of area A at constant spacing D is approximately equal to the following:
The energy (in SI, measured in joules) stored in a capacitor is equal to the work done to charge it up. Consider a capacitor with capacitance C, holding a charge +q on one plate and -q on the other. Moving a small element of charge dq from one plate to the other against the potential difference V = q/C requires the work dW:
Electrons cannot directly pass across the dielectric from one plate of the capacitor to the other. When a voltage is applied to a capacitor through an external circuit, current flows to one plate, charging it, while flowing away from the other plate, charging it oppositely. In other words, when the voltage across a capacitor changes, the capacitor will be charged or discharged. The associated current is given by
Physics of the capacitor
Overview
Capacitance
In SI units, a capacitor has a capacitance of one farad when one coulomb of charge causes a potential difference of one volt across the plates. Since the farad is a very large unit, values of capacitors are usually expressed in microfarads (μF), nanofarads (nF) or picofarads (pF).
where C is the capacitance in farads, ε0 is the electrostatic permittivity of vacuum or free space, and εr is the dielectric constant or relative permittivity of the insulator used.Energy
We can find the energy stored in a capacitor by integrating this equation. Starting with an uncharged capacitor (q=0) and moving charge from one plate to the other until the plates have charge +Q and -Q requires the work W:In electric circuits
where I is the current flowing in the conventional direction, and dV/dt is the time derivative of voltage.
In the case of a constant voltage (DC) soon an equilibrium is reached, where the charge of the plates corresponds with the applied voltage by the relation Q=CV, and no further current will flow in the circuit. Therefore direct current cannot pass. However, effectively alternating current (AC) can: every change of the voltage gives rise to a further charging or a discharging of the plates and therefore a current. The amount of "resistance" of a capacitor to AC is known as capacitive reactance, and varies depending on the AC frequency. Capacitive reactance is given by this formula:
Thus the reactance is inversely proportional to the frequency. Since DC has a frequency of zero, the formula confirms that capacitors completely block direct current. For high-frequency alternating currents the reactance is small enough to be considered as zero in approximate analyses.
The impedance of a capacitor is given by:
Hence, capacitive reactance is the negative imaginary component of impedance.
In a tuned circuit such as a radio receiver, the frequency selected is a function of the inductance (L) and the capacitance (C) in series, and is given by
Capacitors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent capacitance (Ceq):
Capacitor networks
Practical capacitors
Discrete capacitors of various types are available commercially with capacitances ranging from the pF range to more than a farad, and voltage ratings up to hundreds of volts. In general, the higher the capacitance and voltage rating, the larger the physical size of the capacitor (and usually a higher price as well). Tolerances for discrete capacitors are usually specified as 5 or 10%.
Capacitors are often classified according to the material used as the dielectric. The following types of dielectric are used.
Ordinary capacitors
Important properties of capacitors, apart from the capacitance, are the maximum working voltage and the amount of energy lost in the dielectric. For high-power capacitors the maximum ripple current and Equivalent Series Resistance (ESR) are further considerations. A typical ESR for most capacitors is between 0.0001 and 0.01 ohm, low values being preferred for high-current applications.
Since capacitors have such low ESRs, they have the capacity to deliver huge currents into short circuits, which can be dangerous. For safety purposes, all large capacitors should be discharged before handling. This is done by placing a small 1 to 10 ohm resistor across the terminals, i.e. shorting through a resistance.
Capacitors can also be fabricated in semiconductor integrated circuit devices using metal lines and insulators on a substrate. Such capacitors are used to store analogue signals in switched-capacitor filters, and to store digital data in dynamic random-access memory (DRAM). Unlike discrete capacitors, however, in most fabrication processes, precise tolerances are not possible (15-20% is considered good).
There are two distinct types of variable capacitors, whose capacitance may be intentionally and repeatedly changed over the life of the device:
Variable capacitors
Electric Double Layer Capacitors (EDLCs)
These devices, often called supercapacitors or ultracapacitors for short, are capacitors that use a molecule-thin layer of electrolyte, rather than a manufactured sheet of material, as the dielectric. As the energy stored is inversely proportional to the thickness of the dielectric, these capacitors have an extremely high energy density. The electrodes are made of activated carbon, which has a high surface area per unit volume, further increasing the capacitor's energy density. Individual EDLCs have capacitances of hundreds or even thousands of farads.
EDLCs can be used as replacements for batteries in applications where a high discharge current is required. They can also be recharged hundreds of thousands of times, unlike conventional batteries which last for only a few hundred or thousand recharge cycles.
Capacitors are commonly used in power supplies where they smooth the output of a full or half wave rectifier.
Because capacitors pass AC but block DC signals, they are often used to separate the AC and DC components of a signal. This method is known as AC coupling.
Capacitors are also used in power factor correction. Such capacitors often come as three capacitors connected as a three phase load. Usually, the values of these capacitors are given not in farads but rather as a reactive power in volts-amps reactive (var).
The displacement current must be included, for example, to apply Kirchhoff's current law to a capacitor.
Applications
History
The Leyden jar, the first form of capacitor, was invented at Leiden University in the Netherlands. It was a glass jar coated inside and out with metal. The inner coating was connected to a rod that passed through the lid and ended in a metal ball.Displacement current
The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampere's law consistent with conservation of charge in cases where charge is accumulating, for example in a capacitor. He interpreted this as a real motion of charges, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the ether. Although this interpretation has been abandoned, Maxwell's correction to Ampere's law remains valid (a changing electric field produces a magnetic field).See also:
External links