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Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field The most common form of charge storage device is a two-plate capacitor. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors If the charges on the plates are +Q and −Q, and V gives the voltage difference between the plates, then the capacitance is given by

$C = \frac{Q}{V}$

The SI unit of capacitance is the farad; 1 farad = 1 coulomb per volt. This is about the capacitance unit of measure For the charge unit see Faraday (unit. The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force.

## Energy

The energy (measured in joules) stored in a capacitor is equal to the work done to charge it. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity Consider a 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:

$\mathrm{d}W = \frac{q}{C}\,\mathrm{d}q$

where

W is the work measured in joules
q is the charge measured in coulombs
C is the capacitance, measured in farads

We can find the energy stored in a capacitance by integrating this equation. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space Starting with an uncharged capacitance (q=0) and moving charge from one plate to the other until the plates have charge +Q and -Q requires the work W:

$W_{charging} = \int_{0}^{Q} \frac{q}{C} \, \mathrm{d}q = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}CV^2 = W_{stored}$

Combining this with the above equation for the capacitance of a flat-plate capacitor, we get:

$W_{stored} = \frac{1}{2} C V^2 = \frac{1}{2} \epsilon \frac{A}{d} V^2$ .

where

W is the energy measured in joules
C is the capacitance, measured in farads
V is the voltage measured in volts

## Capacitance and 'displacement current'

The physicist James Clerk Maxwell invented the concept of displacement current, $\frac{\partial \vec{D}}{\partial t}$, to make Ampère's law consistent with conservation of charge in cases where charge is accumulating, for example in a capacitor. James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. Displacement current is a quantity that arises in a changing electric field 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. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a According to ancient and medieval science, aether (Greek grc αἰθήρ aithēr) also spelled æther or ether, is the material that fills Although this interpretation has been abandoned, Maxwell's correction to Ampère's law remains valid (a changing electric field produces a magnetic field).

Maxwell's equation combining Ampère's law with the displacement current concept is given as $\vec{\nabla} \times \vec{H} = \vec{J} + \frac{\partial \vec{D}}{\partial t}$. (Integrating both sides, the integral of $\vec{\nabla}\times \vec{H}$ can be replaced — courtesy of Stokes's theorem — with the integral of $\vec{H} \cdot \mathrm{d} \vec{l}$ over a closed contour, thus demonstrating the interconnection with Ampère's formulation. In Differential geometry, Stokes' theorem is a statement about the integration of Differential forms which generalizes several Theorems from )

## Coefficients of Potential

The discussion above is limited to the case of two conducting plates, although of arbitrary size and shape. The definition C=Q/V still holds if only one plate is given a charge, provided that we recognize that the field lines produced by that charge terminate as if the plate were at the center of an oppositely charged sphere at infinity.

C=Q/V does not apply when there are more than two charged plates, or when the net charge on the two plates is non-zero. To handle this case, Maxwell introduced his "coefficients of potential". If three plates are given charges Q1,Q2,Q3, then the voltage of plate 1 is given by

V1 = p11Q1 + p12Q2 + p13Q3 ,

and similarly for the other voltages. Maxwell showed that the coefficients of potential are symmetric, so that p12 = p21, etc.

## Capacitance/inductance duality

In mathematical terms, the ideal capacitance can be considered as an inverse of the ideal inductance, because the voltage-current equations of the two phenomena can be transformed into one another by exchanging the voltage and current terms. In Electrical circuits, any Electric current i produces a Magnetic field and hence generates a total Magnetic flux \Phi acting

## Self-capacitance

In electrical circuits, the term capacitance is usually a shorthand for the mutual capacitance between two adjacent conductors, such as the two plates of a capacitor. Mutual capacitance is intentional or unintentional Capacitance that occurs between two charge-holding objects or conductors in which the current passing through one passes There also exists a property called self-capacitance, which is the amount of electrical charge that must be added to an isolated conductor to raise its electrical potential by one volt. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field The reference point for this potential is a theoretical hollow conducting sphere, of infinite radius, centred on the conductor. Using this method, the self-capacitance of a conducting sphere of radius R is given by:

$C=4\pi\epsilon_0R \,$ [1]

Typical values of self-capacitance are:

• for the top "plate" of a van de Graaf generator, typically a sphere 20 cm in radius: 20 pF
• the planet Earth: about 710 µF

## Elastance

The inverse of capacitance is called elastance, and its unit is the reciprocal farad. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Electrical elastance is the inverse of Capacitance. The SI unit is the reciprocal Farad.

## Stray capacitance

Any two adjacent conductors can be considered as a capacitor, although the capacitance will be small unless the conductors are close together or long. This (unwanted) effect is termed "stray capacitance". Stray capacitance can allow signals to leak between otherwise isolated circuits (an effect called crosstalk), and it can be a limiting factor for proper functioning of circuits at high frequency. In Electronics, the term crosstalk ( XT) refers to any phenomenon by which a signal transmitted on one circuit or channel of a Transmission system High frequency (HF radio frequencies are between 3 and 30 MHz.

Stray capacitance is often encountered in amplifier circuits in the form of "feedthrough" capacitance that interconnects the input and output nodes (both defined relative to a common ground). It is often convenient for analytical purposes to replace this capacitance with a combination of one input-to-ground capacitance and one output-to-ground capacitance. (The original configuration — including the input-to-output capacitance — is often referred to as a pi-configuration. ) Miller's theorem can be used to effect this replacement. Miller's theorem states that, if the gain ratio of two nodes is 1:K, then an impedance of Z connecting the two nodes can be replaced with a Z/(1-k) impedance between the first node and ground and a KZ/(K-1) impedance between the second node and ground. In Electronics, the Miller effect accounts for an increase in the equivalent input Capacitance of an inverting voltage Amplifier due to amplification of Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC (Since impedance varies inversely with capacitance, the internode capacitance, C, will be seen to have been replaced by a capacitance of KC from input to ground and a capacitance of (K-1)C/K from output to ground. ) When the input-to-output gain is very large, the equivalent input-to-ground impedance is very small while the output-to-ground impedance is essentially equal to the original (input-to-output) impedance.

## Capacitors

Main article: Capacitor

The capacitance of the majority of capacitors used in electronic circuits is several orders of magnitude smaller than the farad. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors The most common subunits of capacitance in use today are the millifarad (mF), microfarad (µF), the nanofarad (nF) and the picofarad (pF)

The capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. "Milli" redirects here for the village in Azerbaijan see Birinci Milli; for similar-sounding words see Millie. micro- ( µ) is a prefix in the SI and other systems of units denoting a factor of 10&minus6 (one Millionth. For example, the capacitance of a parallel-plate capacitor constructed of two parallel plates of area A separated by a distance d is approximately equal to the following:

$C = \epsilon_{r}\epsilon_{0} \frac{A}{d}$ (in SI units)

where

C is the capacitance in farads, F
A is the area of each plate, measured in square metres
εr is the relative static permittivity (sometimes called the dielectric constant) of the material between the plates, (vacuum =1)
ε0 is the permittivity of free space where ε0 = 8. This is about the capacitance unit of measure For the charge unit see Faraday (unit. M^2 redirects here For other uses see M². CM2 redirects here Measurement The relative static permittivity εr can be measured for static Electric fields as follows first the Capacitance of a test Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical 854x10-12 F/m
d is the separation between the plates, measured in metres

The equation is a good approximation if d is small compared to the other dimensions of the plates. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International In CGS units the equation has the form:

$C = \epsilon_{r} \frac{A}{d}$

where C in this case has the units of length. The centimetre-gram-second system ( CGS) is a system of physical units.

The dielectric constant for a number of very useful dielectrics changes as a function of the applied electrical field, e. g. ferroelectric materials, so the capacitance for these devices is no longer purely a function of device geometry. Ferroelectricity is a physical property of a material whereby it exhibits a spontaneous electric polarization, the direction of which can be switched between equivalent If a capacitor is driven with a sinusoidal voltage, the dielectric constant, or more accurately referred to as the relative static permittivity, is a function of frequency. A changing dielectric constant with frequency is referred to as a dielectric dispersion, and is governed by dielectric relaxation processes, such as Debye relaxation. In physics dielectric dispersion is the dependence of the Permittivity of a Dielectric material on the frequency of an applied Electric field. Dielectric relaxation is the momentary delay (or lag in the Dielectric constant of a material Debye relaxation is the Dielectric relaxation response of an ideal noninteracting population of Dipoles to an alternating external Electric field.

## References

• Tipler, Paul (1998). A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of Electronics refers to the flow of charge (moving Electrons through Nonmetal conductors (mainly Semiconductors, whereas electrical An inductor is a passive electrical component designed to provide Inductance in a circuit Physics for Scientists and Engineers: Vol. 2: Electricity and Magnetism, Light (4th ed. ). W. H. Freeman. ISBN 1-57259-492-6
• Serway, Raymond; Jewett, John (2003). Physics for Scientists and Engineers (6 ed. ). Brooks Cole. ISBN 0-534-40842-7
• Saslow, Wayne M. (2002). Electricity, Magnetism, and Light. Thomson Learning. ISBN 0-12-619455-6. See Chapter 8, and especially pp. 255-259 for coefficients of potential.