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Capacitance

2007 Schools Wikipedia Selection. Related subjects: Electricity and
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   Capacitance is a measure of the amount of electric charge stored (or
   separated) for a given electric potential.

                C = \frac{Q}{V}

   In a capacitor, there are two conducting electrodes which are insulated
   from one another. The charge on the electrodes is +Q and -Q, and V
   represents the potential difference between the electrodes. The SI unit
   of capacitance is the farad; 1 farad = 1 coulomb per volt.

Capacitors

   The capacitance of the majority of capacitors used in electronic
   circuits is several orders of magnitude smaller than the farad. The
   most common units 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. For example, the capacitance of a parallel-plate capacitor
   constructed of two parallel plane electrodes of area A separated by a
   distance d is approximately equal to the following:

          C = \epsilon \frac{A}{d}

   where

          C is the capacitance in farads, F
          ε is the permittivity of the insulator used (or ε[0] for a
          vacuum)
          A is the area of each plane electrode, measured in square metres
          d is the separation between the electrodes, measured in metres

   The equation is a good approximation if d is small compared to the
   other dimensions of the electrodes.

   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. If a capacitor is driven with a sinusoidal
   voltage, the dielectric constant, or more accurately referred to as the
   dielectric 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.

Energy

   The energy (measured in joules) stored in a capacitor is equal to the
   work done to charge it. 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. 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 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).

   Maxwell's equation combining Ampere'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 Ampere's formulation.)

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.

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. 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. 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 \,

   Typical values of self-capacitance are:
     * for the top electrode of a van de Graaf generator, typically a
       sphere 20 cm in diameter: 20 pF
     * the planet Earth: about 710 µF

Elastance

   The inverse of capacitance is called elastance, and its unit is the
   reciprocal farad, also informally called the daraf.

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.

   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/K impedance between the first node and ground and a
   KZ/(K-1) impedance between the second node and ground. (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.
   Retrieved from " http://en.wikipedia.org/wiki/Capacitance"
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