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Encyclopedia > Stray capacitance

Contents


Definition

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The capacitance is usually defined as the total electric charge placed on the object divided by the potential of the object: ‹ The template below has been proposed for deletion. ... Electric potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ...

C = frac{Q}{V}

or, according to Gauss's law, the capacitance can be expressed as the electric flux per volt In physics and mathematical analysis, Gausss law gives the relation between the electric flux flowing out a closed surface and the electric charge enclosed in the surface. ...

C = frac{Phi}{V}

where

C is the capacitance in farads
Q is the charge in coulombs
V is the potential in volts
Φ is the electric flux associated with the charge Q in coulombs

Compare this form with the definition of inductance. The farad (symbol: F) is the SI unit of capacitance. ... The coulomb (symbol: C) is the SI unit of electric charge. ... The volt (symbol: V) is the SI derived unit of electric potential difference. ... The coulomb (symbol: C) is the SI unit of electric charge. ... // Definition Inductance is a measure of the amount of magnetic flux produced for a given electric current. ...


Introduction

Capacitance exists between any two conductors insulated from one another. The formula defining capacitance above is valid if it is understood that the conductors have equal but opposite charge Q, and the voltage V is the potential difference between the two conductors. Potential difference is a quantity in physics related to the amount of energy that would be required to move an object from one place to another against various types of force. ...


The SI unit of capacitance is the farad (F). A capacitance of one farad results in a potential of one volt for one coulomb of charge. 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 microfarad (µF), the nanofarad (nF) and the picofarad (pF). Cover of brochure The International System of Units. ... The term microfarad is used to note the storage capacity value of electrolytic capacitors and represents one millionth of a farad, or 0. ... The nanofarad (symbol nF) is a submultiple of the SI unit of electrical capacitance, the farad. ... The picofarad (pronounced or ) is the smallest measurable unit of electrical capacitance. ...


It should be noted that the above equation (C = Q/V) is only applicable 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 100 nV, the equation would predict a charge Q = 10-19 C, which is smaller than the charge on a single electron. Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ...


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 identical plane electrodes of area A at constant spacing d is approximately equal to the following: A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. ...

C = epsilon_0 epsilon_r frac{A}{d}

where

C is the capacitance in farads
ε0 is the permittivity of free space, measured in farads per meter
εr is the dielectric constant or relative permittivity of the insulator used
A is the area of each plane electrode, measured in square metres
d is the separation between the electrodes, measured in metres

The farad (symbol F) is the SI unit of capacitance (named after Michael Faraday). ... In science, a physical constant is a physical quantity whose numerical value does not change. ... This article is in need of attention. ... The dielectric constant εr (represented as or K in some cases) is defined as the ratio: where εs is the static permittivity of the material in question, and ε0 is the vacuum permittivity. ... Permittivity is a physical quantity that describes how an electric field affects and is affected by a medium. ... A square metre (US spelling: square meter) is by definition the area enclosed by a square with sides each 1 metre long. ... The metre, or meter, is a measure of length. ...

Energy

The energy (measured in joules) stored in a capacitance 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: The joule (symbol: J) is the SI unit of energy, or work with base units of kg·m2/s2. ...

dW = frac{q}{C}dq

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: The joule (symbol: J) is the SI unit of energy, or work with base units of kg·m2/s2. ... The coulomb (symbol: C) is the SI unit of electric charge. ... In calculus, the integral of a function is a generalization of area, mass, volume and total. ...

W_{charging} = int_{0}^{Q} frac{q}{C} dq = 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} epsilon_0 epsilon_r frac{A}{d} V^2

Capacitance and '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). James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematical physicist, born in Edinburgh. ... Displacement current is a quantity related to a changing electric field; it is not a real current (movement of charge) in a vacuum, but it has the units of current, as movement of charge does, and has an associated magnetic field. ... In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ... A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. ... The Earths magnetic field, which is approximately a dipole. ... The aether is the fifth classical element in ancient Greek philosophy and science. ... In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ...


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. // Definition Inductance is a measure of the amount of magnetic flux produced for a given electric current. ...


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 = 4πε0R [1]

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. Electrical elastance is the inverse of capacitance. ... The daraf is the unit of electrical elastance (symbol: F-1), the ability of an electric potential to charge a capacitor; it is the reciprocal of the farad. ...


Stray capacitance

Any two conductors will function as a capacitor of some capacitance, although this effect is small for conductors which are not close together. This unwanted and unavoidable capacitance is termed "stray capacitance". Stray capacitance allows energy to leak between circuits, and can be the limiting factor for correct functioning of circuits, particularly at high frequency. High frequency (HF) radio frequencies are between 3 and 30 MHz. ...


References

  • Tipler, Paul (1998). Physics for Scientists and Engineers: Vol. 2: Electricity and Magnetism, Light (4th ed.). W. H. Freeman. ISBN 1572594926
  • Serway, Raymond; Jewett, John (2003). Physics for Scientists and Engineers (6 ed.). Brooks Cole. ISBN 0534408427

See also

 

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