Differential capacitance in
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
,
electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, and
electrochemistry
Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outco ...
is a measure of the voltage-dependent
capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized ar ...
of a
nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many othe ...
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
, such as an
electrical double layer or a
semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
diode. It is defined as the derivative of charge with respect to potential.
Description
In
electrochemistry
Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outco ...
differential capacitance is a parameter introduced for characterizing
electrical double layers:
:
where σ is
surface charge and ψ is
electric surface potential
A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...
.
Capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized ar ...
is usually defined as the stored charge between two conducting surfaces separated by a dielectric divided by the voltage between the surfaces. Another definition is the rate of change of the stored charge or surface charge (σ) divided by the rate of change of the voltage between the surfaces or the electric surface potential (ψ). The latter is called the "differential capacitance," but usually the stored charge is directly proportional to the voltage, making the capacitances given by the two definitions equal.
This type of differential capacitance may be called "parallel plate capacitance," after the usual form of the capacitor. However, the term is meaningful when applied to any two conducting bodies such as spheres, and not necessarily ones of the same size, for example, the elevated terminals of a Tesla wireless system and the earth. These are widely spaced insulated conducting bodies positioned over a spherically conducting ground plane.
"The differential capacitance between the spheres is obtained by assuming opposite charges ±q on them...""Capacitance Calculations" by Antonio Carlos M. de Queiroz, Section VIII. CAPACITANCES OF TWO SPHERES.
/ref>
Another form of differential capacitance refers to single isolated conducting bodies. It is usually discussed in books under the topic of "electrostatics." This capacitance is best defined as the rate of change of charge stored in the body divided by the rate of change of the potential of the body. The definition of the absolute potential of the body depends on what is selected as a reference. This is sometimes referred to as the "self-capacitance" of a body. If the body is a conducting sphere, the self-capacitance is proportional to its radius, and is roughly 1pF per centimetre of radius.
See also
*
Capacitive coupling
*
Electric displacement field
In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...
References
External links
''McGraw-Hill Dictionary of Scientific and Technical Terms'' definition of "differential capacitance"
Electrochemistry
Colloidal chemistry
Telecommunications engineering
Power electronics
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