Differential capacitance
Encyclopedia
Differential capacitance in physics
, electronics
, and electrochemistry
is a measure of the voltage-dependent capacitance
of a nonlinear capacitor
, such as an electrical double layer or a semiconductor
diode
. It is defined as the derivative of charge with respect to potential.
differential capacitance is a parameter introduced for characterizing electrical double layers:
where σ is surface charge
and ψ is electric surface potential
----
Capacitance
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.
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.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, electronics
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
, and electrochemistry
Electrochemistry
Electrochemistry is a branch of chemistry that studies chemical reactions which take place in a solution at the interface of an electron conductor and an ionic conductor , and which involve electron transfer between the electrode and the electrolyte or species in solution.If a chemical reaction is...
is a measure of the voltage-dependent capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
of a nonlinear capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
, such as an electrical double layer or a semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
. It is defined as the derivative of charge with respect to potential.
Description
In electrochemistryElectrochemistry
Electrochemistry is a branch of chemistry that studies chemical reactions which take place in a solution at the interface of an electron conductor and an ionic conductor , and which involve electron transfer between the electrode and the electrolyte or species in solution.If a chemical reaction is...
differential capacitance is a parameter introduced for characterizing electrical double layers:
where σ is surface charge
Surface charge
Surface charge is the electric charge present at an interface. There are many different processes which can lead to a surface being charged, including adsorption of ions, protonation/deprotonation, and the application of an external electric field...
and ψ is electric surface potential
----
Capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
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. . . ."
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.