Capacitance Basics and Properties
– Self capacitance: measure of electric charge needed to raise the electric potential of an isolated conductor by one unit
– Self capacitance formula: C = 4πε₀R, where R is the radius of the conductor
– Example values of self capacitance: 22.24 pF for the top plate of a van de Graaff generator, 710 µF for the Earth
– Mutual capacitance: capacitance between two adjacent conductors
– Capacitance in parallel-plate capacitor: proportional to surface area of plates and inversely proportional to separation distance
– Energy stored in a capacitor: W = 1/2CV², where C is the capacitance and V is the potential difference
– Capacitors used in electronic circuits have values in microfarads (µF), nanofarads (nF), or picofarads (pF)
– Supercapacitors can have much larger capacitance values, reaching hundreds of farads
– Parasitic capacitance (stray capacitance): occurs between adjacent conductors and affects circuit performance at high frequencies
Capacitance Matrix and Calculation
– Capacitance matrix: describes relationship between voltages and charges of multiple charged plates
– Inverse of elastance matrix
– Mutual capacitance calculation using elastance matrix and total charge
– Capacitors report mutual capacitance due to imperfect charge distribution on plates
– Capacitance matrix defined by partial derivatives of charges with respect to voltages
Capacitors
– Capacitors: electronic components designed to add capacitance to a circuit
– Capacitance units: microfarads (µF), nanofarads (nF), picofarads (pF)
– Capacitance depends on conductor geometry and dielectric properties of insulator
– Stray capacitance (parasitic capacitance) can occur between adjacent conductors and affect circuit performance
Capacitance in Different Systems
– Capacitance in amplifier circuits can cause instability and parasitic oscillation
– Calculation of capacitance for conductors with simple shapes involves solving Laplace equation
– Nanoscale systems may have different capacitance behavior due to unique properties
– Single-electron devices and few-electron devices have specific capacitance characteristics
– Capacitance in electronic and semiconductor devices includes both conduction and displacement components
– Negative capacitance can occur in semiconductor devices under certain conditions
Measurement of Capacitance
– Capacitance can be measured using a capacitance meter or DVMs
– More sophisticated instruments use capacitance bridges and Kelvin connections for greater precision
– Techniques include passing high-frequency alternating current through the device and measuring the resulting voltage
– Polarized capacitors cannot be measured using high-frequency alternating current method Source: https://en.wikipedia.org/wiki/Capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: self capacitance and mutual capacitance. An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operation of the capacitor, an elementary linear electronic component designed to add capacitance to an electric circuit.
Common symbols | C |
|---|---|
| SI unit | farad |
Other units | μF, nF, pF |
| In SI base units | F = A2 s4 kg−1 m−2 |
Derivations from other quantities | C = charge / voltage |
| Dimension |
The capacitance between two conductors is a function only of the geometry; the opposing surface area of the conductors and the distance between them, and the permittivity of any dielectric material between them. For many dielectric materials, the permittivity, and thus the capacitance, is independent of the potential difference between the conductors and the total charge on them.
The SI unit of capacitance is the farad (symbol: F), named after the English physicist Michael Faraday. A 1 farad capacitor, when charged with 1 coulomb of electrical charge, has a potential difference of 1 volt between its plates. The reciprocal of capacitance is called elastance.
