Elasticity

Physical size
Surname	Elasticity
Formula symbol	${\displaystyle S}$
Derived from	capacity
Size and unit system unit dimension SI F −1 M · L 2 · T −4 · I −2 Gauss ( cgs ) cm −1 L −1 esE ( cgs ) cm −1 L −1 emE ( cgs ) abF −1 T −2 · L −1

The electrical elastance ( English elastance ) is the ratio of the electric voltage to the stored charge in a capacitive component: ${\displaystyle U}$ ${\displaystyle Q}$

${\displaystyle S={\frac {1}{C}}={\frac {U}{Q}}}$

unit

The SI unit of elastance is the inverse farad . A capacitor has the elastance 1 farad ⁻¹ ( symbol : or ) if the application of a charge of 1  coulomb generates a voltage of 1  volt between its electrodes. ${\displaystyle F^{-1}}$ ${\displaystyle {\tfrac {1}{F}}}$

${\displaystyle 1\,\mathrm {F} ^{-1}=1\,\mathrm {\frac {1}{F}} =1\,\mathrm {\frac {V}{C}} =1\,\mathrm {\frac {V}{A\cdot s}} =1\,\mathrm {\frac {kg\cdot m^{2}}{A^{2}\cdot s^{4}}} }$

In the Anglo-American area this SI unit of elastance is sometimes called daraf (farad read backwards).

history

The designation of quantity as elastance and elastivity was introduced in 1886 by Oliver Heaviside , who also coined terms such as impedance , inductance , admittance and conductance . Heaviside used the ending -ance for intensive sizes and -ivity for extensive . The extensive quantities were intended for electrical circuits for specifying the values ​​of electronic components, the intensive ones for the consideration of electrical fields. Heaviside's designations thus showed the analogies of the quantities of electrical circuits and fields. Thus elasticity would be the intensive quantity of a material that corresponds to the extensive elasticity of a component:

"Permittivity gives rise to permittance, and elastivity to elastance."

"Permittivity leads to permittance, and elasticity to elasticity."

- Oliver Heaviside

Heaviside uses the word permittance for electrical capacity .

Heaviside chose its names so that the words for electrical quantities were unique and there was no risk of confusion with mechanical quantities. The analogous terms for mechanical quantities were later coined based on the electrical designations. The term elastance was also introduced in fluid mechanics.

Individual evidence

1. ^ GWO Howe: The nomenclature of the fundamental concepts of electrical engineering . In: Journal of the Institution of Electrical Engineers . tape 70 , no. 420 , 1931, pp. 60 , doi : 10.1049 / jiee-1.1931.0203 .
2. ^ Ido Yavetz: From Obscurity to Enigma: The Work of Oliver Heaviside, 1872-1889 . Springer, 2011, ISBN 3-0348-0177-7 , pp. 236 ( limited preview in Google Book search).
3. ↑ Oliver Heaviside: Electromagnetic Theory: Volume I . Cosimo, 2007, ISBN 1-60206-271-4 , pp. 28 (first edition: 1893).
4. ^ John Enderle, Joseph Bronzino: Introduction to Biomedical Engineering . Academic Press, 2011, ISBN 0-08-096121-5 , pp. 197-201 , especially equation 4.72 .