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Concept
Elastance
Summary
Electrical elastance is the reciprocal of capacitance. The SI unit of elastance is the inverse farad (F−1). The concept is not widely used by electrical and electronic engineers. The value of capacitors is invariably specified in units of capacitance rather than inverse capacitance. However, it is used in theoretical work in network analysis and has some niche applications at microwave frequencies.
The term elastance was coined by Oliver Heaviside through the analogy of a capacitor as a spring. The term is also used for analogous quantities in some other energy domains. It maps to stiffness in the mechanical domain, and is the inverse of compliance in the fluid flow domain, especially in physiology. It is also the name of the generalised quantity in bond-graph analysis and other schemes analysing systems across multiple domains.
The definition of capacitance (C) is the charge (Q) stored per unit voltage (V).
Elastance (S) is the reciprocal of capacitance, thus,
Expressing the values of capacitors as elastance is not done much by practical electrical engineers, although it is sometimes convenient for capacitors in series. The total elastance is simply the sum of the individual elastances in that case. However, it is used by network theorists in their analysis. One advantage is that an increase in elastance increases impedance. This is in the same direction as the other two basic passive elements, resistance and inductance. An example of the use of elastance can be found in the 1926 doctoral thesis of Wilhelm Cauer. On his path to founding network synthesis, he formed the loop matrix A,
where L, R, S and Z are the network loop matrices of inductance, resistance, elastance and impedance respectively and s is complex frequency. This expression would be significantly more complicated if Cauer had tried to use a matrix of capacitances instead of elastances. The use of elastance here is merely for mathematical convenience, in much the same way as mathematicians use radians rather than the more common units for angles.
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Related courses (1)
EE-407: Fundamentals of electrical circuits and systems II
This course provides an introduction to the theory and analysis methods of electrical circuits.
Related concepts (3)
Impedance analogy
The impedance analogy is a method of representing a mechanical system by an analogous electrical system. The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially in the field of filters. By converting to an electrical representation, these tools in the electrical domain can be directly applied to a mechanical system without modification.
Capacitor
A capacitor is a device that stores electrical energy in an electric field by accumulating electric charges on two closely spaced surfaces that are insulated from each other. It is a passive electronic component with two terminals. The effect of a capacitor is known as capacitance. While some capacitance exists between any two electrical conductors in proximity in a circuit, a capacitor is a component designed to add capacitance to a circuit.
Leyden jar
A Leyden jar (or Leiden jar, or archaically, sometimes Kleistian jar) is an electrical component that stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar. It typically consists of a glass jar with metal foil cemented to the inside and the outside surfaces, and a metal terminal projecting vertically through the jar lid to make contact with the inner foil. It was the original form of the capacitor (also called a condenser).