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In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the
reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...
of impedance, analogous to how conductance & resistance are defined. The SI unit of admittance is the siemens (symbol S); the older, synonymous unit is
mho The siemens (symbol: S) is the unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and ...
, and its symbol is ℧ (an upside-down uppercase omega Ω). Oliver Heaviside coined the term ''admittance'' in December 1887. Heaviside used ''Y'' to represent the magnitude of admittance, but it quickly became the conventional symbol for admittance itself through the publications of
Charles Proteus Steinmetz Charles Proteus Steinmetz (born Karl August Rudolph Steinmetz, April 9, 1865 – October 26, 1923) was a German-born American mathematician and electrical engineer and professor at Union College. He fostered the development of alternating c ...
. Heaviside probably chose ''Y'' simply because it is next to ''Z'' in the alphabet, the conventional symbol for impedance. Admittance is defined as :Y \equiv \frac \, where :''Y'' is the admittance, measured in siemens :''Z'' is the impedance, measured in ohms Resistance is a measure of the opposition of a circuit to the flow of a steady current, while impedance takes into account not only the resistance but also dynamic effects (known as reactance). Likewise, admittance is not only a measure of the ease with which a steady current can flow, but also the dynamic effects of the material's susceptance to polarization: :Y = G + j B \, where *Y is the admittance, measured in siemens. *G is the conductance, measured in siemens. *B is the
susceptance In electrical engineering, susceptance (''B'') is the imaginary part of admittance, where the real part is conductance. The reciprocal of admittance is impedance, where the imaginary part is reactance and the real part is resistance. In SI uni ...
, measured in siemens. *j^2 = -1 The dynamic effects of the material's susceptance relate to the
universal dielectric response In physics and electrical engineering, the universal dielectric response, or UDR, refers to the observed emergent behaviour of the dielectric properties exhibited by diverse solid state systems. In particular this widely observed response involves ...
, the power law scaling of a system's admittance with frequency under alternating current conditions.


Conversion from impedance to admittance

The impedance, ''Z'', is composed of real and imaginary parts, :Z = R + jX \, where *''R'' is the resistance, measured in ohms *''X'' is the reactance, measured in ohms :Y = Z^= \frac = \left( \frac \right) \left(R - jX\right) Admittance, just like impedance, is a complex number, made up of a
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part (the conductance, ''G''), and an imaginary part (the susceptance, ''B''), thus: :Y = G + jB \,\! where ''G'' (conductance) and ''B'' (susceptance) are given by: :\begin G &= \Re(Y) = \frac \\ B &= \Im(Y) = -\frac \end The magnitude and phase of the admittance are given by: :\begin \left , Y \right , &= \sqrt = \frac \\ \angle Y &= \arctan \left( \frac \right) = \arctan \left( -\frac \right) \end where *''G'' is the conductance, measured in siemens *''B'' is the
susceptance In electrical engineering, susceptance (''B'') is the imaginary part of admittance, where the real part is conductance. The reciprocal of admittance is impedance, where the imaginary part is reactance and the real part is resistance. In SI uni ...
, also measured in siemens Note that (as shown above) the signs of reactances become reversed in the admittance domain; i.e. capacitive susceptance is positive and inductive susceptance is negative.


Shunt admittance in electrical power systems modeling

In the context of electrical modeling of transformers and transmission lines, shunt components that provide paths of least resistance in certain models are generally specified in terms of their admittance. Each side of most transformer models contains shunt components which model magnetizing current and core losses. These shunt components can be referenced to the primary or secondary side. For simplified transformer analysis, admittance from shunt elements can be neglected. When shunt components have non-negligible effects on system operation, the shunt admittance must be considered. In the diagram below, all shunt admittances are referred to the primary side. The real and imaginary components of the shunt admittance, conductance and susceptance, are represented by Gc and B, respectively. Transmission lines can span hundreds of kilometers, over which the line's capacitance can affect voltage levels. For short length transmission line analysis, which applies to lines shorter than 80 kilometers, this capacitance can be ignored and shunt components are not necessary in the model. Lines between 80 and about 250 kilometers, generally considered to be in the medium-line category, contain a shunt admittance governed by Y=yl=j\omega Cl where * ''Y'' = total shunt admittance * ''y'' = shunt admittance per unit length * ''l'' = length of line * ''C'' = capacitance of line


See also

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Nodal admittance matrix In power engineering, nodal admittance matrix (or just admittance matrix) or Y Matrix or Ybus is an ''N x N'' matrix describing a linear power system with ''N'' buses. It represents the nodal admittance of the buses in a power system. In realis ...
*
SI electromagnetism units See also * SI * Speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory o ...
*
Immittance In electrical engineering and acoustics, immittance is a concept combining the impedance and admittance of a system or circuit. The term ''immittance'' was invented by H. W. Bode. It is sometimes convenient to use ''immittance'' to re ...


References

{{Authority control Physical quantities Electrical resistance and conductance