Admittance

In Electrical Engineering , the admittance (''Y'') is the Inverse of the Impedance (''Z''). The SI unit of admittance is the Siemens . Oliver Heaviside coined the term in December 1887 .

:

Y = Z^{-1} = 1/Z  \,

where

Y

Z

Note that the synonymous unit Mho , and the symbol ℧ (an upside-down Omega Ω), are also in common use.

Then as
:

Z = R + iX \,

Y = Z^{-1}= rac{1}{R+iX} = \left( rac{1}{R+iX} 
ight) \cdot \left( rac{R-iX}{R-iX} 
ight) = \left( rac{R}{R^2+X^2} 
ight) + i\left(rac{-X}{R^2+X^2}
ight)

Admittance, just like Impedance, is therefore a complex number, made up of a Real part (the conductance, G), and an Imaginary part (the Susceptance , B), shown by the Equation :

:

Y = G + i B \,

Y = G + iB = \left( rac{R}{R^2+X^2} 
ight) + i \left( rac{-X}{R^2+X^2} 
ight)

Then G (Conductance) and B (Susceptance) are given by:

:

G = Re(Y) = \left( rac{R}{R^2+X^2} 
ight)

B = Im(Y) = \left( rac{-X}{R^2+X^2}
ight)

The magnitude of admittance is given by:

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Admittance