Susceptance

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In electrical engineering, the susceptance (B) is the imaginary part of the admittance. In SI units, the susceptance is measured in siemens. Oliver Heaviside first defined this property, which he called permittance, in June 1887^{[citation needed]}.

Formula

The general equation defining admittance is given by

Failed to parse (Missing texvc executable; please see math/README to configure.): Y = G + j B \,

where

Y is the admittance, measured in siemens i.e. mho (inverse of ohm).

G is the conductance, measured in siemens i.e. mho (inverse of ohm).

j is the imaginary unit, and

B is the susceptance, measured in siemens i.e. mho (inverse of ohm).

Rearranging yields

Failed to parse (Missing texvc executable; please see math/README to configure.): B = \frac{Y - G} {j}

But since

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{j} =\frac{j}{j \cdot j} = \frac{j}{-1} = -j

we obtain

Failed to parse (Missing texvc executable; please see math/README to configure.): B = -j \cdot (Y -G)

The admittance (Y) is the inverse of the impedance (Z)

Failed to parse (Missing texvc executable; please see math/README to configure.): Y = \frac {1} {Z} = \frac {1} {R + j X} = \left( \frac {R} {R^2+X^2} \right) + j \left( \frac{-X} {R^2+X^2} \right) \,

Failed to parse (Missing texvc executable; please see math/README to configure.): B = Im(Y) = \left( \frac{-X} {R^2+X^2} \right)

where

Failed to parse (Missing texvc executable; please see math/README to configure.): Z = R + j X \,

Z is the impedance, measured in ohms

R is the resistance, measured in ohms

X is the reactance, measured in ohms.

Note: The susceptance is the imaginary part of the admittance.

The magnitude of admittance is given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \left | Y \right | = \sqrt {G^2 + B^2} \,