Susceptance

In electrical engineering, susceptance (B) is the imaginary part of admittance. The inverse of admittance is impedance and the real part of admittance is conductance. In SI units, susceptance is measured in siemens. Oliver Heaviside first defined this property, which he called permittance, in June 1887.[1]

Formula

The general equation defining admittance is given by

$Y = G + j B \,$

where

Y is the admittance, measured in siemens (a.k.a. mho, the inverse of ohm).
G is the conductance, measured in siemens.
j is the imaginary unit, and
B is the susceptance, measured in siemens.

Rearranging yields

$B = \frac{Y - G} {j}$.

But since

$\frac{1}{j} =\frac{j}{j \cdot j} = \frac{j}{-1} = -j$,

we obtain

$B = -j \cdot (Y -G)$.

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

$Y = \frac {1} {Z} = \frac {1} {R + j X} = \left( \frac {R} {R^2+X^2} \right) + j \left( \frac{-X} {R^2+X^2} \right) \,$

or

$B = Im(Y) = \left( \frac{-X} {R^2+X^2} \right) = \frac{-X}{|Z|^2}$

where

$Z = R + j X \,$
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:

$\left | Y \right | = \sqrt {G^2 + B^2} \,$