# admittance

Admittance is the reciprocal of impedance.
Admittance (** Y**) consists of two components: the conductance (

*G*) and the susceptance (

*B*). The relationship between

**,**

*Y**G*, and

*B*is expressed in complex form as follows:

** Y** =

*G*-

*iB*. (1)

The relationship between *G* and *B* on the one hand and *R* (resistance) and *X* (reactance) on the other is easily derived.
Thus,

** Y** = 1/

**= 1/(**

*Z**R*+

*iX*) = (

*R*-

*iX*) / (

*R*

^{ 2}+

*X*

^{ 2}). (2)

By comparing equations (1) and (2), we see that

*G* = *R*/(*R *^{2} + *X*^{ 2})
and *B* = *X*/(*R *^{2} + *X*^{ 2}).

Evidently, for purely resistive elements, the conductance is the reciprocal of the resistance (in keeping with the definition of conductance in parallel DC circuits), while, for purely reactive elements, the susceptance is the reciprocal of the reactance. Also, the total admittance of a group of impedances in parallel is the sum of their separate admittances.

Useful analogies between series and parallel circuits are established by describing the former in terms of impedance and its components and the latter in terms of admittance and its components. For example, the total impedance (admittance) of a series (parallel) circuit is the sum of the individual complex impedances (admittances).