# admittance (*Y*)
The reciprocal of the 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/*Z*
= 1/(*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 impeance
(admittance) of a series (parallel) circuit is the sum of the individual
complex impedances (admittances). ## Related category
• ELECTRICITY
AND MAGNETISM
Source: Duckworth,
Henry E. *Electricity and Magnetism*, pp. 372-372. New York: Holt,
Rinehart and Winston (1960). |