Conductance,Susceptance, and Admittance

Author: E.E. Kimberly

The in-phase and quadrature components of complex numbers may be found by a method differing somewhat from that explained on page 24. In a simple series circuit containing resistance and inductance.

When complex-number notation is used,

If the right-hand member of the last equation be multiplied by its value will not be changed. Thus,

or

in which Ig is the component of current in phase with V and Ib is the component of current in quadrature with V. The vector diagram for current is shown in Fig. 5-13.

Fig. 5-13. Vector Diagram for Current

The quantity

(5-9)

(5-10)

Just as all the reactances of a series circuit may be added algebraically, so may all the susceptances of parallel circuits be added algebraically. Also, all conductances of several parallel circuits may be added algebraically.

The complex quantity whose components are g and b is called admittance, and its symbol is Y. Thus,

[5-11]

The admittance is the reciprocal of the impedance; that is,

Y = 1/Z

[5-12]

Also

I = VY

[5-13]