ABSTRACT
Admittance is defined as the current I flowing in an a.c. circuit divided by the supply voltage V (i.e. it is the reciprocal of impedance Z). The symbol for admittance is Y. Thus
Y = I V =
1 Z
The unit of admittance is the Siemen, S. An impedance may be resolved into a real part R and an imaginary part
X, giving Z D Rš jX. Similarly, an admittance may be resolved into two parts-the real part being called the conductance G, and the imaginary part being called the susceptance B-and expressed in complex form. Thus admittance
Y = G ± jB
Z D R and Y D 1 Z
D 1 R
D G
(b) pure inductance, then
Z D jXL and Y D 1 Z
D 1 jXL
D j jXLj D
j XL
D −jBL
thus a negative sign is associated with inductive susceptance, BL (c) pure capacitance, then
Z D jXC and Y D 1 Z
D 1jXC D j
jXCj D j
XC D YjBC
thus a positive sign is associated with capacitive susceptance, BC (d) resistance and inductance in series, then
Z D RC jXL and Y D 1 Z
D 1 RC jXL D
R jXL R2 C X2L
i.e. Y D R R2 C X2L
j XL R2 C XL2 or Y =
R jZ j2 − j
XL jZ j2
Thus conductance, G D R/jZj2 and inductive susceptance, BL D XL/jZj2. (Note that in an inductive circuit, the imaginary term of the impedance, XL, is positive, whereas the imaginary term of the admittance, BL , is negative.)
(e) resistance and capacitance in series, then
Z D R jXC and Y D 1 Z
D 1 R jXC D
RC jXC R2 C X2C
i.e. Y D R R2 C X2C
C j XC R2 C X2C
or Y = R
jZ j2 Y j XC jZ j2
Thus conductance, G D R/jZj2 and capacitive susceptance, BC D XC/jZj2. (Note that in a capacitive circuit, the imaginary term of the impedance, XC, is negative, whereas the imaginary term of the admittance, BC, is positive.)
(f) resistance and inductance in parallel, then 1
D 1
C 1
D jXL C R
from which, Z = L R Y jXL
i.e.
