Susceptance and Admittance
In the study of DC circuits, the student of
electricity comes across a term meaning the opposite of
resistance: conductance. It is a useful term when
exploring the mathematical formula for parallel resistances:
Rparallel = 1 / (1/R1 + 1/R2
+ . . . 1/Rn). Unlike resistance, which
diminishes as more parallel components are included in the
circuit, conductance simply adds. Mathematically,
conductance is the reciprocal of resistance, and each 1/R
term in the "parallel resistance formula" is actually a
conductance.
Whereas the term "resistance" denotes the
amount of opposition to flowing electrons in a circuit,
"conductance" represents the ease of which electrons may
flow. Resistance is the measure of how much a circuit
resists current, while conductance is the measure of how
much a circuit conducts current. Conductance used to
be measured in the unit of mhos, or "ohms" spelled
backward. Now, the proper unit of measurement is Siemens.
When symbolized in a mathematical formula, the proper letter
to use for conductance is "G".
Reactive components such as inductors and
capacitors oppose the flow of electrons with respect to
time, rather than with a constant, unchanging friction as
resistors do. We call this time-based opposition,
reactance, and like resistance we also measure it in the
unit of ohms.
As conductance is the complement of
resistance, there is also a complementary expression of
reactance, called susceptance. Mathematically, it is
equal to 1/X, the reciprocal of reactance. Like conductance,
it used to be measured in the unit of mhos, but now is
measured in Siemens. Its mathematical symbol is "B",
unfortunately the same symbol used to represent magnetic
flux density.
The terms "reactance" and "susceptance" have
a certain linguistic logic to them, just like resistance and
conductance. While reactance is the measure of how much a
circuit reacts against change in current over time,
susceptance is the measure of how much a circuit is
susceptible to conducting a changing current.
If one were tasked with determining the
total effect of several parallel-connected, pure reactances,
one could convert each reactance (X) to a susceptance (B),
then add susceptances rather than diminish reactances: Xparallel
= 1/(1/X1 + 1/X2 + . . . 1/Xn).
Like conductances (G), susceptances (B) add in parallel and
diminish in series. Also like conductance, susceptance is a
scalar quantity.
When resistive and reactive components are
interconnected, their combined effects can no longer be
analyzed with scalar quantities of resistance (R) and
reactance (X). Likewise, figures of conductance (G) and
susceptance (B) are most useful in circuits where the two
types of opposition are not mixed, i.e. either a purely
resistive (conductive) circuit, or a purely reactive
(susceptive) circuit. In order to express and quantify the
effects of mixed resistive and reactive components, we had
to have a new term: impedance, measured in ohms and
symbolized by the letter "Z".
To be consistent, we need a complementary
measure representing the reciprocal of impedance. The name
for this measure is admittance. Admittance is
measured in (guess what?) the unit of Siemens, and its
symbol is "Y". Like impedance, admittance is a complex
quantity rather than scalar. Again, we see a certain logic
to the naming of this new term: while impedance is a measure
of how much alternating current is impeded in a
circuit, admittance is a measure of how much current is
admitted.
Given a scientific calculator capable of
handling complex number arithmetic in both polar and
rectangular forms, you may never have to work with figures
of susceptance (B) or admittance (Y). Be aware, though, of
their existence and their meanings. |
