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.
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