Understanding Conductance, Susceptance, and Admittance in AC Circuits

What Is Conductance?

In DC circuit analysis, the concept that serves as the inverse of resistance is called conductance. It becomes especially useful when simplifying networks of parallel resistors:

R_{parallel} = 1 / (1/R_1 + 1/R_2 + … + 1/R_n)

While adding resistors in parallel reduces the overall resistance, conductances simply accumulate. Mathematically, conductance is the reciprocal of resistance: G = 1/R. Each 1/R term in the parallel‑resistance equation is, in fact, a conductance.

Resistance quantifies how much a component opposes electron flow, whereas conductance measures how readily electrons can pass. Where “resistance” is a measure of opposition, “conductance” is a measure of ability.

Historically, conductance was expressed in mhos (ohms spelled backward). Today the SI unit is the Siemens (symbol S). In formulas the symbol G denotes conductance.

Reactive elements—inductors and capacitors—oppose current changes over time rather than providing a constant resistance. This time‑dependent opposition is called reactance and is also measured in ohms.

What Is Susceptance?

Just as conductance complements resistance, the reciprocal of reactance is called susceptance. It is defined as B = 1/X and, like conductance, is measured in Siemens.

The symbol for susceptance is B—the same letter that denotes magnetic flux density in electromagnetism, but in circuit analysis it refers exclusively to the imaginary part of admittance.

Reactance vs. Susceptance

The terminology mirrors that of resistance and conductance: reactance describes how a circuit resists changes in current over time, while susceptance describes how readily a circuit accepts a time‑varying current.

When evaluating several parallel, pure reactances, it is often easier to convert each reactance X into its corresponding susceptance B, sum the B values, and then take the reciprocal to obtain the equivalent reactance:

X_{parallel} = 1 / (1/X_1 + 1/X_2 + … + 1/X_n)

Susceptances, like conductances, add in parallel and combine in series. Both are scalar quantities. However, when resistive and reactive elements coexist, a single scalar quantity no longer suffices.

In mixed networks, the concepts of impedance (Z, measured in ohms) and its reciprocal, admittance (Y, measured in Siemens), become essential. Impedance is a complex number that encapsulates both resistance and reactance; admittance is its complex reciprocal.

What Is Admittance?

Admittance, denoted Y and measured in Siemens, is the reciprocal of impedance. While impedance quantifies how much a circuit impedes AC, admittance quantifies how much it permits current flow.

Because impedance is a complex quantity, admittance is also complex. Modern scientific calculators can handle complex arithmetic in both polar and rectangular form, so you may rarely need to use the separate figures for susceptance (B) or admittance (Y) explicitly. Nevertheless, understanding their meaning remains valuable.

RELATED WORKSHEET:

• Series and Parallel AC Circuits Worksheet