susceptances

Susceptance, denoted B, is the imaginary part of an electrical admittance Y. Admittance is the reciprocal of impedance and can be written as Y = G + jB, where G is conductance and B is susceptance. Susceptance is measured in siemens (S) and describes how readily a circuit allows alternating current to flow due to reactive energy storage.

In a phasor representation, the impedance is Z = R + jX, with X the reactance, and the corresponding admittance is Y = 1/Z. For a pure reactive element Z = jX, the admittance becomes Y = -j/X, so B = -1/X. This yields a sign convention: B is positive for capacitive behavior and negative for inductive behavior. Equivalently, for common reactive elements, B_C = ωC for capacitors and B_L = -1/(ωL) for inductors, where ω = 2πf.

In networks, Y = G + jB and Z = 1/Y. Susceptance is especially important in AC circuit analysis, RF design, and power systems. It helps characterize reactive power flow and voltage control, particularly in shunt branches and transmission lines, where B represents the ease with which voltage changes drive reactive current.

Examples: a 1 μF capacitor at 60 Hz has B = ωC ≈ 2π·60·1e-6 ≈ 3.77×10^-4 S. An inductor of 10 mH at 60 Hz has B ≈ -1/(ωL) ≈ -0.265 S.

Overall, susceptance provides a compact way to quantify the reactive component of a network’s admittance and its effect on current for a given voltage in sinusoidal steady state.