AC Phenomena: Admittance, Conductance, Susceptance

Why This Chapter Matters

Chapter VIII introduces the reciprocal language of impedance. Steinmetz motivates it from the practical difference between series and parallel circuits: resistance and impedance are convenient in series; conductance and admittance are convenient in parallel.

The OCR candidate indicates that Steinmetz defines admittance as the reciprocal of impedance and resolves it into conductance and susceptance.

Core Relations

Z = r + jx

Y = \frac{1}{Z}

Y = g - jb

y = \sqrt{g^2 + b^2}

where g is conductance and b is susceptance.

Conceptual Meaning

Impedance resolves voltage into in-phase and quadrature components relative to current. Admittance resolves current into in-phase and quadrature components relative to voltage.

That is the key to the chapter. It is not merely reciprocal algebra. It is a change in what is being decomposed:

Impedance language: voltage components produced by a current.
Admittance language: current components produced by a voltage.

Common Mistake

Steinmetz explicitly warns in the OCR candidate that conductance is not generally just the reciprocal of resistance, and susceptance is not generally just the reciprocal of reactance. They depend on the full impedance relation except in special cases.

Modern Electrical Engineering Interpretation

Modern circuit analysis still uses this distinction in parallel networks, transformers, load modeling, filter analysis, and transmission-line theory. The modern notation is often Y = G + jB; Steinmetz’s sign convention must be checked against the specific edition before canonical conversion.

Links To Build

Verification Tasks

Verify the OCR around Y = g - jb.
Extract Fig. 49 and related curves.
Build a worked example converting Z = r + jx to Y.