Admittance, Conductance, Susceptance

Source Relation

Steinmetz introduces admittance as the reciprocal of impedance:

Y = \frac{1}{Z}

The OCR candidate gives the component form:

Y = g - jb

where g is conductance and b is susceptance.

Conversion From Impedance

If:

Z = r + jx

then:

Y = \frac{1}{r + jx}

Multiply numerator and denominator by the conjugate:

Y = \frac{r - jx}{r^2 + x^2}

So, under this sign convention:

g = \frac{r}{r^2 + x^2}

b = \frac{x}{r^2 + x^2}

Why It Matters

This page is essential because it prevents a common beginner error:

Conductance is not generally 1/r.
Susceptance is not generally 1/x.

They are components of the reciprocal of the full complex impedance.

Worked Example

If:

Z = 6 + j8\ \Omega

then:

Y = \frac{6 - j8}{6^2 + 8^2} = 0.06 - j0.08\ \text{S}

Thus:

g = 0.06\ \text{S},\quad b = 0.08\ \text{S}

Modern Translation

Modern notation often writes admittance as Y = G + jB. When translating Steinmetz, the sign convention should be named explicitly rather than silently rewritten.