Inductive and Condensive Reactance

Original Forms To Preserve

For inductance:

x = 2\pi f L

For capacity in series:

x_1 = \frac{1}{2\pi f C}

Steinmetz calls the second quantity condensive reactance. The OCR around these lines has visible symbol defects, so these formulas are treated as source-located candidates until the scan is checked.

Modern Notation

X_L = \omega L = 2\pi f L

X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}

With the usual modern sign convention:

Z = R + j(X_L - X_C)

Mathematical Meaning

Inductive reactance increases with frequency. Capacitive reactance decreases with frequency. This is why the same circuit can be inductive at one frequency, capacitive at another, and resonant when the two are equal.

Worked Example

Let:

f = 60\ \mathrm{Hz},\quad L = 0.1\ \mathrm{H},\quad C = 100\ \mu\mathrm{F}

Then:

X_L = 2\pi(60)(0.1) \approx 37.7\ \Omega

X_C = \frac{1}{2\pi(60)(100 \times 10^{-6})} \approx 26.5\ \Omega

The net reactance is inductive:

X = X_L - X_C \approx 11.2\ \Omega

Physical Meaning

Reactance is not consumed energy. It is the opposition associated with field storage and return: magnetic storage in inductance, electrostatic storage in capacity.