AC Phenomena: Impedance And Reactance

Source: Theory and Calculation of Alternating Current Phenomena - Location: Chapters I, IV, V, VIII, IX; OCR candidates needs scan verification View source record

Source Meaning

In the AC book, impedance is not a casual synonym for resistance. It is the alternating-current opposition formed when resistance and reactance are combined. Reactance is the part that appears in quadrature with the current and is associated with inductance or capacity.

The first OCR pass places the topic across the opening chapter, vector representation, symbolic method, admittance, and circuits containing both inductive and condensive reactance. That distribution matters: Steinmetz treats impedance as a physical and mathematical structure, not only as a number.

Core Relation

$$Z = r + jx$$ $$z = \sqrt{r^2 + x^2}$$

Here r is resistance, x is reactance, Z is the complex impedance, and z is its magnitude.

Inductive And Condensive Reactance

Steinmetz’s older phrase “condensive reactance” corresponds to what modern courses usually call capacitive reactance. The important point is the sign opposition:

$$X_L = 2\pi f L$$ $$X_C = \frac{1}{2\pi f C}$$

Inductive and capacitive reactance oppose one another in the symbolic expression. This is the mathematical basis of resonance and phase control.

Modern Translation

Modern EE teaches:

$$Z = R + jX$$

with X = X_L - X_C under one common sign convention. The physical translation remains the same: resistance dissipates energy, while reactance stores and returns energy through magnetic and electric fields.

Hidden Conceptual Value

The older language keeps the two kinds of opposition visible. Resistance is a power-consuming opposition. Reactance is a field-storage opposition. Modern notation is efficient, but it can hide this physical difference if taught only as algebra.

Research Tasks

• Verify the exact notation for inductive and condensive reactance in each edition.
• Extract figures related to impedance and reactance geometry.
• Compare Steinmetz’s sign convention with modern textbook convention.
• Link to resonance, power factor, admittance, and dielectric loss pages.