Effective Resistance
Effective resistance
Modern Equivalent
Section titled “Modern Equivalent”AC resistance, equivalent resistance, or equivalent real-power-loss resistance, depending on the circuit.
Steinmetz Usage
Section titled “Steinmetz Usage”Steinmetz separates true ohmic resistance from effective resistance. True ohmic resistance is the conductor resistance measured by direct-current methods. Effective resistance is broader: it represents real power consumed by the alternating-current system.
The Chapter XII OCR candidate says that effective resistance represents “the total expenditure of power.” Chapter I then lists mechanisms that can make it exceed conductor resistance, including magnetic hysteresis, mutual induction, and dielectric hysteresis.
Mathematical Meaning
Section titled “Mathematical Meaning”For sinusoidal AC using RMS quantities:
so:
This does not mean all losses are physically ohmic. It means their real-power effect can be represented by an in-phase resistance term for calculation.
Modern Interpretation
Section titled “Modern Interpretation”Modern engineering still uses equivalent resistance models: core-loss resistance in transformers, equivalent series resistance in capacitors, skin-effect resistance in conductors, and loss components in transmission-line models. Steinmetz’s language is unusually clear because it refuses to reduce all real-power loss to the copper conductor.
Common Misunderstanding
Section titled “Common Misunderstanding”Effective resistance is not simply DC resistance measured more accurately. It is an AC working quantity that may depend on voltage, current, frequency, magnetic saturation, dielectric condition, current distribution, and surrounding materials.
Ether-Field Interpretive Reading
In an ether-field interpretation, effective resistance is where field-lag, field memory, dielectric loss, magnetic hysteresis, and secondary field motion become visible as real power expenditure. That is an interpretive layer. The historically grounded layer is that Steinmetz explicitly includes loss outside the conductor in effective resistance.
Current Status
Section titled “Current Status”Still used, broadened under many names. Modern texts may say AC resistance, equivalent resistance, ESR, core-loss resistance, or real part of impedance/admittance. Steinmetz’s term remains conceptually useful because it asks what total physical process is being represented by the real part of the calculation.