Counter-Electromotive Force
Counter-electromotive force, usually printed by Steinmetz as counter e.m.f.
Modern Equivalent
Section titled “Modern Equivalent”Depending on context:
- back EMF in motors or generators,
- induced opposing voltage,
- voltage drop or impedance voltage in circuit calculation,
- phasor voltage term opposing or balancing an impressed voltage.
Steinmetz Usage
Section titled “Steinmetz Usage”Steinmetz uses the term in more than one way. In machine contexts, a counter e.m.f. may be a physically generated voltage. In vector circuit calculation, he also uses counter e.m.f. for the resistance, reactance, or impedance voltage represented as opposing the impressed voltage.
The OCR candidate in Chapter IV gives a key caution: these counter e.m.f.s of resistance and reactance “have no independent existence” apart from the current. This is a subtle distinction. He is not saying every counter e.m.f. is a separate source; he is giving an alternate phasor representation of how the circuit balances impressed voltage.
Mathematical Meaning
Section titled “Mathematical Meaning”For a sinusoidal current I through impedance:
Modern textbooks usually call E_Z an impedance voltage or voltage drop. Steinmetz may instead describe the same vector as a counter e.m.f. when it is drawn as opposing the impressed voltage.
Why It Matters
Section titled “Why It Matters”The phrase keeps a mechanical and field-opposition picture alive. A modern student may memorize voltage drops as algebraic bookkeeping. Steinmetz’s wording forces the reader to ask: what field process is opposing the change, where is energy being stored, and which part is dissipative?
Ether-Field Interpretive Reading
A Wheeler-style reading may treat counter e.m.f. as a field reaction: a resistance-like or reactance-like opposition arising when the circuit condition attempts to alter field state. That reading is interpretive. The source-grounded claim is that Steinmetz explicitly distinguishes dependent counter e.m.f.s of resistance/reactance from independently generated machine e.m.f.s.
Current Status
Section titled “Current Status”Still used, narrowed. Modern electrical engineering still says back EMF, especially in motors, but it less often calls ordinary impedance voltage a counter e.m.f. The older Steinmetz usage is valuable because it preserves a phasor-opposition viewpoint that can clarify AC circuit balance.