For a generator with sinusoidal flux linkage, the generated EMF per phase is approximately given by which expression?

For a generator with sinusoidal flux linkage, the generated EMF per phase is approximately given by which expression?

• A. E_phase ≈ 4.44 f N Φ_m
• B. E_phase ≈ 2.0 f N Φ_m
• C. E_phase ≈ 1/(2π) f N Φ_m
• D. E_phase ≈ 0.5 f N Φ_m

Answer: (A)

When a generator has sinusoidal flux linkage, the phase EMF comes from how fast the flux is changing in time. For a winding with N turns, the instantaneous EMF is e = N dφ/dt. If the flux varies sinusoidally as φ(t) = Φ_m cos(ωt), then e(t) = -N Φ_m ω sin(ωt). The peak EMF is E_peak = N Φ_m ω. The RMS value of a sinusoid is E_rms = E_peak / √2, so E_rms = N Φ_m ω / √2. Since ω = 2π f, this becomes E_phase ≈ N Φ_m (2π f) / √2 = 4.44 f N Φ_m. In practice, winding and distribution effects introduce additional factors, but the ideal sinusoidal case gives this 4.44 f N Φ_m form. This is exactly the expression shown.

When a generator has sinusoidal flux linkage, the phase EMF comes from how fast the flux is changing in time. For a winding with N turns, the instantaneous EMF is e = N dφ/dt. If the flux varies sinusoidally as φ(t) = Φ_m cos(ωt), then e(t) = -N Φ_m ω sin(ωt). The peak EMF is E_peak = N Φ_m ω. The RMS value of a sinusoid is E_rms = E_peak / √2, so E_rms = N Φ_m ω / √2. Since ω = 2π f, this becomes E_phase ≈ N Φ_m (2π f) / √2 = 4.44 f N Φ_m. In practice, winding and distribution effects introduce additional factors, but the ideal sinusoidal case gives this 4.44 f N Φ_m form. This is exactly the expression shown.