A synchronous motor on load draw a current at a leading power factor angle ϕ. If the internal power factor angle which is the phase angle between the excitation emf and the current in the time phasor diagram is ψ. Then the air gap excitation mmf lags the armature mmf by?

Option 3 : π/2 – ψ

Causes of voltage drop:

1. Drop due to armature resistance, I_a R_a drop
2. Drop due to leakage reactance, I_a X_L drop
3. Drop due to armature reaction, I_a X_a drop

Synchronous reactance X_s = X_L + X_a 

Synchronous impedance Z_s = R_a + j X_s 

Vector diagram for the synchronous motor on lagging load:

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Where,

E is the induced EMF

I_a is the armature current

ψ is the angle between E and I_a also called an internal power factor angle.

ψ = ϕ ± δ 

Where,

' + ' is for lagging load 

' - ' is for leading load

Air gap voltage E_r = V + I_a R_a + j I_a X_L 

For synchronous motor:

The air gap excitation mmf lags the armature mmf by π/2 – ψ

For synchronous Alternator:

The air gap excitation mmf lags the armature mmf by π/2 + ψ