How do you obtain the relation between no load EMF and terminal voltage in an alternator at leading a negligible power factor?

To determine the relationship between no-load EMF (electromotive force) & terminal voltage in an alternator with a minimal power factor, we must examine the phasor diagram and voltage equations in the alternator under these conditions.

In an alternator, the no-load EMF (E0) is the voltage created by the rotating armature when no load is attached to it.

This voltage is caused by electromagnetic induction.

When a load is attached to the alternator, the armature current (Ia) flowing across the armature winding generates an armature response ampere-turns that counteracts the main field ampere-turns. The armature reaction effects reduce the resultant air-gap flux, resulting in a terminal voltage (V) that is slightly lower than the no-load EMF (E0).

At a high power factor (near unity), the armature current (Ia) lags behind the no-load EMF (E0) by a minor angle (δ). In this case, the phasor diagram will be expressed as follows:

The terminal voltage (V) is defined as

  • The vector sum of the no-load EMF (E0) &
  • The armature resistance drop (Ia x Ra),


Ra represents the armature resistance.

V = E0 – (Ia x Ra)

Rearranging the equation yields:

E0 = V + (Ia x Ra)

The armature resistance drop (Ia x Ra) at a leading power factor causes the no-load EMF (E0) to be somewhat greater than the terminal voltage (V), as seen in this equation.

The difference between E0 & V is usually minimal, particularly in alternators with low armature resistance. As the power factor approaches unity (δ → 0), the armature resistance drop decreases and the no-load EMF (E0) approaches the terminal voltage.

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