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

**URL:** <https://forumautomation.com/t/how-do-you-obtain-the-relation-between-no-load-emf-and-terminal-voltage-in-an-alternator-at-leading-a-negligible-power-factor/12040>\
**Category:** Electrical\
**Tags:** voltage\
**Created:** [May 7, 2024, 8:33am UTC](https://forumautomation.com/t/how-do-you-obtain-the-relation-between-no-load-emf-and-terminal-voltage-in-an-alternator-at-leading-a-negligible-power-factor/12040 "2024-05-07T08:33:19Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Rabert](https://forumautomation.com/user_avatar/forumautomation.com/rabert/32/6784_2.png) [@Rabert](https://forumautomation.com/u/Rabert)\
**Post date:** [May 7, 2024, 8:33am UTC](https://forumautomation.com/t/how-do-you-obtain-the-relation-between-no-load-emf-and-terminal-voltage-in-an-alternator-at-leading-a-negligible-power-factor/12040/1 "2024-05-07T08:33:19Z")

</div>

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.

 ![7](https://cdn.forumautomation.com/original/2X/3/3007dc829af4ca06ee3d41aa6107a549164d369e.jpeg)

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](https://forumelectrical.com/faradays-laws-of-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](https://forumelectrical.com/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),

where,

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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