The armature of a three-phase alternator has 240 slots. The armature has 8 poles. Its distribution factor is _________.

The correct answer is option 2):\(\frac{\sin 30^\circ}{10 \sin 3^\circ}\)

Concept:

The distribution factor is given as,

\({k_d} = \frac{{\sin \frac{{m\beta }}{2}}}{{m\sin \frac{\beta }{2}\;}}\)

Where m is the number of slots per pole per phase

β is the slot angle in degrees

Calculation:

Given

3-phase, 8-pole synchronous machine.

No. of slots = 240 (stator slots)

m = \(240\over 3×8\)

=10

\(m = \frac{{240}}{{3\; × \;8}} = 10\)

\(\beta = \frac{{180^\circ }}{{slots\;per\;pole}}\)

\(\beta = \frac{{180^\circ }}{{240/8}} = 6^\circ\)

\({K_d} = \frac{{\sin \frac{{10 × 6}}{2}}}{{10\sin \frac{{6}}{2}}} = \frac{{\sin 30^\circ }}{{10\sin 3^\circ }}\)