Discussion
Determine the distribution factor for a 6-pole, single-layer, 3-phase winding with 36 slots.
Answer: D
The distribution factor of a winding is \(k_d = \dfrac{\sin(m\beta/2)}{m \sin(\beta/2)}\), where \(m\) is the number of slots per pole per phase and \(\beta\) is the slot angle in electrical degrees.
\[ \begin{aligned} m = \frac{36}{6 \times 3} = 2,\qquad \beta \\ &= \frac{180^\circ \times P}{S} \\ &= \frac{180^\circ \times 6}{36} = 30^\circ \end{aligned} \]
\[ \begin{aligned} k_d \\ &= \frac{\sin(2 \times 30^\circ / 2)}{2 \sin(30^\circ / 2)} \\ &= \frac{\sin 30^\circ}{2 \times \sin 15^\circ} \approx 0.966 \end{aligned} \]
That is the fourth option. The other fractions have the wrong denominators for \(m = 2\): the third option would be right for \(m = 3\) with a 30 degree angle, and the first two use angles of 20 degrees that do not occur here. The answer is option D.
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