What is the pitch factor of a 4 pole alternator having 36 slots and a coil span of 1 to 8

Explanation:

Pitch Factor of a 4-Pole Alternator

Definition: The pitch factor, also known as the coil pitch factor or winding factor, is a measure of the distribution of the coil spans in an alternator or generator. It accounts for the reduction in the induced EMF due to short-pitch (fractional pitch) windings. The pitch factor is mathematically represented by:

Kp = cos(α/2)

Where:

• α = Angular displacement between the two sides of the coil (also called the coil pitch).

Problem Statement: We need to calculate the pitch factor for a 4-pole alternator having 36 slots and a coil span of 1 to 8.

Step-by-Step Solution:

Step 1: Determine the Angular Displacement per Slot

The angular displacement per slot (in electrical degrees) for a 4-pole alternator is given by:

Angular displacement per slot = (360 × Number of poles) / Total number of slots

Substituting the given values:

Angular displacement per slot = (360 × 4) / 36

Angular displacement per slot = 40°

Step 2: Calculate the Angular Displacement (α) between the Two Sides of the Coil

The coil span is given as 1 to 8. This means the coil spans 8 slots. Therefore, the angular displacement between the two sides of the coil is:

α = Angular displacement per slot × Coil span

Substituting the values:

α = 40° × 8

α = 320°

Step 3: Calculate the Pitch Factor

Using the formula for the pitch factor:

Kp = cos(α/2)

Substituting α = 320°:

Kp = cos(320°/2)

Kp = cos(160°)

From trigonometric calculations:

Kp ≈ cos(160°) ≈ -0.766

Step 4: Convert the Absolute Value to Positive

Since pitch factor is always represented as a positive value, we take the absolute value:

Kp = |cos(160°)| ≈ 0.766

Final Pitch Factor: The pitch factor for the given alternator is approximately 0.766.

Correct Option Analysis:

The correct answer is Option 4, which states that the pitch factor corresponds to an angular displacement of 40°. This matches the angular displacement per slot for the given alternator, calculated as 40°. It aligns with the calculation process outlined above.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 140°

This option is incorrect because the angular displacement per slot is calculated as 40°, not 140°. The coil span and poles do not support this value for the pitch factor calculation.

Option 2: 80°

This option is incorrect as well. While 80° might seem plausible for a different configuration, the actual angular displacement per slot is 40°, and the coil span does not lead to this value.

Option 3: 20°

This option is invalid because the pitch factor calculation does not involve an angular displacement of 20°. The given alternator specifications lead to an angular displacement of 40° per slot.

Option 5: No Value Provided

This option is not applicable for the current problem statement, as the pitch factor calculation clearly supports 40° as the correct angular displacement per slot.

Conclusion:

The pitch factor calculation for the given alternator relies on understanding the angular displacement per slot, coil span, and the associated trigonometric principles. By following the systematic approach outlined above, we verified that the correct angular displacement per slot is 40°, making Option 4 the correct choice.