In the design of single-phase induction motor. The length of a mean turn of each coil per pole,

Question

Examoogle · Accepted Answer

Option A: 𝑳𝒎𝒕 = [𝟖.𝟒 (𝑫+𝒅𝒔𝒔)/𝑺𝒔 ] × 𝒔𝒍𝒐𝒕𝒔 𝒔𝒑𝒂𝒏 + 𝟐𝑳

Explanation & Concepts:
In single-phase induction motor design, the mean length of turn ($L_{mt}$) for a coil per pole accounts for both the embedded core portion (two slot lengths, $2L$) and the overhang portion at both ends. The overhang portion depends on the pole pitch, which is proportional to the mean diameter $(D + d_{ss})$, number of stator slots ($S_s$), and the slot span.

Working Principle: The stator winding consists of coils placed in slots, with part of the coil residing inside the slot length ($L$) and the remaining part forming the end-connections (overhang). The length of the overhang for both sides is empirically calculated as $8.4 \left(\frac{D + d_{ss}}{S_s}ight) 	imes 	ext{slots span}$. Adding the length of two straight slot sides ($2L$) yields the complete length of a mean turn $L_{mt}$.

Key Formulas: $L_{mt} = \left[ 8.4 \frac{D + d_{ss}}{S_s} ight] 	imes 	ext{slots span} + 2L$ — Mean length of turn of stator coil; $	au_s = \frac{\pi (D + d_{ss})}{S_s}$ — Stator slot pitch at mean depth of slot

Key Points: $D$ represents the internal diameter of the stator core.; $d_{ss}$ represents the depth of the stator slot.; $S_s$ represents the total number of stator slots.; $L$ represents the gross length of the stator core.; The term $2L$ accounts for the active conductor lengths embedded within two stator slots.

Advantages: Provides accurate resistance estimation during design stage.; Helps in estimating total copper weight required for stator winding.

Disadvantages: Empirical constant (8.4) varies slightly depending on winding type and end-shaping.

Applications: Design and winding calculations of single-phase induction motors.; Estimation of stator copper losses ($I^2R$) and material cost.

Additional Info: Option A is the correct standard design formula for single-phase induction motor stator coils.. Option B incorrectly uses addition instead of multiplication for the overhang calculation.. Option C incorrectly multiplies $2L$ with the overhang term instead of adding it.. Option D omits one slot length by using $L$ instead of $2L$ (since a full turn has two conductor sides).

Answer: A is correct — The mean length of turn $L_{mt}$ consists of the two straight slot lengths ($2L$) plus the end-connection overhang given by $\left[8.4 \frac{D + d_{ss}}{S_s}ight] 	imes 	ext{slots span}$.

Exam Tip: Remember that every turn of a coil has two active sides passing through two slots, which is why the straight length component is always $2L$ in turn-length calculations for electrical machines.

Examoogle · Answer

Option B: 𝑳𝒎𝒕 = [𝟖.𝟒 (𝑫+𝒅𝒔𝒔)/𝑺𝒔 ] + 𝒔𝒍𝒐𝒕𝒔 𝒔𝒑𝒂𝒏 + 𝟐𝑳

Examoogle · Answer

Option C: 𝑳𝒎𝒕 = [𝟖.𝟒 (𝑫+𝒅𝒔𝒔)/𝑺𝒔 ] × 𝒔𝒍𝒐𝒕𝒔 𝒔𝒑𝒂𝒏 × 𝟐𝑳

Examoogle · Answer

Option D: 𝑳𝒎𝒕 = [𝟖.𝟒 (𝑫+𝒅𝒔𝒔)/𝑺𝒔 ] × 𝒔𝒍𝒐𝒕𝒔 𝒔𝒑𝒂𝒏 + 𝑳

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