Which of the following is not an output equation of three-phase induction motor?

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Examoogle · Accepted Answer

Option C:

Q = \sqrt{3} C_{0} D^{2} L n_{s}

Explanation & Concepts: The output equation of a three-phase induction motor represents the relationship between the motor power output (Q) and its main dimensions, specifically the bore diameter (D) and core length (L). The standard output equation is derived as $Q = C_0 D^2 L n_s$, where $C_0$ is the output coefficient involving specific magnetic and electric loadings. Working Principle: The output coefficient $C_0$ incorporates the specific magnetic loading ($B_{av}$), specific electric loading ($ac$), and the winding factor ($K_w$). The constant $C_0$ is inherently defined such that it accounts for the three-phase nature of the system (the $\sqrt{3}$ factor is already absorbed into the definition of $C_0$). Therefore, including an additional $\sqrt{3}$ as shown in option C results in an incorrect dimensioned equation. Key Formulas: $Q = C_0 D^2 L n_s$ — Output equation of an induction motor; $C_0 = 1.11 \pi^2 K_w B_{av} ac 10^{-3}$ — Expression for the output coefficient Key Points: The output coefficient $C_0$ is defined as $1.11 \pi^2 K_w B_{av} ac 10^{-3}$.; The product $D^2 L$ is known as the output constant dimension.; The $\sqrt{3}$ factor is integrated into the calculation of $C_0$ for 3-phase machines, making option C redundant and incorrect. Advantages: Provides a quick estimation of machine size for a given power rating.; Useful in initial design stages of electrical machines. Disadvantages: It is a design approximation based on average flux and current densities.; Does not account for temperature rise or efficiency losses directly. Applications: Preliminary sizing of industrial AC motors.; Comparison of machine designs based on volume utilization. Additional Info: Option B is a standard form of the output equation where $C_0$ is fully expanded.. Option D is an alternative simplified form often used where numerical constants are condensed.. The constant $1.11$ comes from the form factor of the AC supply voltage. Answer: C is correct — The $\sqrt{3}$ factor is already embedded within the output coefficient $C_0$ definition; multiplying it again is mathematically incorrect. Exam Tip: Always verify if the $\sqrt{3}$ factor is inside your constant $C_0$ or $K$ when calculating power for 3-phase machines; don't count it twice!

Examoogle · Answer

Option A: Q=C0 D2L ns

Examoogle · Answer

Option B: Q=(1.11 π2 Kw Bav ac 10-3)  D2L ns

Examoogle · Answer

Option D: Q=(11 Kw Bav ac 10-3)  D2L ns

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