Size (product of 𝐷2 𝐿) of the machine depends on which of the following parameters?

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Option D: All of these

Explanation & Concepts:
The physical size of an electrical machine is represented by its main dimensions, the stator bore diameter ($D$) and the core length ($L$). The product $D^2L$ determines the volume of the active material required and is directly proportional to the output rating and inversely proportional to the speed and the output coefficient of the machine.

Working Principle: The design of a rotating machine is governed by the output equation $Q = C_0 D^2 L n_s$, where $Q$ is the power rating, $C_0$ is the output coefficient (which depends on magnetic and electric loadings), and $n_s$ is the synchronous speed. Thus, $D^2 L = \frac{Q}{C_0 n_s}$. This relationship implies that for a fixed output, increasing the speed or the efficiency of material utilization (output coefficient) allows for a smaller machine size.

Key Formulas: $D^2 L = \frac{Q}{C_0 n_s}$ — fundamental output equation relating volume to rating, coefficient, and speed.; $C_0 = 11 B_{av} ac 	imes 10^{-3}$ — defines the output coefficient in terms of specific magnetic loading ($B_{av}$) and electric loading ($ac$).

Key Points: The product $D^2L$ is known as the output constant or machine size constant.; Higher output coefficient $C_0$ implies better utilization of active material, leading to a smaller $D^2L$ for a given rating.; For higher synchronous speeds, the required $D^2L$ decreases for a constant power rating.; Magnetic loading ($B_{av}$) and Electric loading ($ac$) are constrained by the saturation of iron and thermal limits of insulation respectively.

Advantages: Allows for standardized sizing of electrical machines.; Provides a clear design pathway for selecting motor frame sizes.

Disadvantages: Requires iterative design processes to optimize $D$ vs $L$ ratios.; Does not account for non-active material requirements like casing and cooling fins.

Applications: Preliminary sizing of Induction Motors.; Performance optimization of Synchronous Generators.

Additional Info: The Output Coefficient $C_0$ is constant for a specific type of machine (e.g., induction motor) and cooling method.. Option B (Output Co-efficient) is a measure of how efficiently the flux density and current density are utilized in the machine space.

Answer: D is correct — The machine size $D^2L$ is directly derived from the output equation, making it a function of the machine's power output, its design efficiency (output coefficient), and its operating speed.

Exam Tip: Always remember that for a given $D^2L$, increasing $n_s$ (synchronous speed) allows the machine to provide more power output (or handle a larger load).

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Option A: Output of the machine

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Option B: Output Co-efficient of the machine

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Option C: Synchronous Speed of the machine

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