The torque developed in the squirrel cage induction motor with auto-starter is ____________.

Question

Examoogle · Accepted Answer

The correct answer is Option C: K 2 × torque with direct switching. The starting torque of an induction motor is proportional to the square of the applied voltage ($T \propto V^2$). When using an auto-transformer starter with a transformation ratio $K$ (where $K < 1$), the voltage applied to the motor terminals is reduced to $K 	imes V_{line}$, leading to a starting torque equal to $K^2$ times the direct-on-line (DOL) starting torque.

Step-by-Step Solution & Concepts:
The starting torque of an induction motor is proportional to the square of the applied voltage ($T \propto V^2$). When using an auto-transformer starter with a transformation ratio $K$ (where $K

Working Principle: An auto-transformer reduces the voltage applied to the stator windings during starting to limit the high inrush current. Since the electromagnetic torque developed by the induction motor is directly proportional to the square of the applied stator voltage, applying a fraction $K$ of the rated voltage results in a torque reduction factor of $K^2$.

Key Formulas: $$T_{st} \propto V^2$$; $$T_{auto} = K^2 	imes T_{DOL}$$

Key Points: Torque in an induction motor depends on the square of the applied voltage.; Auto-transformer starters limit starting current at the cost of reduced starting torque.; The factor $K$ represents the tapping ratio of the auto-transformer, where $K = \frac{V_{applied}}{V_{rated}}$.; Direct-on-line (DOL) starting provides the maximum possible starting torque.

Advantages: Adjustable starting current and torque by changing transformer tappings.; Lower power line disturbance compared to DOL starting.

Disadvantages: Reduced starting torque limits application to light loads.; Increased cost and complexity due to the auto-transformer unit.

Applications: Large squirrel cage induction motors.; Applications where reduced voltage starting is required to protect power systems.

Additional Info: The relationship $T \propto V^2$ is derived from the expression $T = \frac{k \cdot s \cdot E_2^2 \cdot R_2}{R_2^2 + (sX_2)^2}$, where the rotor induced EMF $E_2$ is proportional to the stator voltage $V$.. Options A and B suggest a linear relationship, which is incorrect as the torque sensitivity to voltage is quadratic.

Answer: C is correct — The torque developed with an auto-transformer starter is $K^2$ times the torque developed with direct-on-line switching.

Exam Tip: Always remember that for induction motors, both current and torque scale with voltage; current scales linearly ($I \propto V$), but torque scales quadratically ($T \propto V^2$).

Examoogle · Answer

Option A: k 2 /torque with direct switching

Examoogle · Answer

Option B: k/torque with direct switching

Examoogle · Answer

Option D: K × torque with direct switching

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