All questions of Three-Phase Induction Motor for Electrical Engineering (EE) Exam

Explanation:


Introduction:


In a 3-phase squirrel cage induction motor, the starting current and torque can be reduced by using an auto-transformer starter. When the applied voltage is reduced to x times its rated value, the starting line current and starting torque would reduce by a certain factor. The factor depends on the value of x and the type of starting method used. In this case, we are using an auto-transformer starter.

Auto-Transformer Starting:


Auto-transformer starting is a method of starting a 3-phase squirrel cage induction motor using an auto-transformer. The auto-transformer is connected in series with the motor during the starting process. The auto-transformer reduces the voltage applied to the motor and hence reduces the starting current and torque. The auto-transformer has a tapping that can be adjusted to vary the starting voltage.

Reduction factor:


When the applied voltage is reduced to x times its rated value, the starting line current and starting torque would reduce by a certain factor. The reduction factor depends on the value of x and the type of starting method used. In this case, we are using an auto-transformer starter.

The reduction factor for the starting line current is given by:

$K_{I} = \dfrac{1}{x}$

The reduction factor for the starting torque is given by:

$K_{T} = \dfrac{1}{x^{2}}$

Answer:


Therefore, when the applied voltage is reduced to x times its rated value, the starting line current from mains and starting torque by auto-transformer starting would reduce respectively from their corresponding direct switching values by a factor of x2, x. Hence, the correct answer is option C.