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

Correct option is A

$$\text{Given:} \\[4pt]\text{The torque developed in a squirrel cage induction motor with auto-starter.} \\[4pt]\text{Starting torque } (T_{st}), \text{ Full load torque } (T_n), \text{ Starting current } (I_{st}), \\[4pt]\text{Full load current } (I_n), \text{ and full load slip } (S_f). \\[6pt]\text{For an auto transformer starter, } K \text{ represents the tapping of transformation ratio.} \\[8pt]\textbf{Formula Used:} \\[4pt]\text{For Direct Online Starter:} \\[4pt]\dfrac{T_{st}}{T_n} = \left(\dfrac{I_{st}}{I_n}\right)^2 S_f \\[10pt]\text{For Auto Transformer Starter:} \\[4pt]\dfrac{T_{st}}{T_n} = K^2 \left(\dfrac{I_{st}}{I_n}\right)^2 S_f \\[10pt]\text{Where:} \\[4pt]T_{st} \rightarrow \text{Starting torque} \\[4pt]T_n \rightarrow \text{Full load torque} \\[4pt]I_{st} \rightarrow \text{Starting current} \\[4pt]I_n \rightarrow \text{Full load current} \\[4pt]S_f \rightarrow \text{Full load slip} \\[4pt]K \rightarrow \text{Tapping of transformation ratio} \\[10pt]\textbf{Solution:} \\[4pt]\text{The torque developed in a squirrel cage induction motor with an auto-starter is } \\[4pt]K^2 \times \text{torque with direct switching, as per the formula for the Auto Transformer Starter.}$$​​