A $3-$phase, $100$ kW$,400$ V$,6-$pole, $50$ Hz induction

motor runs at $950$ rpm at full load. It takes $1203$ A on

direct$-$on$-$line starting. Determine the ratio of starting

torque to full load torque, when the motor is

a$)$ started direct$-$on$-$line,

b$)$ started by using a star$-$delta starter,

c$)$ started by an autotransformers with $70\%$ tapping,

d$)$ started by stator resistance, limiting the starting current

to $401$A$.$

Assume that the full load efficiency and the power factor of

the motor are $0\mathrm{.}9$ and $0\mathrm{.}8,$respectively.