Solve Star-Delta Starter Problem: Find Starting Torque

[Lunat1c]

Hi, I got a small problem which I'm not sure I'm solving correctly. A small induction motor has a short circuit current equal to 5 times the full-load current. I need to find the starting torque as a percentage of full load torque if the motor is started by a star-delta starter. It is also known that the motor has a full load slip of 4%.

$$Torque = \frac{3I_{R}^2R_r}{(s*\omega_s)}$$

$$T_{start}= \frac{3(\frac{5}{3} I_{FL})^2R_r}{\omega_s}$$

Note that in the above equation i divided the current by three because in a star-delta starter the current is supposed to be 1/3 the direct online current.

and $$T_{FL} = \frac{3I_{FL}^2R_r}{0.04\omega_s}$$

Then dividing (1) by (2) i should get $$\frac{T_{start}}{T_{FL}}=(25/9)*0.04=0.11$$.

That is equivalent to 11.1% of the Full load torque. However my lecturer got the answer as 33.33%, which is probably because he did $$\frac{i^2}{3}$$ instead of $$(\frac{i}{3})^2$$. Is my answer incorrect?

 

[Lunat1c]

Anyone please? I have done some additional reading about the problem but I still can't see where I could have made a mistake. The problem is that in another very similar question I also got the answer wrong by using this "method", if you can call it that.