# Unsolved Examples

29.   A small 3·phase induction motor has a short-circuit current equal to 4 times the full-load current. Determine the starting torque as a percentage of full-load torque if full-load slip is 2.5 per cent.

30.   A 3·phase, squirrel-cage induction motor has a short-circuit current equal to 5 times the full-load current. Find the starting torque as a percentage of full-load torque if the motor is started by
a)                 direct switching to the supply;
b)                a star-delta starter;
c)                 an auto-transformer ; and
d)                a resistance in the stator circuit.
The starting current in (iii) and (iv) is limited to 2.5 times the full-load current and the full-load slip is 4 per cent.

[Ans. Tf, 33.3% Tf; 50% Tf, 25% Tf ]

31.   Determine a suitable auto-transformer ratio for starting an induction motor with a supply current not exceeding twice full-load current. Use the following data: Short-circuit current = 5 times the full-load current, full-load slip = 3%. Estimate the torque in terms of full-load torque. Ignore magnetising current.

[Ans. 30%]

32.   Find the percentage tapping required on an auto-transformer required for a cage motor to start the motor against 1/4 of full-load torque. The short-circuit current at normal voltage is 1/4 times the full-load current and the full-load slip is 3 per cent.

[Ans. K = 72.2%]

33.   A squirrel-cage type induction motor when started by means of a star-delta starter takes 20 percent of full-load line current and develops 40 per cent of full-load torque at starting. Calculate the starting torque and current in terms of full-load values, if an auto-transformer with 75 per cent tapping were employed.