**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.

[**Ans.** 40% of full-load torque]

**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**. T_{f}, 33.3% T_{f}; 50% T_{f}, 25% T_{f} ]

**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.

[**Ans**. 3.375T_{r}, 67% full-load torque]

**34. **A 10 kW, 200 V, 3-phase induction motor has at full-load an efficiency of 87% and power factor of 0.85. At standstill the motor draws 5 times the full-load current and develops 1.5 times full-load torque. An auto-transformer is installed to reduce the starting current to give full-load torque at starting. Neglecting magnetising current, determine :

a) The voltage to be applied at starting.

b) The full-load line current.

c) The current drawn by the motor at start.

d) The current supplied to the primary of the autotransformer,

[**Ans.** 163.3 V, 39 A, 159.2 A, 130 A]

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