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Unsolved Examples

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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. 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.

[Ans. 3.375Tr, 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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