1
GATE EE 2008
+2
-0.6
A $$400$$ $$V,$$ $$50$$ $$Hz,$$ $$30$$ $$hp,$$ three-phase induction motor is drawing $$50$$ A current at $$0.8$$ power factor lagging. The stator and rotor copper losses are $$1.5kW$$ and $$900$$ $$W$$ respectively. The friction and windage losses are $$1050$$ $$W$$ and the core losses are $$1200$$ $$W.$$ The air-gap power of the motor will be
A
$$23.06$$ $$kW$$
B
$$24.11$$ $$kW$$
C
$$25.01$$ $$kW$$
D
$$26.21$$ $$kW$$
2
GATE EE 2008
+2
-0.6
A $$3$$-phase, $$440$$ $$V,$$ $$50$$ $$Hz,$$ $$4$$ pole, slip ring induction motor is feed from the rotor side through an auto transformer and the stator is connected to a variable resistance as shown in the figure.

The motor is coupled to a $$220$$ $$V$$, separately excited $$d.c.$$ generator feeding power to fixed resistance of $$10\Omega .$$ Two watt-meter method is used to measure the input power to induction motor. The variable resistance is adjusted such that motor recorded
$${W_1} = 1800\,W,\,\,{W_2} = - 200\,W.$$

The Speed of rotation of stator magnetic field with respect to rotor structure will be

A
$$90$$ $$rpm$$ in the direction of rotation
B
$$90$$ $$rpm$$ in the opposite direction of rotation
C
$$1500$$ $$rpm$$ in the direction of rotation
D
$$1500$$ $$rpm$$ in the opposite direction of rotation
3
GATE EE 2008
+2
-0.6
A $$3$$-phase, $$440$$ $$V,$$ $$50$$ $$Hz,$$ $$4$$ pole, slip ring induction motor is feed from the rotor side through an auto transformer and the stator is connected to a variable resistance as shown in the figure.

The motor is coupled to a $$220$$ $$V$$, separately excited $$d.c.$$ generator feeding power to fixed resistance of $$10\Omega .$$ Two watt-meter method is used to measure the input power to induction motor. The variable resistance is adjusted such that motor recorded
$${W_1} = 1800\,W,\,\,{W_2} = - 200\,W.$$

Neglecting all losses of both the machines, the $$dc$$ generator power output and the current through resistance $$\left( {{R_{ex}}} \right)$$ will respectively be

A
$$96$$ $$W,$$ $$3.10$$ $$A$$
B
$$120$$ $$W,$$ $$3.46$$ $$A$$
C
$$1504$$ $$W,$$ $$12.26$$ $$A$$
D
$$1880$$ $$W,$$ $$13.71$$ $$A$$
4
GATE EE 2007
+2
-0.6
A three-phase squirrel cage induction motor has a starting torque of $$150\%$$ and a maximum torque of $$300\%$$ with respect to rated torque at rated voltage and rated frequency. Neglect the stator resistance and rotational losses. The value of slip for maximum torque is
A
$$13.48\%$$
B
$$16.42\%$$
C
$$18.92\%$$
D
$$26.79\%$$
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