286. A 3 phase, 400 V, 5 k W, star connected synchronous motor having an internal reactance of 10 W is operating at 50% load, unity pf. Now, the excitation is increased by 1%. What will be the new load in percent, if the power factor is to be kept same? Neglect all losses and consider
     

1. 1. 67.9%

   
   
   

   2. 56.9%

   
   
   

   3. 51%

   
   
   

   4. 50%

   
   
   

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   NA

   Correct Option: A

   NA

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287. A 3 phase, 10 kW, 400 V, 4 pole, 50 Hz, star connected induction motor draws 20 A on full load. Its no load and blocked rotor test data are given below :
     

     No Load test :	400V	6 A	1002 W
     Blocked Rotor test :	90 V	15 A	762 W

     
     Neglecting copper loss in no Load test and core loss in Blocked Rotor test, estimate motor 's full load efficiency.
     

1. 1. 76%

   
   
   

   2. 81%

   
   
   

   3. 82.4%

   
   
   

   4. 85%

   
   
   

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   Value of power loss in case of blocked rotor at full load =		20		2	× 762 = 1354.6 watts
   		15

   
   ∴ Total losses= 1354.6 + 1002 = 2356.6 watts.
   Total input = 10000 + 2386.6 = 12356.6
   

   ∴ % Efficiency =	10000	× 100 = 81%
   	12356.6

   Correct Option: B

   Value of power loss in case of blocked rotor at full load =		20		2	× 762 = 1354.6 watts
   		15

   
   ∴ Total losses= 1354.6 + 1002 = 2356.6 watts.
   Total input = 10000 + 2386.6 = 12356.6
   

   ∴ % Efficiency =	10000	× 100 = 81%
   	12356.6

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288. A 3 phase, 4 pole, 400 V, 50 Hz, star connected induction motor has following circuit parameters
     r₁ = 1.0 Ω , r₂' = 0.5 Ω
     x₁ = x₂' = 1.2 Ω, x_m = 35 Ω
     The starting torque when the motor is started direct- on-line is (use approximate equivalent circuit model)
     

1. 1. 63.6 Nm

   
   
   

   2. 74.3 Nm

   
   
   

   3. 190.8 Nm

   
   
   

   4. 222.9 Nm

   
   
   

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   NA

   Correct Option: B

   NA

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289. The speed of a 4-pole induction motor is controlled by varying the supply frequency while maintaining the ratio of supply voltage to supply frequency (V/f) constant. At rated frequency of 50 Hz and rated voltage of 400 V its speed is 1440 rpm. What is the speed at 30 Hz, if the load torque is constant?
     

1. 1. 882 rpm

   
   
   

   2. 864 rpm

   
   
   

   3. 840 rpm

   
   
   

   4. 828 rpm

   
   
   

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   Since , NS1 =	120 f	=	120 × 50	= 1500
   	P		4

   
   ∴ N = N_S1 (1 – S)
   ⇒ 1440 = 1500 (1 – S)
   ⇒ (1 – S) = 0.96
   ⇒ S = 0.04
   

   ∴ NS2 =	120 × 30	= 900 rpm.
   	4

   
   ∴ N = 900 (1 – 0.04) = 864 rpm.
   

   Correct Option: B

   Since , NS1 =	120 f	=	120 × 50	= 1500
   	P		4

   
   ∴ N = N_S1 (1 – S)
   ⇒ 1440 = 1500 (1 – S)
   ⇒ (1 – S) = 0.96
   ⇒ S = 0.04
   

   ∴ NS2 =	120 × 30	= 900 rpm.
   	4

   
   ∴ N = 900 (1 – 0.04) = 864 rpm.
   

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290. Two transformers are to be operated in parallel such that they share load in proportion to their kVA ratings. The rating of the first transformer is 500 kVA and its pu leakage impedance is 0.05 pu. I f the rating of second transformer is 250 kVA, then its pu leakage impedance is
     

1. 1. 0.20

   
   
   

   2. 0.10

   
   
   

   3. 0.05

   
   
   

   4. 0.025

   
   
   

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   Per unit leakage impedance ∝	1
   	kVA

   
   500 kVA × 0.05 = 250 kVA × x
   

   ∴ x =	500	× 0.05 = 0.10
   	250

   Correct Option: B

   Per unit leakage impedance ∝	1
   	kVA

   
   500 kVA × 0.05 = 250 kVA × x
   

   ∴ x =	500	× 0.05 = 0.10
   	250

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