EEE Job Math Solution-1

Question 1:  A  400V, 10hp, 4 pole, 50Hz, Y-connected induction motor operates at full load speed of 5%. Determine the synchronous speed, rotor speed and shaft torque at this operating condition.

Solution 1:
Here, frequency, f= 50Hz
Number of poles, P= 4
Slip, s= 5% = 0.05
We know that,
Synchronous speed,  Ns = 120f/P = 120×50/4 = 1500 rpm

Rotor speed, Nr = (1-s)Ns = (1-0.05)1500 = 1425 rpm

Shaft Torque, τshaft =  Poutm  = (10×746)/{Nr x (2π/60)} = 7460/(1425x 0.1046) =  50Nm

or, Shaft Torque, τshaft =  9.55*Pout /Nr = (9.55*7460)/1425 = 50Nm

Question 2:  A 2 hp three phase delta connected motor operates at a power factor of 0.8  (lagging).  The  motor  has  an  efficiency  of  82%.  If  the  motor  is  connected  to  a  3  phase  supply of line to line voltage of 400 V, calculate the line current and phase current of the motor.

Solution 2:

Output power of the motor (mechanical), Pout= 2 hp = 2 x 746 W = 1492 W
Efficiency, η= 0.82
So, input power (electrical), Pin= P = Pout / η= 1492/0.82 = 1819.5 W
Power factor, cosθ= 0.8

Now,  P = √3VL IL cosθ

IL = P/√3VL cosθ  = 1819.5/√3x400x0.8 = 3.28A

For a delta connected system, Ip =  IL/√3 = 1.9A

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