A 50 Hz, 8-pole, 3-phase induction motor has ...
A 50 Hz,  8-pole, 3-phase induction motor has full-load slip of 4%. The rotor resistance and standstill reactance per phase are 0.01 Ω and 0.1 Ω respectively. The ratio of maximum torque to full-load torque is
• a)
1.45
• b)
1.1
• c)
2.5
• d)
3.4
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A 50 Hz, 8-pole, 3-phase induction motor has full-load slip of 4%. The...
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A 50 Hz, 8-pole, 3-phase induction motor has full-load slip of 4%. The...
Ohm and 0.05 ohm, respectively. The stator voltage is 400 V.

To find:
a) The synchronous speed of the motor
b) The rated speed of the motor
c) The rotor frequency at full-load
d) The rotor current at full-load
e) The rotor copper losses at full-load
f) The output power of the motor at full-load
g) The efficiency of the motor at full-load

Solution:

a) The synchronous speed of the motor can be calculated using the formula:

Ns = 120f/P

where Ns is the synchronous speed in RPM, f is the supply frequency in Hz, and P is the number of poles.

Substituting the given values, we get:

Ns = 120 x 50/8 = 750 RPM

b) The rated speed of the motor is the speed at which it operates at full-load. The rated speed is calculated by subtracting the slip from the synchronous speed.

Rated speed = (1 - slip) x synchronous speed

Substituting the given values, we get:

Rated speed = (1 - 0.04) x 750 = 720 RPM

c) The rotor frequency at full-load can be calculated using the formula:

fr = s x f

where fr is the rotor frequency, s is the slip, and f is the supply frequency.

Substituting the given values, we get:

fr = 0.04 x 50 = 2 Hz

d) The rotor current at full-load can be calculated using the formula:

I2 = (s x I1)/(sqrt(s^2 + X^2/R^2))

where I2 is the rotor current, I1 is the stator current, X is the standstill reactance, and R is the rotor resistance.

At full-load, the stator current is equal to the rated current, which can be calculated using the formula:

I1 = Pout/(sqrt(3) x V x cos(θ))

where Pout is the output power, V is the stator voltage, and θ is the power factor angle (assumed to be 0.85 for this problem).

Substituting the given values, we get:

I1 = 746/(sqrt(3) x 400 x 0.85) = 1.93 A

Substituting the values of s, X, and R, we get:

I2 = (0.04 x 1.93)/(sqrt(0.04^2 + 0.05^2/0.01^2)) = 0.74 A

e) The rotor copper losses at full-load can be calculated using the formula:

Pc = 3 x I2^2 x R

Substituting the calculated value of I2 and the given value of R, we get:

Pc = 3 x 0.74^2 x 0.01 = 0.0164 kW

f) The output power of the motor at full-load can be calculated using the formula:

Pout = 3 x V x I2 x cos(θ)

Substituting the calculated values of V, I2, and θ, we get:

Pout = 3 x 400 x 0.74 x 0.85 = 746 W

g) The efficiency of the motor at full-load
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