Question

A 218-V, 5 hp, four pole , 50 Hz, Y-connected
induction motor has a full. Load slip of 5 percent.
1) What is the synchronous speed of this motor?
ii) What is the rotor speed of this motor at rated load?
iii) What is the rotor frequency of this motor at rated load?
(iv) What is the shaft torqué of this motor at rated Load?​

Answer 1

Answer:

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Answer 2

Given:

Voltage $V=218\ V$

Power$=5\ hp$=$5\times 746=3730\ W$

Number of poles $P=4$

Load slip$=5\%$

frequency $f=50 Hz$

To Find:

i) The synchronous speed of this motor

ii) The rotor speed of this motor at rated load

iii) The rotor frequency of this motor at rated load

(iv) The shaft torque of this motor at rated load

Solution:

(i) The synchronous speed of the motor

$N_{s}=\dfrac{120 f}{P}$

$N_{s}=\dfrac{120\times50}{4}\\=1500\ rpm$

(ii) The rotor speed of the motor at rated load

$N_{r}=N_{s}-\left\left[\dfrac{s\%}{100}\times N_{s} \right]$

$=1500-0.5\times1500\\=750\ rpm$

(iii) The Rotor frequency of motor at rated load

$f_{r}=\dfrac{N_{s}\times P }{120}\\=\dfrac{[0.05\times1500]\times4}{120}\\=2.5\ Hz$

(iv) Shaft torque of the motor at rated load

$\tau_{sh}=\dfrac{Power\ in\ watt}{2 \pi N}\\=\dfrac{3730}{2\pi \times1500}\\=0.396\ N-m.$