# A 3-phase. 6-pole, 50 Hz, squirrel cage induction motor is running at a slip of 5%. The speed of stator magnetic field to rotor magnetic field and spe

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A 3-phase. 6-pole, 50 Hz, squirrel cage induction motor is running at a slip of 5%. The speed of stator magnetic field to rotor magnetic field and speed of rotor with respect to stator magnetic field are
1. Zero, -50 rpm
2. Zero, 955 rpm
3. 1000 rpm, -50 rpm
4. 1000 rpm, 955 rpm

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Correct Answer - Option 1 : Zero, -50 rpm

Concept:

In an induction motor,

• The stator is stationary and the stator field rotates with synchronous speed.
• The rotor field rotates with synchronous speed and the rotor rotates at a speed less than the synchronous speed.

Synchronous speed in rpm of a three-phase induction motor is given by,

${N_s} = \frac{{120f}}{P}$

Where f is the frequency in Hz

P is the number of poles

A rotor of a three-phase induction motor rotates at a speed close to the synchronous speed but not equal to the synchronous speed.

The difference between the synchronous speed and the rotor speed is known as slip speed. It is given by

Slip speed = Ns - Nr

Slip is defined as the ratio of slip speed to the rotor speed.

$s = \frac{{{N_s} - {N_r}}}{{{N_s}}}$

⇒ Nr = Ns (1 – s)

Calculation:

Given that,

Number of poles (P) = 6

Frequency (f) = 50 Hz

Synchronous speed, ${N_s} = \frac{{120 \times 50}}{6} = 1000\;rpm$

Slip at no load, s = 5 %

Rotor speed N = Ns (1 – s) = 1000(1 – 0.05) = 950 rpm

The speed of stator magnetic field = speed of rotor magnetic field = 1000 rpm

The speed of stator magnetic field with respect to rotor magnetic field = 1000 – 1000 = 0

The speed of rotor with respect to stator magnetic field = 950 – 1000 = -50 rpm