Understanding Induction Motor Speed and Rotating Flux

The question asks about the speed of the rotating stator flux in a 3-phase induction motor operating at a supply frequency of 50 Hz. The rotating magnetic field (or flux) produced by the stator currents in a 3-phase induction motor rotates at a constant speed, known as the synchronous speed (\(N_s\)).

The synchronous speed is determined by the frequency of the power supply (\(f\)) and the number of poles (\(P\)) for which the stator winding is designed. The relationship is given by the formula:

\(N_s = \frac{120f}{P}\)

where:

• \(N_s\) is the synchronous speed in revolutions per minute (r.p.m.)
• \(f\) is the supply frequency in Hertz (Hz)
• \(P\) is the total number of poles in the stator winding

We are given the supply frequency, \(f = 50\) Hz. To find the synchronous speed, we need the number of poles (\(P\)). The information about "3 slots per pole per phase" tells us about the winding design but does not directly give the total number of poles. However, standard induction motors are constructed with an even number of poles (like 2, 4, 6, 8, etc.). The possible synchronous speeds for a 50 Hz supply frequency corresponding to common pole numbers are:

• For \(P = 2\), \(N_s = \frac{120 \times 50}{2} = 3000\) r.p.m.
• For \(P = 4\), \(N_s = \frac{120 \times 50}{4} = 1500\) r.p.m.
• For \(P = 6\), \(N_s = \frac{120 \times 50}{6} = 1000\) r.p.m.
• For \(P = 8\), \(N_s = \frac{120 \times 50}{8} = 750\) r.p.m.

Let's look at the given options for the speed of the rotating stator flux: 800 r.p.m., 1000 r.p.m., 1200 r.p.m., and 1500 r.p.m.

Comparing these options with the standard synchronous speeds calculated above for common pole numbers at 50 Hz:

• 1500 r.p.m. corresponds to a 4-pole motor.
• 1000 r.p.m. corresponds to a 6-pole motor.
• 800 r.p.m. and 1200 r.p.m. do not correspond to standard synchronous speeds for common integer pole numbers at 50 Hz.

Given the options, the speed of the rotating stator flux must be either 1500 r.p.m. (for a 4-pole motor) or 1000 r.p.m. (for a 6-pole motor). The presence of 1500 r.p.m. among the options suggests that the motor is designed with 4 poles. The information about "3 slots per pole per phase" is consistent with a 4-pole, 3-phase motor (e.g., total slots = 3 slots/pole/phase × 4 poles × 3 phases = 36 slots, which is a common design).

Therefore, assuming the motor is a standard design resulting in one of the synchronous speeds presented in the options, the speed of the rotating stator flux is 1500 r.p.m., corresponding to a 4-pole motor operating at 50 Hz.

Calculation Steps

1. Identify the given supply frequency, \(f = 50\) Hz.
2. Recognize that the speed of the rotating stator flux is the synchronous speed, \(N_s\).
3. Recall the formula for synchronous speed: \(N_s = \frac{120f}{P}\).
4. Consider the options for \(N_s\) and determine the corresponding number of poles \(P = \frac{120f}{N_s}\) for each.
5. For \(N_s = 1500\) r.p.m.: \(P = \frac{120 \times 50}{1500} = \frac{6000}{1500} = 4\) poles.
6. For \(N_s = 1000\) r.p.m.: \(P = \frac{120 \times 50}{1000} = \frac{6000}{1000} = 6\) poles.
7. Since 4 poles is a standard number of poles for induction motors, 1500 r.p.m. is a valid synchronous speed.

Thus, the speed of the rotating stator flux is 1500 r.p.m.

Revision Table: Key Concepts for Induction Motors

Additional Information: The Rotating Magnetic Field

In a 3-phase induction motor, when a balanced 3-phase AC voltage is applied to the stator windings, it creates a magnetic field that rotates in the air gap between the stator and the rotor. This field rotates at the synchronous speed (\(N_s\)). This rotating magnetic field is fundamental to the operation of the induction motor because it induces voltage and current in the rotor conductors (by electromagnetic induction), which in turn produces a torque that causes the rotor to rotate. The rotor speed is always slightly less than the synchronous speed under load conditions; this difference is called slip. However, the question specifically asks for the speed of the rotating stator flux, which is the synchronous speed itself, independent of the rotor's motion. The number of poles (\(P\)) is determined by how the stator windings are arranged. For example, winding coils can be connected to form 2, 4, 6, or more poles. The higher the number of poles, the lower the synchronous speed for a given frequency.