Understanding Induction Motor Torque at Slip s = 0

The question asks about the torque produced by an induction motor when the slip ($s$) is equal to zero. Let's break down what slip means and how it affects the torque.

What is Slip in an Induction Motor?

Slip ($s$) in an induction motor is a measure of the difference between the synchronous speed ($N_s$) of the rotating magnetic field and the actual rotor speed ($N_r$). It is usually expressed as a fraction or percentage:

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

• Synchronous Speed ($N_s$): This is the constant speed at which the stator's magnetic field rotates. It depends on the supply frequency and the motor's construction (number of poles).
• Rotor Speed ($N_r$): This is the actual mechanical speed at which the motor's rotor rotates.

In a working induction motor, the rotor must always rotate slower than the synchronous speed ($N_r < N_s$) to produce torque. This difference in speed is crucial for inducing voltage and current in the rotor.

Torque Production Mechanism

Torque in an induction motor is generated due to the interaction between the rotor's magnetic field and the stator's rotating magnetic field. The process is as follows:

1. The stator creates a rotating magnetic field at synchronous speed ($N_s$).
2. For torque to be produced, there must be a relative speed difference between this field and the rotor. This relative speed causes voltage to be induced in the rotor conductors (like a transformer's secondary winding).
3. This induced voltage drives a current through the rotor conductors (assuming the rotor circuit is closed).
4. The interaction between the rotor currents and the stator's rotating magnetic field produces the motor's torque.

Torque when Slip (s) = 0

When the slip $s = 0$, it implies:

$$0 = \frac{N_s - N_r}{N_s}$$

This means $N_s - N_r = 0$, or $N_s = N_r$. This is the condition where the rotor speed is exactly equal to the synchronous speed.

At synchronous speed ($N_r = N_s$), there is no relative motion between the stator's rotating magnetic field and the rotor conductors. Because there is no relative motion:

• No voltage is induced in the rotor.
• Consequently, no current flows in the rotor.
• Without rotor current, there is no electromagnetic interaction to produce torque.

Therefore, when the slip $s = 0$, the torque ($T$) developed by the induction motor is zero.

Summary Table

The condition $s = 0$ represents the motor running at its synchronous speed, a theoretical state where no torque is generated because the fundamental requirement for induction (relative motion) is absent.