Induction Motor Rotor Frequency at Startup

When a 3-phase induction motor is connected to the supply and switched on, it begins to rotate. Understanding the frequency of the currents induced in the rotor during this starting phase is key. This frequency depends on the motor's slip.

Understanding Slip and Rotor Frequency

In an induction motor, the stator winding produces a rotating magnetic field (RMF) at the supply frequency ($f_s$). The rotor conductors cut this magnetic field. The frequency of the voltage induced in the rotor ($f_r$) depends on the relative speed difference between the RMF and the rotor conductors.

This difference is quantified by 'slip' ($s$), which is defined as:

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

Where:

• $N_s$ is the synchronous speed (speed of the RMF).
• $N_r$ is the actual speed of the rotor.

The rotor frequency ($f_r$) is related to the slip and supply frequency ($f_s$) by the formula:

$$f_r = s \times f_s$$

Rotor Frequency When Switched On

Consider the moment the motor is switched on. At this point, the rotor is stationary, meaning its speed ($N_r$) is 0.

Using the slip formula with $N_r = 0$:

$$s = \frac{N_s - 0}{N_s} = \frac{N_s}{N_s} = 1$$

So, at startup, the slip ($s$) is 1.

Now, substituting $s=1$ into the rotor frequency formula:

$$f_r = 1 \times f_s$$

$$f_r = f_s$$

This calculation clearly shows that the rotor frequency is equal to the supply frequency when the motor is initially switched on.

Evaluating the Options

Based on the analysis:

• 50 Hz: This might be the supply frequency, but the rotor frequency is only 50 Hz if the supply frequency is 50 Hz. It's not universally true.
• same as supply frequency: This matches our derived result ($f_r = f_s$) for the starting condition where slip is 1.
• same as slip frequency: Slip frequency is defined as $s \times f_s$. At startup, $s=1$, so slip frequency equals supply frequency. While technically true in this specific case, the most direct answer describing the rotor frequency itself is that it matches the supply frequency.
• zero: Rotor frequency becomes zero only when the rotor runs at synchronous speed ($N_r = N_s$), which means $s=0$. This happens under no-load or light-load conditions at very high speeds, not at startup.

Therefore, when a 3-phase induction motor is switched on, the rotor frequency is indeed the same as the supply frequency.