A 0.5 Hp, 6 pole wound rotor induction motor is excited by a 3 phase 60 Hz source. Calculate the frequency of the rotor current at standstill. 

Explanation:

Frequency of Rotor Current in a Wound Rotor Induction Motor

Definition: The frequency of the rotor current in an induction motor is determined by the relative speed between the stator's rotating magnetic field and the rotor. At standstill (when the rotor is not moving), this relative speed is maximum, and the rotor current frequency equals the supply frequency.

Problem Statement: A 0.5 Hp, 6-pole wound rotor induction motor is excited by a 3-phase 60 Hz source. We are tasked with calculating the frequency of the rotor current at standstill.

Calculation:

1. At standstill, the rotor is stationary, meaning its speed is zero. The slip, denoted by s, is defined as:

   s = (N_s - N_r) / N_s

   where:
   • N_s = Synchronous speed of the stator's magnetic field in RPM.
   • N_r = Rotor speed in RPM.
   At standstill:

   N_r = 0

   Therefore:

   s = 1

2. The rotor current frequency is given by:

   f_r = s × f_s

   where:
   • f_r = Rotor current frequency.
   • f_s = Supply frequency.
   Substituting s = 1 and f_s = 60 Hz:

   f_r = 1 × 60 = 60 Hz

Conclusion: At standstill, the frequency of the rotor current is equal to the supply frequency, which is 60 Hz.

Correct Option: Option 3

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 50 Hz

This option is incorrect. The rotor current frequency at standstill is not 50 Hz because it is determined by the supply frequency (f_s), which in this case is 60 Hz. At standstill, the rotor frequency is always equal to the supply frequency.

Option 2: 30 Hz

This option is incorrect. A rotor current frequency of 30 Hz would imply that the rotor is not at standstill and is rotating at a certain speed relative to the stator's magnetic field. However, the problem explicitly states that the rotor is at standstill, where the slip is s = 1, making the rotor frequency equal to the supply frequency of 60 Hz.

Option 4: 120 Hz

This option is incorrect. The rotor current frequency cannot exceed the supply frequency. At standstill, the rotor frequency is equal to the supply frequency, which is 60 Hz in this case. A frequency of 120 Hz would be physically unrealistic under the given conditions.

Conclusion:

The correct frequency of the rotor current at standstill for the given 6-pole wound rotor induction motor excited by a 60 Hz source is 60 Hz. This matches Option 3. Understanding the relationship between rotor speed, slip, and rotor frequency is crucial for analyzing induction motor operation and performance.