In an induction motor if the rotor is locked, then the rotor frequency of the induction motor will be:

Question

Examoogle · Accepted Answer

The correct answer is Option A: equal to supply frequency. When an induction motor is locked (stationary), its rotor speed is zero. Consequently, the slip of the motor becomes unity (1), causing the induced frequency in the rotor circuit to be exactly equal to the stator supply frequency.

Step-by-Step Solution & Concepts:
When an induction motor is locked (stationary), its rotor speed is zero. Consequently, the slip of the motor becomes unity (1), causing the induced frequency in the rotor circuit to be exactly equal to the stator supply frequency.

Working Principle: The frequency of the EMF induced in the rotor is determined by the relative speed between the rotating magnetic field and the rotor. The relationship is defined by $f_{r} = s 	imes f$, where $s$ is the slip. When the rotor is blocked ($N_{r} = 0$), the slip $s = \frac{N_{s} - N_{r}}{N_{s}}$ becomes $\frac{N_{s} - 0}{N_{s}} = 1$. Thus, $f_{r} = 1 	imes f = f$.

Key Formulas: $s = \frac{N_{s} - N_{r}}{N_{s}}$ — Definition of slip; $f_{r} = s 	imes f$ — Relationship between rotor frequency and supply frequency

Key Points: At standstill or locked rotor condition, the slip is $1$ (or 100\%).; Under locked rotor conditions, the induction motor acts like a static transformer with a short-circuited secondary.; Rotor frequency depends linearly on the slip value.

Advantages: Used to measure equivalent circuit parameters (short-circuit test).; Provides maximum starting torque conditions.

Disadvantages: High current flow leads to rapid overheating of windings.; May lead to insulation failure if maintained for extended durations.

Applications: Locked rotor test for motor parameter estimation.; Understanding starting characteristics of induction machines.

Additional Info: The rotor frequency is also known as the slip frequency.. Option B is incorrect because rotor frequency cannot exceed supply frequency in normal motoring operation.. Option D is incorrect as it represents the condition at synchronous speed ($N_{r} = N_{s}$).

Answer: A is correct — When the rotor is locked, the slip is 1, making the rotor frequency equal to the supply frequency.

Exam Tip: Remember that at synchronous speed ($s=0$), rotor frequency is 0Hz, and at standstill ($s=1$), rotor frequency is equal to supply frequency ($f$).

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Option B: more than supply frequency

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Option C: less than supply frequency

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Option D: zero

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