A rotating electrical machine having its self-inductances of both the stator and the rotor windings, independent of rotor position will definitely not develop

(a) starting torque.
(b) synchronising torque.
(c) hysteresis torque.
(d) reluctance torque.

Answer: (d) reluctance torque.

Explanation:

CONCEPT: Reluctance Torque

1. Reluctance torque is produced due to the variation of magnetic reluctance with rotor position.

2. This variation occurs only when:

   • The air gap is non-uniform

   • The rotor is salient

3. The rotor always tends to move toward a position of minimum reluctance and maximum flux linkage.

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Key Condition Given

4. The question states:

   • Self-inductance of stator is independent of rotor position

   • Self-inductance of rotor is independent of rotor position

5. This implies:

   • Uniform air gap

   • No saliency

   • No change in reluctance with rotation

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Explanation

6. Since reluctance does not change with rotor position:

$$\frac{\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">d</span></span>}\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">L</span></span>}}{\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">d</span></span>}\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">\theta </span></span>}}<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">0</span></span>}$$

7. And since:

$${\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">T</span></span>}}_{\text{<span style="font-family: Source Serif Pro;"><span style="font-size: medium;">reluctance</span></span>}}<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">\propto </span></span>\frac{\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">d</span></span>}\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">L</span></span>}}{\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">d</span></span>}\mathrm{<span\; style="font-family:\; Source\; Serif\; Pro;"><span\; style="font-size:\; medium;">\theta </span></span>}}$$

8. Reluctance torque cannot be developed.

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Why Other Options Are Incorrect

(a) Starting Torque ❌

9. Starting torque can be produced in machines with a uniform air gap, such as:

   • Induction motors

10. It is produced due to electromagnetic induction, not reluctance variation.

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(b) Synchronising Torque ❌

11. Synchronising torque exists in synchronous motors, including:

• Cylindrical-rotor (uniform air gap) machines

12. It depends on field interaction, not reluctance variation.

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(c) Hysteresis Torque ❌

13. Hysteresis torque is produced due to:

• Magnetic hysteresis in the rotor material

14. It does not depend on inductance variation or air-gap saliency.

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FINAL CONCLUSION

15. Since inductance does not vary with rotor position, reluctance torque cannot be produced.

16. All other torques can exist even with a uniform air gap.

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Correct Answer

✅ Reluctance torque

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✔️ Key One-Line Exam Statement

Reluctance torque requires position-dependent inductance; with a uniform air gap, it cannot be developed.