(Solved) A 400 V, 50 Hz, star-connected, 3-phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply. The torque that the motor can provide while drawing rated current will:

A) reduce
B) increase
C) remain the same
D) increase or reduce depending upon rotor resistance

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✅ Answer:

➡️ A) reduces

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🧠 Detailed Solution

◆ Step 1: Key Concept (V/f Ratio)

➡️ Air-gap flux:

$$\varphi \propto \frac{V}{f}$$

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◆ Step 2: Compare Conditions

→ Original:

$$\frac{V}{f}=\frac{400}{50}=8$$

→ New:

$$\frac{V}{f}=\frac{400}{75}\approx 5.33$$

➡️ Flux decreases

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◆ Step 3: Torque Relation

$$T\propto \varphi \times I$$

➡️ Given: Current = rated (constant)

So:

$$T\propto \varphi$$

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◆ Step 4: Final Effect

→ Flux ↓ ⇒ Torque ↓

➡️ Motor becomes under-fluxed (under-excited)

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❌ Why Other Options Are Incorrect

◆ B) increase → Opposite effect
◆ C) same → Only if V/f constant
◆ D) depends on rotor resistance → Not relevant here

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🔑 Key Points to Remember

◆ $\varphi \propto \frac{V}{f}$
◆ Increasing frequency at constant voltage ⇒ flux decreases
◆ Torque ∝ flux (for constant current)
◆ Used concept in V/f control

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🎯 Final Conclusion

➡️ Torque capability will:
Reduce ✔️