(Solved) The starting torque of a 3-phase induction motor varies as:

A) V²
B) V
C) √V
D) 1/V

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✅ Answer:

➡️ A) V²

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🧠 Detailed Solution

◆ Step 1: Starting Condition

➡️ At starting:

$$s=1$$

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◆ Step 2: Torque Equation

$$T\propto \frac{E_2^2{R}_2}{R_2^2+X_2^2}$$

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◆ Step 3: Relation with Voltage

➡️ Rotor induced EMF:

$$E_2\propto V$$

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◆ Step 4: Substitute

$$T\propto E_2^2\propto V^2$$

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◆ Step 5: Interpretation

➡️ Starting torque is highly sensitive to voltage

→ If voltage ↓ by 50%
→ Torque ↓ to 25%

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❌ Why Other Options Are Incorrect

◆ B) V → Linear relation (not correct)
◆ C) √V → Not applicable
◆ D) 1/V → Opposite relation

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🔑 Key Points to Remember

◆ Starting condition → $s=1$
◆ Torque ∝ $E_2^2$
◆ $E_2\propto V$ ⇒ $T\propto V^2$
◆ Voltage drop severely reduces starting torque

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🎯 Final Conclusion

➡️ Starting torque varies as:
Square of voltage (V²) ✔️