(Solved) The torque developed in an induction motor is nearly proportional to:

A) 1/V
B) V
C) V²
D) none of these

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✅ Answer:

➡️ C) V²

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🧠 Detailed Solution

◆ Step 1: Key Concept

➡️ Torque depends on air-gap flux and rotor current

$$T\propto \varphi \times I_2$$

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◆ Step 2: Flux Relation

➡️ Flux is proportional to applied voltage

$$\varphi \propto V$$

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◆ Step 3: Rotor Current Relation

➡️ Rotor induced EMF:

$$E_2\propto \varphi \propto V$$

➡️ Hence rotor current:

$$I_2\propto V$$

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◆ Step 4: Combine Relations

$$T\propto \varphi \times I_2$$$$T\propto V\times V=V^2$$

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❌ Why Other Options Are Incorrect

◆ A) 1/V → Opposite relation
◆ B) V → Incomplete relation
◆ D) none → Incorrect

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🔑 Key Points to Remember

◆ Flux $\varphi \propto V$
◆ Rotor current $I_2\propto V$
◆ Torque $T\propto V^2$
◆ Small voltage drop ⇒ large torque reduction

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🎯 Final Conclusion

➡️ Torque developed in induction motor ∝
Square of voltage (V²) ✔️