(Solved) The torque developed by a 3-phase induction motor is approximately proportional to:

A) √s
B) s²
C) s
D) 1/s

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✅ Answer:

➡️ C) s

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🧠 Detailed Solution

◆ Step 1: General Torque Expression

➡️ Torque depends on slip as:

$$T\propto \frac{s{E}_2^2}{R_2^2+(s{X}_2{)}^2}$$

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◆ Step 2: Normal Operating Condition

➡️ In practical operation:
→ Slip $s$ is very small (≈ 0.02–0.05)

➡️ So:

$$(s{X}_2{)}^2\ll R_2^2$$

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◆ Step 3: Simplification

$$T\propto \frac{s{E}_2^2}{R_2^2}$$

➡️ Since $E_2$ and $R_2$ are constant:

$$T\propto s$$

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◆ Step 4: Interpretation

➡️ In normal region:
→ Torque increases linearly with slip

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❌ Why Other Options Are Incorrect

◆ A) √s → Not valid relation
◆ B) s² → Not correct proportionality
◆ D) 1/s → Valid only in high slip region (unstable)

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🔑 Key Points to Remember

◆ Low slip region → $T\propto s$
◆ High slip region → $T\propto \frac{1}{s}$
◆ Maximum torque independent of rotor resistance
◆ Normal operation occurs in linear region

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🎯 Final Conclusion

➡️ Torque is approximately proportional to:
Slip (s) ✔️