(Solved) In an induction motor operating at fixed speed and constant frequency,:

A) both line current and torque are proportional to voltage
B) both line current and torque are proportional to square of voltage
C) line current is proportional to voltage and torque is proportional to square of voltage
D) line current is constant and torque is proportional to voltage

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✅ Answer:

➡️ C) line current is proportional to voltage and torque is proportional to square of voltage

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🧠 Detailed Solution

◆ Step 1: Key Assumptions

→ Speed = constant ⇒ Slip $s$ = constant
→ Frequency = constant
→ Hence impedance $Z$ ≈ constant

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◆ Step 2: Line Current Relation

$$I=\frac{V}{Z}$$

➡️ Since $Z$ is constant:

$$I\propto V$$

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◆ Step 3: Torque Relation

$$T\propto \frac{V^2}{(R_2\mathrm{/}s{)}^2+X_2^2}$$

➡️ Since denominator is constant:

$$T\propto V^2$$

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◆ Step 4: Interpretation

➡️ Current varies linearly with voltage
➡️ Torque varies squarely with voltage

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❌ Why Other Options Are Incorrect

◆ A) both ∝ V → Torque relation incorrect
◆ B) both ∝ $V^2$ → Current relation incorrect
◆ D) current constant → Not true

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🔑 Key Points to Remember

◆ At constant speed → slip constant
◆ Current: $I\propto V$
◆ Torque: $T\propto V^2$
◆ Small voltage drop ⇒ large torque reduction

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🎯 Final Conclusion

➡️ Correct relation is:
Current ∝ V and Torque ∝ V² ✔️