(Solved) The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of supply voltage at rated frequency is:

A) magnetizing reactance
B) rotor leakage reactance
C) rotor resistance
D) stator resistance

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✅ Answer:

➡️ A) magnetizing reactance

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🧠 Detailed Solution

◆ Step 1: Key Concept

➡️ Air-gap flux $\varphi$ depends on V/f ratio

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

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◆ Step 2: Given Condition

→ Frequency = constant (rated)
→ Voltage ↓

➡️ Therefore:

$$\frac{V}{f}\downarrow \Rightarrow \varphi \downarrow$$

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◆ Step 3: Magnetizing Reactance Relation

➡️ Magnetizing reactance depends on flux

$$X_m\propto \varphi$$

➡️ Hence:

→ Voltage ↓ ⇒ Flux ↓ ⇒ $X_m$ ↓

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◆ Step 4: Other Parameters

→ Rotor resistance → depends on material (constant)
→ Stator resistance → constant
→ Leakage reactance → geometry dependent

➡️ These are not affected by voltage change

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❌ Why Other Options Are Incorrect

◆ B) rotor leakage reactance → depends on leakage path, not voltage
◆ C) rotor resistance → constant parameter
◆ D) stator resistance → constant

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🔑 Key Points to Remember

◆ $\varphi \propto \frac{V}{f}$
◆ Magnetizing reactance depends on flux
◆ Only $X_m$ changes with voltage variation
◆ Other parameters are independent of supply voltage

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🎯 Final Conclusion

➡️ Parameter affected by voltage reduction =
Magnetizing reactance ✔️