The voltage actually used for setting up the useful flux in the air gap of a 3-phase induction motor is

1️⃣ Applied voltage
2️⃣ Stator induced voltage (Back EMF)
3️⃣ Rotor induced voltage
4️⃣ Leakage voltage drop

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✅ Correct Answer

✔ 2️⃣ Stator induced voltage (Back EMF)

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📘 Detailed Explanation

In a 3-phase induction motor, when the stator is connected to AC supply:

➡ Applied voltage (V₁) is given to stator windings
➡ Stator current (I₁) flows
➡ A rotating magnetic field (RMF) is produced
➡ This rotating field induces an EMF in stator itself

This induced EMF is called:

★ Back EMF (E₁)

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➤ Voltage Relationship

The applied voltage is not fully used to produce flux.

It is divided as:

$${\mathrm{<span\; style="font-size:\; medium;">V</span>}}_{\mathrm{<span\; style="font-size:\; medium;">1</span>}}<span\; style="font-size:\; medium;">=</span>{\mathrm{<span\; style="font-size:\; medium;">E</span>}}_{\mathrm{<span\; style="font-size:\; medium;">1</span>}}<span\; style="font-size:\; medium;">+</span>{\mathrm{<span\; style="font-size:\; medium;">I</span>}}_{\mathrm{<span\; style="font-size:\; medium;">1</span>}}{\mathrm{<span\; style="font-size:\; medium;">Z</span>}}_{\mathrm{<span\; style="font-size:\; medium;">1</span>}}$$

Where:
V₁ ➝ Applied voltage
E₁ ➝ Stator induced EMF (Back EMF)
I₁Z₁ ➝ Voltage drop in stator resistance and leakage reactance

Only E₁ (back EMF) is responsible for establishing the useful air-gap flux.

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➤ EMF and Flux Relation

From EMF equation:

$${\mathrm{<span\; style="font-size:\; medium;">E</span>}}_{\mathrm{<span\; style="font-size:\; medium;">1</span>}}<span\; style="font-size:\; medium;">=</span>\mathrm{<span\; style="font-size:\; medium;">4.44</span>}\mathrm{<span\; style="font-size:\; medium;">f</span>}\mathrm{<span\; style="font-size:\; medium;">N</span>}\mathrm{<span\; style="font-size:\; medium;">\varphi </span>}{\mathrm{<span\; style="font-size:\; medium;">k</span>}}_{\mathrm{<span\; style="font-size:\; medium;">w</span>}}$$

Where:
f ➝ Supply frequency
N ➝ Number of turns
φ ➝ Air gap flux
k_w ➝ Winding factor

⟹ Flux (φ) ∝ E₁ / f

Thus, the useful air-gap flux depends on induced EMF, not directly on applied voltage.

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➤ Why Applied Voltage Is Not Fully Used

Applied voltage (V₁):

✔ Part is dropped in stator resistance (I₁R₁)
✔ Part is dropped in leakage reactance (I₁X₁)
✔ Remaining portion becomes back EMF (E₁)

⟹ Only E₁ maintains mutual air-gap flux.

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➤ Practical Approximation

In normal operation:

Stator impedance drop is small

⟹ V₁ ≈ E₁

Therefore, in simplified analysis, flux is often said to be proportional to:

$$\frac{\mathrm{<span\; style="font-size:\; medium;">V</span>}}{\mathrm{<span\; style="font-size:\; medium;">f</span>}}$$

But technically, the voltage actually setting up flux is E₁ (back EMF).

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✘ Why Other Options Are Incorrect

✘ 1️⃣ Applied voltage

Applied voltage includes stator voltage drops.
It is not entirely responsible for air-gap flux.

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✘ 3️⃣ Rotor induced voltage

Rotor voltage is induced due to slip.
It does not establish main air-gap flux.

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✘ 4️⃣ Leakage voltage drop

Leakage voltage produces leakage flux, not useful mutual flux.

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⭐ Important Concept – Effect of Increasing Air Gap

If air gap is increased:

⟹ Reluctance increases
⟹ Permeability decreases
⟹ Magnetizing inductance decreases
⟹ Magnetizing current increases
⟹ Leakage flux increases
⟹ Power factor becomes poorer

Therefore:

★ Small air gap is preferred in induction motors.

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✍ Exam One-Line Statement

The voltage actually used for setting up useful air-gap flux in a 3-phase induction motor is the stator induced EMF (back EMF).

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✅ Final Conclusion

Applied voltage supplies energy.
Back EMF (E₁) establishes air-gap flux.

✔ Correct Answer: 2️⃣ Stator induced voltage (Back EMF).