What is the operating slip of a 400 V, 50 Hz, 6-pole, 3-phase induction motor, while the speed is 936 rpm with a 400 V, 48 Hz supply?

1️⃣ 0.036

2️⃣ 0.064
3️⃣ 0.025
4️⃣ 0.075

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✅ Answer (Detailed Solution Below)

✔️ Option 3: 0.025

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📖 Detailed Solution

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🔷 Step 1: Use Actual Supply Frequency

Even though the motor is rated at 50 Hz, it is operating at 48 Hz.
Slip must be calculated using the actual supply frequency.

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🔷 Step 2: Calculate Synchronous Speed

$${\mathrm{<span\; style="font-size:\; medium;">N</span>}}_{\mathrm{<span\; style="font-size:\; medium;">s</span>}}<span\; style="font-size:\; medium;">=</span>\frac{\mathrm{<span\; style="font-size:\; medium;">120</span>}\mathrm{<span\; style="font-size:\; medium;">f</span>}}{\mathrm{<span\; style="font-size:\; medium;">P</span>}}$$

Where:
➤ $f=48\text{Hz}$
➤ $P=6$

$${\mathrm{<span\; style="font-size:\; medium;">N</span>}}_{\mathrm{<span\; style="font-size:\; medium;">s</span>}}<span\; style="font-size:\; medium;">=</span>\frac{\mathrm{<span\; style="font-size:\; medium;">120</span>}<span\; style="font-size:\; medium;">\times </span>\mathrm{<span\; style="font-size:\; medium;">48</span>}}{\mathrm{<span\; style="font-size:\; medium;">6</span>}}$$$${\mathrm{<span\; style="font-size:\; medium;">N</span>}}_{\mathrm{<span\; style="font-size:\; medium;">s</span>}}<span\; style="font-size:\; medium;">=</span>\frac{\mathrm{<span\; style="font-size:\; medium;">5760</span>}}{\mathrm{<span\; style="font-size:\; medium;">6</span>}}$$$${\mathrm{<span\; style="font-size:\; medium;">N</span>}}_{\mathrm{<span\; style="font-size:\; medium;">s</span>}}<span\; style="font-size:\; medium;">=</span>\mathrm{<span\; style="font-size:\; medium;">960</span>}\text{<span style="font-size: medium;">\hspace{0.17em}</span>}\text{<span style="font-size: medium;">rpm</span>}$$

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🔷 Step 3: Calculate Slip

Slip formula:

$$\mathrm{<span\; style="font-size:\; medium;">s</span>}<span\; style="font-size:\; medium;">=</span>\frac{{\mathrm{<span\; style="font-size:\; medium;">N</span>}}_{\mathrm{<span\; style="font-size:\; medium;">s</span>}}<span\; style="font-size:\; medium;">-</span>{\mathrm{<span\; style="font-size:\; medium;">N</span>}}_{\mathrm{<span\; style="font-size:\; medium;">r</span>}}}{{\mathrm{<span\; style="font-size:\; medium;">N</span>}}_{\mathrm{<span\; style="font-size:\; medium;">s</span>}}}$$

Given:
➤ Rotor speed $N_r=936\text{rpm}$

$$\mathrm{<span\; style="font-size:\; medium;">s</span>}<span\; style="font-size:\; medium;">=</span>\frac{\mathrm{<span\; style="font-size:\; medium;">960</span>}<span\; style="font-size:\; medium;">-</span>\mathrm{<span\; style="font-size:\; medium;">936</span>}}{\mathrm{<span\; style="font-size:\; medium;">960</span>}}$$$$\mathrm{<span\; style="font-size:\; medium;">s</span>}<span\; style="font-size:\; medium;">=</span>\frac{\mathrm{<span\; style="font-size:\; medium;">24</span>}}{\mathrm{<span\; style="font-size:\; medium;">960</span>}}$$$$\mathrm{<span\; style="font-size:\; medium;">s</span>}<span\; style="font-size:\; medium;">=</span>\mathrm{<span\; style="font-size:\; medium;">0.025</span>}$$

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📌 Final Answer

$$\boxed{{\displaystyle \mathrm{<span\; style="font-size:\; medium;">s</span>}<span\; style="font-size:\; medium;">=</span>\mathrm{<span\; style="font-size:\; medium;">0.025</span>}}}$$

✔️ Correct Option: 3

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⭐ Important Exam Concept

✔ Always use actual operating frequency to calculate synchronous speed.
✔ Slip is dimensionless (fraction or percentage).
✔ If expressed in percentage:

$$\mathrm{<span\; style="font-size:\; medium;">\%</span>}\mathrm{<span\; style="font-size:\; medium;">s</span>}<span\; style="font-size:\; medium;">=</span>\mathrm{<span\; style="font-size:\; medium;">0.025</span>}<span\; style="font-size:\; medium;">\times </span>\mathrm{<span\; style="font-size:\; medium;">100</span>}<span\; style="font-size:\; medium;">=</span>\mathrm{<span\; style="font-size:\; medium;">2.5</span>}\mathrm{<span\; style="font-size:\; medium;">\%</span>}$$

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📝 One-Line Exam Statement

Operating slip is calculated using actual supply frequency; here it equals 0.025 (2.5%).