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Synchronous speed of induction motor is

$120P/f$

$120/P$

$120f/P$

$120/f$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalMachine

Option C

$120f/P$

Quick Summary:

The synchronous speed ( $N_s$ ) of an induction motor is the speed at which the stator's rotating magnetic field revolves. It is directly proportional to the supply frequency ( $f$ ) and inversely proportional to the number of pole pairs ( $P/2$ ).

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$N_s = \frac{120f}{P}$ — formula for synchronous speed in RPM

$P = \frac{120f}{N_s}$ — formula for calculating required poles

⚙️ Working Principle

When a 3-phase supply is fed to the stator windings, it creates a rotating magnetic field due to the phase displacement of $120°$ between windings. The speed of this field is determined by the frequency of the supply and the physical arrangement of the stator poles according to $N_s = \frac{120f}{P}$ .

📌 Key Points

▸
Synchronous speed is independent of the rotor's mechanical load.
▸
Increasing supply frequency increases the synchronous speed.
▸
Increasing the number of poles decreases the synchronous speed.
▸
The rotor of an induction motor always runs at a speed $N < N_s$ to experience relative flux cutting.

🛠️ Applications / Uses

▸
Used in determining the slip ( $s = \frac{N_s - N}{N_s}$ ) of induction motors.
▸
Basis for motor speed control via Variable Frequency Drives (VFDs).

📄 Additional Information

▸
f is the frequency in Hertz (Hz).
▸
P is the total number of stator poles.
▸
Option A ( $120p/f$ ) is mathematically inverted and incorrect.
▸
Option B ( $120/p$ ) ignores the frequency component.
▸
Option D ( $120/f$ ) ignores the pole component.

📊 Diagram / Illustration

✅

C is correct — The synchronous speed is defined by the formula $N_s = \frac{120f}{P}$ where $f$ is frequency and $P$ is the number of poles.

Core Concepts Used

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Rotating Magnetic Field (RMF) Stator winding configuration Fundamental frequency relationship

💡 EXAM TIP

Remember that for a 50Hz supply, a 2-pole motor runs at 3000 RPM, and a 4-pole motor runs at 1500 RPM; this is a common mental benchmark for exams.

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