Which of the following is used to find the actual speed of the rotor?

Question

Examoogle · Accepted Answer

Option D: = 𝑵𝒔 (𝟏−𝑺)

Explanation & Concepts:
The actual speed of an induction motor rotor is denoted by $N$ and is determined by its synchronous speed ($N_s$) and the slip ($s$). It is mathematically expressed as $N = N_s(1 - s)$, representing the speed at which the rotor physically rotates relative to the stator magnetic field.

Working Principle: The stator of an induction motor produces a rotating magnetic field that travels at the synchronous speed $N_s = \frac{120f}{P}$. The rotor always attempts to 'catch up' to this field but lags behind due to electromagnetic induction requirements, characterized by the slip $s = \frac{N_s - N}{N_s}$. Rearranging this definition for $N$ yields $N = N_s(1 - s)$, indicating that as slip increases, the rotor speed decreases.

Key Formulas: $N_s = \frac{120f}{P}$ — Synchronous speed of the rotating magnetic field; $s = \frac{N_s - N}{N_s}$ — Definition of slip; $N = N_s(1 - s)$ — Actual rotor speed in RPM

Key Points: At standstill ($N = 0$), the slip $s = 1$.; At synchronous speed ($N = N_s$), the slip $s = 0$.; The rotor speed is always slightly less than the synchronous speed in an induction motor.; Slip is typically expressed as a per-unit value or a percentage.

Advantages: Simple mathematical relationship; Easy to determine rotor speed if slip is known; Fundamental for torque-speed analysis

Disadvantages: Assumes constant frequency supply; Does not account for non-linear load effects directly

Applications: Calculating motor performance characteristics; Design of variable frequency drives (VFDs); Induction motor speed control analysis

Additional Info: Slip is the relative difference between the synchronous speed and the rotor speed. In practical induction motors, slip usually ranges from 2% to 5% at rated load.. Option A ($N_s - N$) represents the slip speed (in RPM), not the rotor speed. Option B ($(\frac{N_s-N}{N_s}) 	imes 100$) represents the percentage slip. Option C ($(\frac{N_s-N}{N_s})$) represents the fractional slip.

Answer: D is correct — The actual rotor speed is the synchronous speed reduced by the slip factor, given by the formula $N = N_s(1 - s)$.

Exam Tip: Always remember that synchronous speed depends on supply frequency ($f$) and the number of poles ($P$), whereas rotor speed is physically limited by the load torque and slip.

Examoogle · Answer

Option A: = 𝑵𝒔−𝑵

Examoogle · Answer

Option B: = (𝑵𝒔−𝑵)/𝑵𝒔 × 𝟏𝟎𝟎

Examoogle · Answer

Option C: = (𝑵𝒔−𝑵)/𝑵𝒔

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)