What is the correct expression for actual shaft speed Nr when considering slip?

• A. Nr = [(60 × f) / P] + slip
• B. Nr = [(60 × f) / P] − slip
• C. Nr = [(60 × f) / P] × slip
• D. Nr = [(60 × f) / (P − slip)]

Answer: (D)

The idea being tested is how actual shaft speed reflects the supply frequency, the number of poles, and slip in an induction machine. Synchronous speed is determined by frequency and pole count; in this convention, it’s written as Ns = 60 f / P. Slip represents how far the rotor lags behind that rotating field, and the way slip is incorporated here is by adjusting the effective pole count downward, giving an actual rotor speed of Nr = 60 f / (P − slip). This form mirrors the idea that the rotor’s speed is tied to the field speed but is modified by how much slip there is under load, and it fits the convention used in the question’s context.

Other expressions would misplace slip (for example, adding slip to the speed would imply the rotor speeds up with more slip, which contradicts the concept of slip reducing speed; multiplying by slip or placing slip elsewhere also doesn’t reflect how slip is used in this framework). Note that a general way to relate rotor speed to slip is Nr = Ns(1 − s) with s being slip, which helps connect this form to the broader understanding of speed–slip relationships.