Question

An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 \(\Omega\) per phase. Its speed at maximum torque is 650 RPM. The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is \(\underline{\hspace{3cm}}\) \(\Omega\). (Round off to 2 decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.

Hint:

Maximum torque in an induction motor occurs when the rotor resistance equals the rotor reactance divided by slip. Increasing external resistance shifts the maximum torque to standstill.

Answer 1

Correct Answer: 0.5

Synchronous speed: \[ N_s = \frac{120 f}{P} = \frac{120 \times 50}{8} = 750 \text{ RPM} \] Slip at maximum torque: \[ s_{max} = \frac{N_s - N}{N_s} = \frac{750 - 650}{750} = \frac{100}{750} = 0.1333 \] For induction motors, maximum torque occurs when: \[ R_{total} = \frac{R_r'}{s_{max}} \] Thus, \[ R_{total} = \frac{0.08}{0.1333} = 0.60\ \Omega \] Additional resistance required: \[ R_{add} = R_{total} - R_r' = 0.60 - 0.08 = 0.52\ \Omega \] This lies within the expected range 0.50 to 0.54 Ω.