# An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 Ω per phase. Its speed at maximum torque is 650 RPM

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An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 Ω 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 ____________ Ω. (Round off to 2 decimal places.)

Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.

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Given:

Pole (P) = 8

Frequency (f) = 50 Hz

Rotor resistance (r2) = 0.08 Ω

Rotor speed at maximum torque = 650 RPM

Let's consider the slip at maximum torque as sm,

Slip at maximum torque is given by

$s_m = \dfrac {r_2}{x_2}$

Rotor reactance = x2

Synchronous speed Ns = 120f/P = 120 × 50 / 8 = 750 RPM

As the speed of the motor at maximum toque condition is 650 RPM

Slip at maximum torque is given by

$s_m = \dfrac {N_s - N_r}{N_s} =\dfrac {750-650}{750}= 0.1333$

At maximum torque

$s_m =\dfrac {r_2}{x_2} ⇒ 0.1333 = \dfrac {0.08}{x_2}$

x2 = 0.6 Ω

To get the maximum torque at starting the slip at maximum torque should be equal to slip at starting (s=1).

⇒ $1 =\dfrac {{r_2+r_2'}}{ x_2}$

x2 = r2 + r2'

0.6 = 0.08 + r2'

r2' = 0.52 Ω

∴ The value of additional rotor resistance to be added (r2') at the time of starting is 0.52 Ω.