# A 4-pole, 50 Hz, 3-phase induction motor with a rotor resistance of 0.25 Ω develops a maximum torque of 25 N.m at 1400 rpm. The rotor reactance x2 and

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A 4-pole, 50 Hz, 3-phase induction motor with a rotor resistance of 0.25 Ω develops a maximum torque of 25 N.m at 1400 rpm. The rotor reactance x2 and slip at maximum torque smax,T respectively would be
1. $2.0\;and\frac{1}{{15}}$
2. $3.75\;and\frac{1}{{12}}$
3. $2.0\;and\frac{1}{{12}}$
4. $3.75\;and\frac{1}{{15}}$

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Correct Answer - Option 4 : $3.75\;and\frac{1}{{15}}$

Synchronous speed, ${N_s} = \frac{{120f}}{P} = \frac{{120 \times 50}}{4} = 1500\;rpm$

${s_m} = \frac{{{N_s} - {N_r}}}{{{N_s}}}$

$= \frac{{1500 - 1400}}{{1500}} = \frac{1}{{15}}$

Also, Sm = R2 / X2

Therefore, X= 0.25 × 15 = 3.75