The slip of a 3-phase, 6-pole, 50 Hz induction motor is 4% at full-load. Assuming rotor resistance per phase as 0.3 ohm, find the value of external resistance to be connected in series with each phase of the rotor to reduce the speed by 10%. Assume torque to remain the same.
Question 10.10: The slip of a 3-phase, 6-pole, 50 Hz induction motor is 4% a...
P = 6 ; f = 50 Hz; S_{1} = 4\% = 0.04; R_{2} = 0.3 \Omega
N_{S} = \frac{120 f}{P} = \frac{120 \times 50}{6} = 1000 rpm ; N_{1} = N_{S} \left(1- S\right) = 1000 \left(1 – 0.04\right) = 960 rpm
N_{S} = N_{1} – \frac{10}{100} \times N_{1} = 960 – \frac{10}{100} \times 960 = 864 rpm
S_{2} = \frac{N_{S} – N_{2}}{N_{S}} = \frac{1500 – 864}{1500} = 0.424
Since, T_{1} = T_{2}; \frac{S_{1}}{R_{2}} = \frac{S_{2}}{R_{2} + r} or R_{2} + r = \frac{S_{2}}{S_{1}} \times R_{2}
or r = \frac{S_{2}}{S_{1}} \times R_{2} – R_{2} = \frac{0.424}{0.04} \times 0.3 – 0.3 = \mathbf{2.88 ohm}
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