GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 56 of 65

Marks: +1, -0

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.

Your Answer:

Validate

Solution:

Synchronous speed,

N_{5}=\;{120 f}/{P}=\;{15 × 50}/{8}=750 {rpm}

.
Slip at maximum torque,

{\s}_{\T_{\max}}=\;{\N_{5}-\N_{\T_{\max }}}/{N_{S}}=\;{750-650}/{750}=\;{100}/{750}=0.1333

{\s}_{ {\T}_{\max }}=\;{ {R}_{2}^{'}}/{ {X}_{2}^{'}} ⇒ {X}_{2}^{'}=\;{ {\R}_{2}^{'}}/{ {\S}_{ {\T}_{\max }}}=\;{0.08}/{0.1333}=0.6 Ω

For producing maximum torque at starting,

{S}_{ {T}_{\max }}=1 ⇒ \;{ {\R}_{2( {\New})}^{'}}/{ {X}_{2}^{'}}=1 ⇒ {\R}_{2( {\New})}^{'}= {X}_{2}^{'}=0.6

⇒ \R_{2}^{'}+R_{\;\text "ext "\;}=0.6

R_{\ext}=0.6-R_{2}^{'}=0.6-0.08=0.52 Ω

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