GATE 2026 EE Q.59: solution and answer

GATE 2026 · EEQ.59 · 2 marks · NAT

A balanced three-phase supply is given to a 30 kW, 4-pole, 400 V, 50 Hz, wound rotor induction motor with Y-connected stator and rotor windings. The motor is driving a constant torque load. With shorted sliprings, the machine runs at 1476 rpm.

When an external non-inductive resistance of 0.27 Ω per phase is connected in series in the rotor circuit, the steady-state speed drops to 1404 rpm.

Neglecting rotational losses, the actual per phase rotor winding resistance is _____ Ω

(Round off to two decimal places)

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Answer and solution

ANSWER

The actual per-phase rotor winding resistance is R₂ = 0.09 Ω.

Official answer: 0.09Source: Official answer key, GATE 2026 EE (IIT Guwahati)

Synchronous speed: $N_{s} = \frac{120 f}{P} = \frac{120 \times 50}{4} = 1500 rpm$
Slip with shorted sliprings: $s_{1} = \frac{1500 - 1476}{1500} = 0.016$
Slip with external resistance added: $s_{2} = \frac{1500 - 1404}{1500} = 0.064$
At low slip the torque expression $T \propto \frac{s E _{2}^{2} R _{2}}{R _{2}^{2} + ( s X _{2} ) ^{2}}$ reduces to $T \propto \frac{s}{R _{2}}$ (the $s X_{2}$ term is negligible), so for the same constant-torque load before and after inserting $r$ : $\frac{s _{1}}{R _{2}} = \frac{s _{2}}{R _{2} + r}$
Cross-multiplying: $s_{1} (R_{2} + r) = s_{2} R_{2} \Rightarrow s_{1} r = R_{2} (s_{2} - s_{1})$
Solve for $R_{2}$ : $R_{2} = \frac{s _{1} r}{s _{2} - s _{1}} = \frac{0.016 \times 0.27}{0.064 - 0.016} = \frac{0.00432}{0.048}$
$R_{2} = 0.09 Ω$

KEY IDEA

For a constant-torque load driven at low slip, torque is approximately proportional to s/R₂ (the sX₂ term in the torque expression is negligible at low slip), so equal torque before and after adding rotor resistance gives s₁/R₂ = s₂/(R₂+r), which can be solved directly for the unknown rotor resistance R₂.

WATCH OUT FOR

Forgetting to neglect the sX₂ term (i.e., trying to use the full torque expression with an unknown X₂, which the problem gives no way to determine) or mixing up which resistance (R₂ vs R₂+r) goes with which slip, both of which make the problem unsolvable or give a wrong sign on r.

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GATE 2026 EE Q.59: solution and answer

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