GATE 2026 EE Q.21: solution and answer

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

1. Double-cage rotor construction: outer cage has small-cross-section bars near the air gap, giving high resistance $R_o$ and low leakage reactance $X_o$ (fewer flux linkages).

2. Inner cage has large-cross-section bars deep in the slots, giving low resistance $R_i$ and high leakage reactance $X_i$ (strongly linked by slot leakage flux).

3. Rotor branch reactance at slip $s$ is $X=s{X}_{20}$ (the standstill, supply-frequency reactance scaled by slip). At starting, $s=1$, so both $X_i$ and $X_o$ are at their maximum values.

4. At starting, $X_i\gg X_o$, so the inner-cage impedance $Z_i=\sqrt{R_i^2+X_i^2}$ is much larger than the outer-cage impedance. Current is therefore forced predominantly into the low-impedance outer cage — this is option (A).

5. This redistribution raises the effective rotor resistance at starting (current flows mainly through the high-$R$ outer cage), which is exactly what produces high starting torque, like an external rotor-resistance starter — so option (D), which claims the structure lowers effective rotor resistance at starting, is false.

6. At rated (near-synchronous) speed, $s$ is small, so $s{X}_i$ and $s{X}_o$ both shrink toward zero; the branches become resistance-dominated and current divides inversely with resistance, concentrating in the low-resistance inner cage — so option (C) (most current in the outer cage at rated speed) is false, and option (B) (larger portion in the inner cage at starting) is false since it is the opposite of step 4.

7. Hence only (A) is consistent with the physics.