Which one of the following options is correct regarding the typical double squirrel-cage structure used in induction motors?

The correct option is: At starting, a larger portion of the rotor current flows in the outer cage.

To understand why this is correct, we can analyze the behavior of a double squirrel-cage induction motor under starting and running conditions.

A double squirrel-cage rotor consists of two distinct cages: an outer cage and an inner cage.
1. The outer cage is made of high-resistance materials (like brass or bronze) and has a smaller cross-sectional area, placing it closer to the rotor surface. Because it is near the surface, it has low self-inductance (low leakage reactance). Thus, the outer cage has high resistance and low reactance.
2. The inner cage is made of low-resistance materials (like copper) and has a larger cross-sectional area, buried deeper in the rotor iron. Because it is surrounded by more iron, it has high self-inductance (high leakage reactance). Thus, the inner cage has low resistance and high reactance.

At starting, the rotor is stationary, which means the slip (s) is equal to 1. The frequency of the rotor currents is equal to the stator supply frequency:
$$f_r=s·f_s=f_s$$
Since the starting frequency is high (typically 50 Hz or 60 Hz), the leakage reactance ($X=2\pi fL$) of both cages is significant.

For the inner cage, the reactance is very high due to its high inductance. This makes the overall impedance of the inner cage much higher than that of the outer cage, despite the inner cage having low resistance.
For the outer cage, the reactance remains relatively low because of its low inductance. As a result, the impedance of the outer cage is much lower than that of the inner cage at starting frequencies.

Since current flows through the path of lower impedance, a larger portion of the rotor current is forced to flow through the high-resistance outer cage during starting. This high resistance is beneficial because it produces a high starting torque and limits the starting current.

When the motor accelerates to its rated speed, the slip decreases to a very small value (typically 0.02 to 0.05). Consequently, the rotor frequency ($f_r=s·f_s$) becomes very low (about 1 to 3 Hz). At this low frequency, the reactance of both cages becomes negligible, and the impedance is determined almost entirely by the resistance. Since the inner cage has much lower resistance than the outer cage, most of the rotor current shifts to flow through the inner cage under normal running conditions, ensuring high efficiency.